ObsPropCode.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e9e5616c-2a8c-44cb-a55d-8717d938155d",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true
   },
   "source": [
    "# Utility functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b328b8a3-a93f-4eec-9885-48e4733c8ffd",
   "metadata": {},
   "source": [
    "## Model hooks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a0a9d579-ab3c-4bb4-ba61-4389e78e6d7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from types import MethodType\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.rcParams[\"font.family\"] = \"serif\" \n",
    "\n",
    "class AttnHack:\n",
    "    # this is a hack that allows us to get intermediate values used in attention\n",
    "    # what we're doing here is copy-and-pasting the attention code, but adding in some lines that grab\n",
    "    # the values that we want\n",
    "    # credit to https://github.com/huggingface/transformers/blob/main/src/transformers/models/gpt_neo/modeling_gpt_neo.py\n",
    "    def __init__(self, module):\n",
    "        self.original_attn_method = module._attn\n",
    "        self.module = module\n",
    "    def attach(self, out_dict):\n",
    "        def my_attn(self, query, key, value, attention_mask=None, head_mask=None):\n",
    "            # Keep the attention weights computation in fp32 to avoid overflow issues\n",
    "            query = query.to(torch.float32)\n",
    "            key = key.to(torch.float32)\n",
    "    \n",
    "            attn_weights = torch.matmul(query, key.transpose(-1, -2))\n",
    "    \n",
    "            query_length, key_length = query.size(-2), key.size(-2)\n",
    "            causal_mask = self.bias[:, :, key_length - query_length : key_length, :key_length]\n",
    "            mask_value = torch.finfo(attn_weights.dtype).min\n",
    "            # Need to be a tensor, otherwise we get error: `RuntimeError: expected scalar type float but found double`.\n",
    "            # Need to be on the same device, otherwise `RuntimeError: ..., x and y to be on the same device`\n",
    "            mask_value = torch.tensor(mask_value, dtype=attn_weights.dtype).to(attn_weights.device)\n",
    "            attn_weights = torch.where(causal_mask, attn_weights, mask_value)\n",
    "\n",
    "            out_dict['attn_raw_weights'] = attn_weights\n",
    "            out_dict['attn_mask'] = attention_mask\n",
    "            out_dict['head_mask'] = head_mask\n",
    "    \n",
    "            if attention_mask is not None:\n",
    "                # Apply the attention mask\n",
    "                attn_weights = attn_weights + attention_mask\n",
    "        \n",
    "            attn_weights = nn.functional.softmax(attn_weights, dim=-1)\n",
    "            attn_weights = attn_weights.to(value.dtype)\n",
    "            attn_weights = self.attn_dropout(attn_weights)\n",
    "    \n",
    "            # Mask heads if we want to\n",
    "            if head_mask is not None:\n",
    "                attn_weights = attn_weights * head_mask\n",
    "    \n",
    "            attn_output = torch.matmul(attn_weights, value)\n",
    "    \n",
    "            return attn_output, attn_weights\n",
    "        self.module._attn = MethodType(my_attn, self.module)\n",
    "    def remove(self):\n",
    "        self.module._attn = self.original_attn_method\n",
    "\n",
    "def attach_hooks(model):\n",
    "    hooks = []\n",
    "    out_list = {\"layers\": [ {} for l in range(len(model.transformer.h)) ]}\n",
    "    \n",
    "    def make_hook(hook_name, out_dict, is_input=False):\n",
    "        def my_hook(model, input, output):\n",
    "            if is_input:\n",
    "                out_dict[hook_name] = input[0]\n",
    "            else:\n",
    "                out_dict[hook_name] = output\n",
    "        return my_hook\n",
    "        \n",
    "    for l in range(len(model.transformer.h)):\n",
    "        hooks.append(model.transformer.h[l].register_forward_hook(\n",
    "            make_hook(\"block_out\", out_list['layers'][l])\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].mlp.register_forward_hook(\n",
    "            make_hook(\"mlp_out\", out_list['layers'][l])\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].mlp.register_forward_hook(\n",
    "            make_hook(\"mlp_in\", out_list['layers'][l], is_input=True)\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].ln_2.register_forward_hook(\n",
    "            make_hook(\"ln_2_in\", out_list['layers'][l], is_input=True)\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].attn.register_forward_hook(\n",
    "            make_hook(\"attn_in\", out_list['layers'][l], is_input=True)\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].attn.register_forward_hook(\n",
    "            make_hook(\"attn_out\", out_list['layers'][l])\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].attn.attention.q_proj.register_forward_hook(\n",
    "            make_hook(\"q_proj_out\", out_list['layers'][l])\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].attn.attention.k_proj.register_forward_hook(\n",
    "            make_hook(\"k_proj_out\", out_list['layers'][l])\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].attn.attention.v_proj.register_forward_hook(\n",
    "            make_hook(\"v_proj_out\", out_list['layers'][l])\n",
    "        ))\n",
    "        hooks.append(model.transformer.h[l].ln_1.register_forward_hook(\n",
    "            make_hook(\"ln_1_in\", out_list['layers'][l], is_input=True)\n",
    "        ))\n",
    "        # now, hook on the attention hacks\n",
    "        hack = AttnHack(model.transformer.h[l].attn.attention)\n",
    "        hack.attach(out_list['layers'][l])\n",
    "        hooks.append(hack)\n",
    "    hooks.append(model.transformer.ln_f.register_forward_hook(\n",
    "        make_hook(\"ln_f_in\", out_list, is_input=True)\n",
    "    ))\n",
    "    hooks.append(model.lm_head.register_forward_hook(\n",
    "        make_hook(\"lm_out\", out_list)\n",
    "    ))\n",
    "        \n",
    "    return out_list, hooks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1ae7d9d9-49ca-48ec-a1d2-cd60d5d7d957",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_with_patched_activations(model, prompt, patch_dicts, pre_tokenized=False, return_np=False, np_patch=None):\n",
    "    # patch_dicts: a list of dicts\n",
    "    # each patched activation dict has format {'layer', 'sublayer', 'token', 'patch'}\n",
    "    # currently-supported sublayers: ln_1_in, ln_2_in, attn_in, mlp_in\n",
    "\n",
    "    if np_patch is None: np_patch = return_np\n",
    "    # create and attach all hooks\n",
    "    out_list, read_hooks = attach_hooks(model)\n",
    "    write_hooks = []\n",
    "    def make_write_hook(token, patch, my_np_patch):\n",
    "        def my_hook(model, input):\n",
    "            # TODO: do we have to clone input?\n",
    "            if my_np_patch:\n",
    "                input[0][0,token,:] = torch.from_numpy(patch)\n",
    "            else:\n",
    "                input[0][0,token,:] = patch\n",
    "            return input\n",
    "        return my_hook\n",
    "    for patch_dict in patch_dicts:\n",
    "        cur_layer = model.transformer.h[patch_dict['layer']]\n",
    "        if patch_dict['sublayer'] == 'ln_1_in':\n",
    "            cur_module = cur_layer.ln_1\n",
    "        elif patch_dict['sublayer'] == 'attn_in':\n",
    "            cur_module = cur_layer.attn\n",
    "        elif patch_dict['sublayer'] == 'ln_2_in':\n",
    "            cur_module = cur_layer.ln_2\n",
    "        elif patch_dict['sublayer'] == 'mlp_in':\n",
    "            cur_module = cur_layer.mlp\n",
    "        write_hooks.append(cur_module.register_forward_pre_hook(\n",
    "            make_write_hook(patch_dict['token'], patch_dict['patch'], np_patch)\n",
    "        ))\n",
    "\n",
    "    if pre_tokenized:\n",
    "        tokens = {\"input_ids\": prompt['input_ids'].to(\"cuda:0\"), 'attention_mask': prompt['attention_mask'].to(\"cuda:0\")}\n",
    "    else:\n",
    "        tokens = tokenizer(prompt, return_tensors=\"pt\").to(\"cuda:0\")\n",
    "    model(**tokens)\n",
    "    for hook in read_hooks: hook.remove()\n",
    "    for hook in write_hooks: hook.remove()\n",
    "    if return_np:\n",
    "        out_list = embeddings_torch_to_np(out_list)\n",
    "    return out_list"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3189e2f1-fecc-42f9-9f96-ce503afb7fb2",
   "metadata": {},
   "source": [
    "## Memory efficiency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "400108c9-7921-44a2-8b9b-bcfa9e28da88",
   "metadata": {},
   "outputs": [],
   "source": [
    "import gc\n",
    "def get_num_tensors():\n",
    "    tensors_count = 0\n",
    "    for obj in gc.get_objects():\n",
    "        try:\n",
    "            if torch.is_tensor(obj) and obj.device.type == \"cuda\":\n",
    "                tensors_count += 1\n",
    "        except:\n",
    "            pass\n",
    "    return tensors_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e7839933-e29f-48ea-8da9-a234deca12cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def do_free():\n",
    "    gc.collect()\n",
    "    torch.cuda.empty_cache()\n",
    "    gc.collect()\n",
    "def free_embeddings(embeddings):\n",
    "    l = 0\n",
    "    while len(embeddings['layers']) > 0:\n",
    "        for key, val in embeddings['layers'][0].items():\n",
    "            embeddings['layers'][0][key] = None\n",
    "        embeddings['layers'][0] = None\n",
    "        del embeddings['layers'][0]\n",
    "        del key\n",
    "        del val\n",
    "    embeddings['layers'] = None\n",
    "    embeddings['ln_f_in'] = None\n",
    "    embeddings = None\n",
    "    do_free()\n",
    "def _convert_embeddings(embeddings, convert_func, free=True):\n",
    "    new_embeddings = {\"layers\": [ {} for l in range(len(model.transformer.h)) ]}\n",
    "    l = 0\n",
    "    for l in range(len(embeddings['layers'])):\n",
    "        #print(f\"Layer {l} num tensors before: {get_num_tensors()}\")\n",
    "        for key, val in embeddings['layers'][l].items():\n",
    "            if val is None:\n",
    "                new_embeddings['layers'][l][key] = None\n",
    "            elif type(val) is tuple:\n",
    "                my_l = []\n",
    "                for x in val:\n",
    "                    if type(x) is tuple:\n",
    "                        my_l.append(tuple(convert_func(y) for y in x))\n",
    "                    else:\n",
    "                        my_l.append(convert_func(x))\n",
    "                new_embeddings['layers'][l][key] = tuple( my_l )\n",
    "                while len(my_l) > 0:\n",
    "                    my_l[0] = None\n",
    "                    del my_l[0]\n",
    "                del my_l\n",
    "            else:\n",
    "                new_embeddings['layers'][l][key] = convert_func(val)\n",
    "    new_embeddings['ln_f_in'] = convert_func(embeddings['ln_f_in'])\n",
    "    new_embeddings['lm_out'] = convert_func(embeddings['lm_out'])\n",
    "    if free:\n",
    "        free_embeddings(embeddings)\n",
    "        del embeddings\n",
    "        del x, key, val\n",
    "        do_free()\n",
    "    return new_embeddings\n",
    "def embeddings_torch_to_np(embeddings, free=True):\n",
    "    return _convert_embeddings(embeddings, lambda x: x.detach().cpu().numpy(), free=free)\n",
    "def embeddings_np_to_torch(embeddings, free=True):\n",
    "    return _convert_embeddings(embeddings, lambda x: torch.from_numpy(x).to(\"cuda\"), free=free)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7de67b33-4b89-41e3-8760-303b63c323fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def embeddings_torch_to_cpu(embeddings):\n",
    "    new_embeddings = {\"layers\": [ {} for l in range(len(model.transformer.h)) ]}\n",
    "    l = 0\n",
    "    while len(embeddings['layers']) > 0:\n",
    "        for key, val in embeddings['layers'][0].items():\n",
    "            if val is None:\n",
    "                new_embeddings['layers'][l][key] = None\n",
    "            elif type(val) is tuple:\n",
    "                new_embeddings['layers'][l][key] = (x.detach().cpu() for x in val)\n",
    "            else:\n",
    "                new_embeddings['layers'][l][key] = val.detach().cpu()\n",
    "            embeddings['layers'][0][key] = None\n",
    "            #do_free()\n",
    "        embeddings['layers'][0] = None\n",
    "        del embeddings['layers'][0]  \n",
    "        l += 1\n",
    "    embeddings['layers'] = None\n",
    "    new_embeddings['ln_f_in'] = embeddings['ln_f_in'].detach().cpu()\n",
    "    embeddings['ln_f_in'] = None\n",
    "    embeddings = None\n",
    "    do_free()\n",
    "    return new_embeddings\n",
    "\n",
    "def embeddings_torch_to_gpu(embeddings):\n",
    "    new_embeddings = {\"layers\": [ {} for l in range(len(model.transformer.h)) ]}\n",
    "    l = 0\n",
    "    while len(embeddings['layers']) > 0:\n",
    "        for key, val in embeddings['layers'][0].items():\n",
    "            if val is None:\n",
    "                new_embeddings['layers'][l][key] = None\n",
    "            elif type(val) is tuple:\n",
    "                new_embeddings['layers'][l][key] = (x.to(\"cuda\") for x in val)\n",
    "            else:\n",
    "                new_embeddings['layers'][l][key] = val.to(\"cuda\")\n",
    "            embeddings['layers'][0][key] = None\n",
    "            #do_free()\n",
    "        embeddings['layers'][0] = None\n",
    "        del embeddings['layers'][0]\n",
    "        l += 1\n",
    "    embeddings['layers'] = None\n",
    "    new_embeddings['ln_f_in'] = embeddings['ln_f_in'].to(\"cuda\")\n",
    "    embeddings['ln_f_in'] = None\n",
    "    embeddings = None\n",
    "    do_free()\n",
    "    return new_embeddings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "138dfd4d-5a8e-4b00-b961-db8fd5892a50",
   "metadata": {},
   "source": [
    "## Range normal setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "27b349a0-5135-43ed-b8ad-2186efd4e125",
   "metadata": {},
   "outputs": [],
   "source": [
    "vocab_size = 50257\n",
    "import torch\n",
    "import torch.nn.functional as F\n",
    "import torch.nn as nn\n",
    "\n",
    "def make_lm_head_normal(pos_list, neg_list, normalize=False, take_first_token=False):\n",
    "    n = torch.zeros(vocab_size)\n",
    "    for tok in pos_list:\n",
    "        if not take_first_token:\n",
    "            n += F.one_hot(torch.tensor(tokenizer(tok).input_ids),vocab_size)[0]\n",
    "        else:\n",
    "            n += F.one_hot(torch.tensor(tokenizer(tok).input_ids[0]),vocab_size)\n",
    "    for tok in neg_list:\n",
    "        if not take_first_token:\n",
    "            n -= F.one_hot(torch.tensor(tokenizer(tok).input_ids),vocab_size)[0]\n",
    "        else:\n",
    "            n -= F.one_hot(torch.tensor(tokenizer(tok).input_ids[0]),vocab_size)\n",
    "    if normalize:\n",
    "        n = n/torch.linalg.norm(n)\n",
    "    return n\n",
    "\n",
    "def make_range_normal(pos_list, neg_list, normalize=False):\n",
    "    n = torch.zeros(vocab_size)\n",
    "    for tok in pos_list:\n",
    "        n += F.one_hot(torch.tensor(tokenizer(tok).input_ids),vocab_size)[0]\n",
    "    for tok in neg_list:\n",
    "        n -= F.one_hot(torch.tensor(tokenizer(tok).input_ids),vocab_size)[0]\n",
    "    print(n.shape)\n",
    "    n = n.T.to(\"cuda\", dtype=torch.float32)\n",
    "    n = model.lm_head.weight.data.T @ n\n",
    "    if normalize:\n",
    "        n = n/torch.linalg.norm(n)\n",
    "    return n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23c11b32-75e8-41ff-baf3-647ad2944943",
   "metadata": {},
   "source": [
    "## Nonlinear approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "822240d5-69c1-4748-bf55-10ca4c17ad0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import mdmm\n",
    "# find point on domain boundary closest to our starting point using mdmm constrained optimization library\n",
    "def torch_domain_boundary_proj(x_0, f, range_normal, range_affine, lr=0.01, eps=0.0001):\n",
    "    x_0 = x_0.detach()\n",
    "    x = x_0.detach().clone().to(\"cuda\")\n",
    "    x.requires_grad_(True)\n",
    "    \n",
    "    constraint = mdmm.EqConstraint(lambda: torch.dot(range_normal, f(x)-range_affine),0)\n",
    "    mdmm_module = mdmm.MDMM([constraint])\n",
    "    \n",
    "    optimizer = mdmm_module.make_optimizer([x], lr=lr)\n",
    "    \n",
    "    loss = None\n",
    "    prev_loss = None\n",
    "    while loss is None or abs(loss.item()) > eps:\n",
    "        prev_loss = loss\n",
    "        \n",
    "        loss_intermediate = torch.linalg.norm(x-x_0)**2\n",
    "        mdmm_return = mdmm_module(loss_intermediate)\n",
    "        \n",
    "        loss = mdmm_return.infs[0]**2\n",
    "        #print(prev_loss, loss)\n",
    "        \n",
    "        if prev_loss is not None and abs(prev_loss.item() - loss.item()) < eps**2: break\n",
    "            \n",
    "        optimizer.zero_grad()\n",
    "        mdmm_return.value.backward()\n",
    "        optimizer.step()\n",
    "    print(\"Final loss:\", loss.item())\n",
    "    print(eps)\n",
    "    if prev_loss is not None: print(abs(prev_loss.item() - loss.item()))\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "75ab09a0-1244-4784-9917-2df42889ed88",
   "metadata": {},
   "outputs": [],
   "source": [
    "def domain_boundary_intersection(x_pos, x_neg, f, range_normal, range_affine, lr=0.01, eps=0.000001):\n",
    "    g = lambda t_: (range_normal.detach() @ ( f((1-t_)*x_neg.detach() + t_*x_pos.detach()) - range_affine.detach()))**2\n",
    "    \n",
    "    t = torch.Tensor([0.5]).detach().to(\"cuda\")\n",
    "    t.requires_grad_(True)\n",
    "    \n",
    "    optimizer = torch.optim.Adam([t], lr=lr)\n",
    "    \n",
    "    loss = None\n",
    "    prev_loss = None\n",
    "    while loss is None or abs(loss.item()) > eps:\n",
    "        optimizer.zero_grad()\n",
    "        prev_loss = loss\n",
    "        loss = g(t)\n",
    "        if prev_loss is not None and abs(prev_loss.item() - loss.item()) < eps**2: break\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        with torch.no_grad():\n",
    "            t[:] = torch.clamp(t, min=0, max=1)\n",
    "    print(\"Final loss:\", loss.item())\n",
    "    print(\"Final t:\", t)\n",
    "    if prev_loss is not None: print(abs(prev_loss.item() - loss.item()))\n",
    "    return (1-t)*x_neg + t*x_pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9b00c8cb-272e-49f8-a2a4-f6190c4ab9ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_tangent_plane_given_point(x_0_new, f, range_normal, range_affine):\n",
    "    # now, find the tangent hyperplane at x_0_new\n",
    "    x_0_new.requires_grad_(True)\n",
    "    g = lambda x: f(x) @ range_normal - (range_normal @ range_affine)\n",
    "    grad = torch.autograd.grad(g(x_0_new), x_0_new)\n",
    "    \n",
    "    return grad[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "78ebee1b-6625-4bd5-abaf-1f3279b66926",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_grad(x0, f):\n",
    "    x0.requires_grad_(True)\n",
    "    grad = torch.autograd.grad(f(x0), x0)    \n",
    "    return grad[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6d330c7f-88b5-4059-958b-ce5e32912376",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_normal_and_affine(x_0, f, range_normal, range_affine, lr=0.01, eps=0.0001):\n",
    "    affine = torch_domain_boundary_proj(x_0, f, range_normal, range_affine, lr=lr, eps=eps)\n",
    "    normal = get_tangent_plane_given_point(affine, f, range_normal, range_affine)\n",
    "    return normal, affine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8e0fd00a-2ee0-4093-a0bc-381bd2eafa5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_absolute_loss(f, embeddings_list, layer, sublayer, dom_normal, dom_affine, range_normal, range_affine, token=-1):\n",
    "    avg_diff_sum = 0\n",
    "    avg_diff_count = 0\n",
    "    for np_embeddings in embeddings_list:\n",
    "        embeddings = embeddings_np_to_torch(np_embeddings, free=False)\n",
    "        if layer is None:\n",
    "            my_point = embeddings[sublayer][:, token, :]\n",
    "        else:\n",
    "            my_point = embeddings['layers'][layer][sublayer][:, token, :]\n",
    "        with torch.no_grad():\n",
    "            avg_diff_sum += torch.abs(( (f(my_point) - range_affine) @ range_normal) - ((my_point-dom_affine) @ dom_normal)).item()\n",
    "        avg_diff_count += 1\n",
    "        free_embeddings(embeddings)\n",
    "    return avg_diff_sum/avg_diff_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dfe17a26-ffaa-4403-a4e5-3bb52588fe44",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_attention_scores_for_single_token(embeddings, token):\n",
    "    with torch.no_grad():\n",
    "        all_scores = []\n",
    "        for layer in range(len(embeddings['layers'])):\n",
    "            scores = embeddings['layers'][layer]['attn_out'][2] #(0, head, dst_token, src_token)\n",
    "            scores = scores[0, :, token, token]\n",
    "            all_scores.append(scores)\n",
    "        all_scores = torch.stack(all_scores)\n",
    "    return all_scores #(layer, head)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0f4fb6c6-1415-4f16-a33a-ca799aefa450",
   "metadata": {},
   "outputs": [],
   "source": [
    "def single_token_ov_circuit(model, embeddings, token, mlp_layers, attn_layers, x, range_normal=None, do_print=False):\n",
    "    mlp_layer_idx = 0\n",
    "    attn_layer_idx = 0\n",
    "\n",
    "    mlp_layers = list(sorted(mlp_layers))\n",
    "    attn_layers = list(sorted(attn_layers))\n",
    "\n",
    "    mlp_layer = mlp_layers[mlp_layer_idx]\n",
    "    attn_layer = attn_layers[attn_layer_idx]\n",
    "\n",
    "    token_attn_scores = get_attention_scores_for_single_token(embeddings, token)\n",
    "    \n",
    "    hidden_states = x\n",
    "    while True:\n",
    "        try:\n",
    "            mlp_layer = mlp_layers[mlp_layer_idx]\n",
    "        except:\n",
    "            mlp_layer = None\n",
    "        \n",
    "        try:\n",
    "            attn_layer = attn_layers[attn_layer_idx]\n",
    "        except:\n",
    "            attn_layer = None\n",
    "\n",
    "        if mlp_layer is None and attn_layer is None:\n",
    "            if range_normal is not None: return hidden_states @ range_normal\n",
    "            return hidden_states\n",
    "        if mlp_layer is None or (attn_layer is not None and attn_layer <= mlp_layer):\n",
    "            if do_print:\n",
    "                print(f\"attn{attn_layer} ====\")\n",
    "                print(f\"\\tattn_scores: {token_attn_scores[attn_layer]}\")\n",
    "            # do attention\n",
    "            residual = hidden_states\n",
    "            hidden_states = model.transformer.h[attn_layer].ln_1(hidden_states)\n",
    "            with torch.no_grad():\n",
    "                attn_module = model.transformer.h[attn_layer].attn.attention\n",
    "                v_proj = attn_module.v_proj.weight\n",
    "                o_proj = attn_module.out_proj.weight\n",
    "                num_heads = attn_module.num_heads\n",
    "                head_dim = attn_module.head_dim\n",
    "\n",
    "                combined_ov_mat = torch.zeros(num_heads*head_dim, num_heads*head_dim).to(\"cuda\")\n",
    "\n",
    "                for head in range(num_heads):\n",
    "                    combined_ov_mat += token_attn_scores[attn_layer, head]\\\n",
    "                        * get_ov_mat_for_head(v_proj, o_proj, num_heads, head_dim, head)\n",
    "            hidden_states = combined_ov_mat @ hidden_states\n",
    "            hidden_states = hidden_states + residual\n",
    "            attn_layer_idx += 1\n",
    "            if do_print: print(f\"\\tafter attn{attn_layer}: {hidden_states @ range_normal}\")\n",
    "        if attn_layer is None or (mlp_layer is not None and mlp_layer < attn_layer):\n",
    "            # do mlp\n",
    "            if do_print: print(f\"mlp{mlp_layer} ====\")\n",
    "            residual = hidden_states\n",
    "            hidden_states = model.transformer.h[mlp_layer].ln_2(hidden_states)\n",
    "            hidden_states = model.transformer.h[mlp_layer].mlp(hidden_states)\n",
    "            hidden_states = hidden_states + residual\n",
    "            mlp_layer_idx += 1\n",
    "            if do_print: print(f\"\\tafter mlp{mlp_layer}: {hidden_states @ range_normal}\")\n",
    "    if range_normal is not None: return hidden_states @ range_normal\n",
    "    return hidden_states    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "31838de8-19bb-4ad0-b378-199cfa287afb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ov_path(model, embeddings, path, x, range_normal=None, do_print=False):    \n",
    "    hidden_states = x\n",
    "    for i, component in enumerate(path):\n",
    "        layer = component['layer']\n",
    "        sublayer = component['sublayer']\n",
    "        token = component['token']\n",
    "        if sublayer == 'attn':\n",
    "            if i == len(path)-1:\n",
    "                next_token = -1\n",
    "            else:\n",
    "                next_token = path[i+1]['token']\n",
    "            token_attn_scores = embeddings['layers'][layer]['attn_out'][2] #(0, head, dst_token, src_token)\n",
    "            token_attn_scores = token_attn_scores[0, :, next_token, token]\n",
    "            if do_print:\n",
    "                print(f\"attn{layer} ====\")\n",
    "                print(f\"\\tattn_scores: {token_attn_scores}\")\n",
    "            # do attention\n",
    "            residual = hidden_states\n",
    "            hidden_states = model.transformer.h[layer].ln_1(hidden_states)\n",
    "            with torch.no_grad():\n",
    "                attn_module = model.transformer.h[layer].attn.attention\n",
    "                v_proj = attn_module.v_proj.weight\n",
    "                o_proj = attn_module.out_proj.weight\n",
    "                num_heads = attn_module.num_heads\n",
    "                head_dim = attn_module.head_dim\n",
    "\n",
    "                combined_ov_mat = torch.zeros(num_heads*head_dim, num_heads*head_dim).to(\"cuda\")\n",
    "\n",
    "                if type(component['head']) == list:\n",
    "                    for head in component['head']:\n",
    "                        combined_ov_mat += token_attn_scores[head]\\\n",
    "                            * get_ov_mat_for_head(v_proj, o_proj, num_heads, head_dim, head)\n",
    "                elif component['head'] == -1:\n",
    "                    for head in range(num_heads):\n",
    "                        combined_ov_mat += token_attn_scores[head]\\\n",
    "                            * get_ov_mat_for_head(v_proj, o_proj, num_heads, head_dim, head)\n",
    "                else:\n",
    "                    head = component['head']\n",
    "                    combined_ov_mat = token_attn_scores[head]\\\n",
    "                            * get_ov_mat_for_head(v_proj, o_proj, num_heads, head_dim, head)\n",
    "            hidden_states = combined_ov_mat @ hidden_states\n",
    "            hidden_states = hidden_states + residual\n",
    "            if do_print: print(f\"\\tafter attn{layer}: {hidden_states @ range_normal}\")\n",
    "        elif sublayer == 'mlp':\n",
    "            # do mlp\n",
    "            if do_print: print(f\"mlp{layer} ====\")\n",
    "            residual = hidden_states\n",
    "            hidden_states = model.transformer.h[layer].ln_2(hidden_states)\n",
    "            hidden_states = model.transformer.h[layer].mlp(hidden_states)\n",
    "            hidden_states = hidden_states + residual\n",
    "            if do_print: print(f\"\\tafter mlp{layer}: {hidden_states @ range_normal}\")\n",
    "    if range_normal is not None: return hidden_states @ range_normal\n",
    "    return hidden_states    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c1ce95e-405b-4187-aad6-bec70f583c21",
   "metadata": {},
   "source": [
    "## Layer decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "11c87add-899f-45a2-9ab1-c79aede2d9f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def decompose_layer_mlp(layer, embeddings_pos, embeddings_neg, token_idx, range_normal):\n",
    "    mlp_y_pos = embeddings_pos['layers'][layer]['mlp_out'][0, token_idx, :]\n",
    "    mlp_y_neg = embeddings_neg['layers'][layer]['mlp_out'][0, token_idx, :]\n",
    "    mlp_dot_pos = range_normal @ mlp_y_pos\n",
    "    mlp_dot_neg = range_normal @ mlp_y_neg\n",
    "    \n",
    "    mlp_resid_pos = embeddings_pos['layers'][layer]['ln_2_in'][0, token_idx, :]\n",
    "    mlp_resid_neg = embeddings_neg['layers'][layer]['ln_2_in'][0, token_idx, :]\n",
    "    mlp_resid_dot_pos = range_normal @ mlp_resid_pos\n",
    "    mlp_resid_dot_neg = range_normal @ mlp_resid_neg\n",
    "\n",
    "    return {\n",
    "        \"layer\": f\"{layer}_mlp\",\n",
    "        \"pos\": mlp_dot_pos.item(), \"neg\": mlp_dot_neg.item(), \"resid_pos\": mlp_resid_dot_pos.item(), \"resid_neg\": mlp_resid_dot_neg.item(),\n",
    "        \"score\": mlp_dot_pos.item()-mlp_dot_neg.item(), \"resid_score\": mlp_resid_dot_pos.item()-mlp_resid_dot_neg.item()\n",
    "    }\n",
    "\n",
    "def decompose_layer_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal):\n",
    "    attn_y_pos = embeddings_pos['layers'][layer]['attn_out'][0][0, token_idx, :]\n",
    "    attn_dot_pos = range_normal @ attn_y_pos\n",
    "    attn_resid_pos = embeddings_pos['layers'][layer]['ln_1_in'][0, token_idx, :]\n",
    "    attn_resid_dot_pos = range_normal @ attn_resid_pos\n",
    "\n",
    "    if embeddings_neg is None:\n",
    "        attn_y_neg = torch.zeros(attn_y_pos.shape).to(\"cuda\")\n",
    "        attn_dot_neg = torch.zeros(attn_dot_pos.shape).to(\"cuda\")\n",
    "        attn_resid_neg = torch.zeros(attn_resid_pos.shape).to(\"cuda\")\n",
    "        attn_resid_dot_neg = torch.zeros(attn_resid_dot_pos.shape).to(\"cuda\")\n",
    "    else:\n",
    "        attn_y_neg = embeddings_neg['layers'][layer]['attn_out'][0][0, token_idx, :]\n",
    "        attn_dot_neg = range_normal @ attn_y_neg\n",
    "        attn_resid_neg = embeddings_neg['layers'][layer]['ln_1_in'][0, token_idx, :]\n",
    "        attn_resid_dot_neg = range_normal @ attn_resid_neg\n",
    "\n",
    "    return {\n",
    "        \"layer\": f\"{layer}_attn\",\n",
    "        \"pos\": attn_dot_pos.item(), \"neg\": attn_dot_neg.item(), \"resid_pos\": attn_resid_dot_pos.item(), \"resid_neg\": attn_resid_dot_neg.item(),\n",
    "        \"score\": attn_dot_pos.item()-attn_dot_neg.item(), \"resid_score\": attn_resid_dot_pos.item()-attn_resid_dot_neg.item()\n",
    "    }\n",
    "\n",
    "def decompose_embedding(embeddings_pos, embeddings_neg, token, range_normal):\n",
    "    embedding_contrib_pos = embeddings_pos['layers'][0]['ln_1_in'][0,token,:]@range_normal\n",
    "    if embeddings_neg is None:\n",
    "        embedding_contrib_neg = torch.zeros(1).to(\"cuda\")\n",
    "    else:\n",
    "        embedding_contrib_neg = embeddings_neg['layers'][0]['ln_1_in'][0,token,:]@range_normal\n",
    "    return {\n",
    "        \"layer\": f\"embedding\",\n",
    "        \"pos\": embedding_contrib_pos.item(), \"neg\": embedding_contrib_neg.item(), \n",
    "        \"score\": embedding_contrib_pos.item()-embedding_contrib_neg.item()\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1b50abb7-b537-410e-b4da-a4e14193029c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal, model, attn_layer, is_embedding=False, is_mlp=False, use_ln_2=False):\n",
    "    if is_embedding:\n",
    "        y_pos = embeddings_pos['layers'][0]['ln_1_in'][0,token_idx,:]\n",
    "    else:\n",
    "        y_pos = embeddings_pos['layers'][layer][f'{\"mlp\" if is_mlp else \"attn\"}_out']\n",
    "        if not is_mlp: y_pos = y_pos[0]\n",
    "        y_pos = y_pos[0, token_idx, :]\n",
    "    if embeddings_neg is None:\n",
    "        y_neg = torch.zeros(y_pos.shape).to(\"cuda\")\n",
    "    else:\n",
    "        if is_embedding:\n",
    "            y_neg = embeddings_neg['layers'][0]['ln_1_in'][0,token_idx,:]\n",
    "        else:\n",
    "            y_neg = embeddings_neg['layers'][layer][f'{\"mlp\" if is_mlp else \"attn\"}_out']\n",
    "            if not is_mlp: y_neg = y_neg[0]\n",
    "            y_neg = y_neg[0, token_idx, :]\n",
    "\n",
    "    if use_ln_2:\n",
    "        pre_attn_resid_pos = embeddings_pos['layers'][attn_layer]['ln_2_in'][0, token_idx, :]\n",
    "    else:\n",
    "        pre_attn_resid_pos = embeddings_pos['layers'][attn_layer]['ln_1_in'][0, token_idx, :]\n",
    "    pre_attn_resid_neg = pre_attn_resid_pos - y_pos + y_neg\n",
    "\n",
    "    if use_ln_2: ln = model.transformer.h[attn_layer].ln_2\n",
    "    else: ln = model.transformer.h[attn_layer].ln_1\n",
    "    \n",
    "    dot_pos = range_normal @ ln(pre_attn_resid_pos)\n",
    "    dot_neg = range_normal @ ln(pre_attn_resid_neg)\n",
    "\n",
    "    return {\n",
    "        \"layer\": f'{layer}_{\"mlp\" if is_mlp else \"attn\"}' if not is_embedding else 'embedding',\n",
    "        \"pos\": dot_pos.item(), \"neg\": dot_neg.item(), \"score\": dot_pos.item()-dot_neg.item()\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ab26b1b7-a8e4-4b8a-9c77-5523afd852a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def decompose_layers(embeddings_pos, embeddings_neg, token_idx, range_normal, all_tokens=False):\n",
    "    retval = []\n",
    "    num_tokens = embeddings_pos['layers'][-1]['ln_1_in'].shape[1]\n",
    "    for layer in range(len(embeddings_pos['layers'])):\n",
    "        if not all_tokens:\n",
    "            retval.append(decompose_layer_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal))\n",
    "            retval.append(decompose_layer_mlp(layer, embeddings_pos, embeddings_neg, token_idx, range_normal))\n",
    "        else:\n",
    "            attn_dict = {\n",
    "                \"layer\": f\"{layer}_attn\",\n",
    "                \"pos\": 0, \"neg\": 0, \"resid_pos\": 0, \"resid_neg\": 0,\n",
    "                \"score\": 0, \"resid_score\": 0\n",
    "            }\n",
    "            for token in range(num_tokens):\n",
    "                cur_attn_dict = decompose_layer_attn(layer, embeddings_pos, embeddings_neg, token, range_normal)\n",
    "                attn_dict['pos'] += cur_attn_dict['pos']\n",
    "                attn_dict['neg'] += cur_attn_dict['neg']\n",
    "                attn_dict['resid_pos'] += cur_attn_dict['resid_pos']\n",
    "                attn_dict['resid_neg'] += cur_attn_dict['resid_neg']\n",
    "            attn_dict['score'] = attn_dict['pos'] - attn_dict['neg']\n",
    "            attn_dict['resid_score'] = attn_dict['resid_pos'] - attn_dict['resid_neg']\n",
    "            retval.append(attn_dict)\n",
    "\n",
    "            mlp_dict = {\n",
    "                \"layer\": f\"{layer}_mlp\",\n",
    "                \"pos\": 0, \"neg\": 0, \"resid_pos\": 0, \"resid_neg\": 0,\n",
    "                \"score\": 0, \"resid_score\": 0\n",
    "            }\n",
    "            for token in range(num_tokens):\n",
    "                cur_mlp_dict = decompose_layer_mlp(layer, embeddings_pos, embeddings_neg, token, range_normal)\n",
    "                mlp_dict['pos'] += cur_mlp_dict['pos']\n",
    "                mlp_dict['neg'] += cur_mlp_dict['neg']\n",
    "                mlp_dict['resid_pos'] += cur_mlp_dict['resid_pos']\n",
    "                mlp_dict['resid_neg'] += cur_mlp_dict['resid_neg']\n",
    "            mlp_dict['score'] = mlp_dict['pos'] - mlp_dict['neg']\n",
    "            mlp_dict['resid_score'] = mlp_dict['resid_pos'] - mlp_dict['resid_neg']\n",
    "            retval.append(mlp_dict)\n",
    "    if not all_tokens:\n",
    "        retval.append(decompose_embedding(embeddings_pos, embeddings_neg, token_idx, range_normal))\n",
    "    else:\n",
    "        embedding_dict = {\n",
    "            \"layer\": \"embedding\",\n",
    "            \"pos\": 0, \"neg\": 0, \"score\": 0\n",
    "        }\n",
    "        for token in range(num_tokens):\n",
    "            cur_embedding_dict = decompose_layer_embedding(embeddings_pos, embeddings_neg, token, range_normal)\n",
    "            embedding_dict['pos'] += cur_embedding_dict['pos']\n",
    "            embedding_dict['neg'] += cur_embedding_dict['neg']\n",
    "        embedding_dict['score'] = embedding_dict['pos'] - embedding_dict['neg']\n",
    "        retval.append(embedding_dict)\n",
    "    return retval\n",
    "    \n",
    "def decompose_layers_wrt_attn(embeddings_pos, embeddings_neg, token_idx, range_normal, model, attn_layer, all_tokens=False, use_ln_2=False):\n",
    "    retval = []\n",
    "    num_tokens = embeddings_pos['layers'][-1]['ln_1_in'].shape[1]\n",
    "    for layer in range(attn_layer+1):\n",
    "        if not all_tokens:\n",
    "            if layer != attn_layer or use_ln_2:\n",
    "                retval.append(decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal, model=model, attn_layer=attn_layer, is_mlp=False, use_ln_2=use_ln_2))\n",
    "            if layer != attn_layer: \n",
    "                retval.append(decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal, model=model, attn_layer=attn_layer, is_mlp=True, use_ln_2=use_ln_2))\n",
    "        else:\n",
    "            if layer != attn_layer or use_ln_2:\n",
    "                attn_dict = {\n",
    "                    \"layer\": f\"{layer}_attn\",\n",
    "                    \"pos\": 0, \"neg\": 0,\n",
    "                    \"score\": 0\n",
    "                }\n",
    "                for token in range(num_tokens):\n",
    "                    cur_attn_dict = decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal, model=model, attn_layer=attn_layer, is_mlp=False, use_ln_2=use_ln_2)\n",
    "                    attn_dict['pos'] += cur_attn_dict['pos']\n",
    "                    attn_dict['neg'] += cur_attn_dict['neg']\n",
    "                attn_dict['score'] = attn_dict['pos'] - attn_dict['neg']\n",
    "                retval.append(attn_dict)\n",
    "            \n",
    "            if layer != attn_layer:\n",
    "                mlp_dict = {\n",
    "                    \"layer\": f\"{layer}_mlp\",\n",
    "                    \"pos\": 0, \"neg\": 0,\n",
    "                    \"score\": 0\n",
    "                }\n",
    "                for token in range(num_tokens):\n",
    "                    cur_mlp_dict = decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal, model=model, attn_layer=attn_layer, is_mlp=True, use_ln_2=use_ln_2)\n",
    "                    mlp_dict['pos'] += cur_mlp_dict['pos']\n",
    "                    mlp_dict['neg'] += cur_mlp_dict['neg']\n",
    "                mlp_dict['score'] = mlp_dict['pos'] - mlp_dict['neg']\n",
    "                retval.append(mlp_dict)\n",
    "    if not all_tokens:\n",
    "        retval.append(decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal, model=model, attn_layer=attn_layer, is_embedding=True, use_ln_2=use_ln_2))\n",
    "    else:\n",
    "        embedding_dict = {\n",
    "            \"layer\": \"embedding\",\n",
    "            \"pos\": 0, \"neg\": 0, \"score\": 0\n",
    "        }\n",
    "        for token in range(num_tokens):\n",
    "            cur_embedding_dict = decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal, model=model, attn_layer=attn_layer, is_embedding=True, use_ln_2=use_ln_2)\n",
    "            embedding_dict['pos'] += cur_embedding_dict['pos']\n",
    "            embedding_dict['neg'] += cur_embedding_dict['neg']\n",
    "        embedding_dict['score'] = embedding_dict['pos'] - embedding_dict['neg']\n",
    "        retval.append(embedding_dict)\n",
    "    return retval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "66370818-06af-4c08-8225-dd8244f2b9a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def decompose_layers_wrt_attn_token_set(embeddings_pos, embeddings_neg, tokens, range_normal, model, attn_layer, use_ln_2=False):\n",
    "    num_tokens = embeddings_pos['layers'][-1]['ln_1_in'].shape[1]\n",
    "    if tokens is None:\n",
    "        tokens = list(range(num_tokens))\n",
    "    total_list = []\n",
    "    for token in tokens:\n",
    "        cur_list = decompose_layers_wrt_attn(\n",
    "            embeddings_pos, embeddings_neg, token, range_normal, model, attn_layer, use_ln_2=use_ln_2, all_tokens=False)\n",
    "        for i in range(len(cur_list)):\n",
    "            cur_list[i]['dst_token'] = token\n",
    "        total_list += cur_list\n",
    "    return total_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4cecc0af-9b46-4975-8b32-7ac494522d01",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sort_decomposed_layers(decomposed): return sorted(decomposed, key=lambda x: x['score'], reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "87874abe-2a53-4681-a5a6-6786fe2cbc28",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def plot_decomposed_layers(decomposed):\n",
    "    fill_xs = (np.sort(list(range(len(decomposed)))*2)-0.5)/2\n",
    "    fill_where = (np.arange(len(decomposed)*2)-1)%4<2\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(np.arange(len(decomposed))/2, [x['score'] for x in decomposed], label=\"Sublayer score\")\n",
    "    try:\n",
    "        ax.plot(np.arange(len(decomposed))/2, [x['resid_score'] for x in decomposed], label=\"Residual score\")\n",
    "    except KeyError: pass\n",
    "    ax.fill_between(fill_xs, ax.get_ylim()[0], ax.get_ylim()[1], where=fill_where, alpha=0.2, color='red', label=\"Attention sublayer\")\n",
    "    old_xlim = ax.get_xlim()\n",
    "    ax.plot(old_xlim, [0,0], color='black')\n",
    "    ax.set_xlim(old_xlim)\n",
    "    ax.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "939933ed-d6f8-44b6-9990-684ceed95182",
   "metadata": {},
   "source": [
    "## Interpreting through attention"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ca6da0ae-2d25-49ee-8f2c-502638f7348d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def split_mat_heads(tensor, num_heads, attn_head_size):\n",
    "    # code stolen (with slight modification) from Huggingface GPT-Neo-1.3b repo\n",
    "    new_shape = tensor.size()[:-1] + (num_heads, attn_head_size)\n",
    "    tensor = tensor.view(new_shape)\n",
    "    return tensor.permute(1,0,2)  # (head, seq_length, head_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9dbb7812-ab41-40a5-bd8c-eb2c1690c841",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_dots_per_head_and_token(i, attn_module, scores, split_weights, split_vals, grad):\n",
    "    dots = torch.zeros((attn_module.num_heads, scores.shape[-1])).to(\"cuda\", dtype=torch.float32)\n",
    "    # couldn't think of an easy way to vectorize this\n",
    "    for head in range(attn_module.num_heads):\n",
    "        for j in range(scores.shape[-1]):\n",
    "            dots[head, j] = torch.dot(grad, split_weights[head] @ split_vals[0,head,j,:])\n",
    "    return dots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7e552b9d-438d-4a7f-b4a1-a926493cb9a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_v_proj_for_head(v_proj, head_dim, head):\n",
    "    return v_proj[head*head_dim:(head+1)*head_dim]\n",
    "def get_ov_mat_for_head(v_proj, o_proj, num_heads, head_dim, head):\n",
    "    o_proj_head = split_mat_heads(o_proj, num_heads, head_dim)[head]\n",
    "    v_proj_head = v_proj[head*head_dim:(head+1)*head_dim]\n",
    "    return o_proj_head @ v_proj_head"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ee6834fa-2d79-49f8-8c25-a02177bce327",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_contribs(model, embeddings, layer, token_idx, range_normal):\n",
    "    attn_module = model.transformer.h[layer].attn.attention\n",
    "    attn_split_weights = split_mat_heads(attn_module.out_proj.weight, attn_module.num_heads, attn_module.head_dim)\n",
    "    attn_split_vals = attn_module._split_heads(embeddings['layers'][layer]['v_proj_out'], attn_module.num_heads, attn_module.head_dim)\n",
    "    attn_scores = embeddings['layers'][layer]['attn_out'][2]\n",
    "    attn_dots = get_dots_per_head_and_token(token_idx, attn_module, attn_scores, attn_split_weights, attn_split_vals, range_normal)\n",
    "    attn_contribs = attn_dots * attn_scores[0, :, token_idx, :]\n",
    "    attn_contribs_list = []\n",
    "    for head, row in enumerate(attn_contribs):\n",
    "        for j, item in enumerate(row):\n",
    "            attn_contribs_list.append((item.item(), attn_dots[head,j].item(), attn_scores[0,head,token_idx,j].item(), head, j))\n",
    "    attn_contribs_list = sorted(attn_contribs_list, key=lambda x: abs(x[0]), reverse=True)\n",
    "    return attn_contribs, attn_contribs_list\n",
    "\n",
    "def get_contribs_per_head_token_naive(model, embeddings_pos, embeddings_neg, layer, token_idx, range_normal, range_layer=None, use_ln_2=False):\n",
    "    attn_module = model.transformer.h[layer].attn.attention\n",
    "    attn_split_weights = split_mat_heads(attn_module.out_proj.weight, attn_module.num_heads, attn_module.head_dim)\n",
    "\n",
    "    c = 1\n",
    "    if not (range_layer is None): \n",
    "        c = get_LN_constant(model, embeddings_pos, embeddings_neg, layer, token_idx, range_normal, range_layer, use_ln_2=use_ln_2)\n",
    "    \n",
    "    attn_split_vals_pos = attn_module._split_heads(embeddings_pos['layers'][layer]['v_proj_out'], attn_module.num_heads, attn_module.head_dim)\n",
    "    attn_scores_pos = embeddings_pos['layers'][layer]['attn_out'][2]\n",
    "    attn_dots_pos = get_dots_per_head_and_token(token_idx, attn_module, attn_scores_pos, attn_split_weights, attn_split_vals_pos, range_normal)*c\n",
    "    attn_contribs_pos = attn_dots_pos * attn_scores_pos[0, :, token_idx, :]\n",
    "\n",
    "    if embeddings_neg is None:\n",
    "        # zero ablation\n",
    "        attn_split_vals_neg = torch.zeros(attn_split_vals_pos.shape).to(\"cuda\")\n",
    "        attn_scores_neg =  torch.zeros(attn_scores_pos.shape).to(\"cuda\")\n",
    "        attn_dots_neg =  torch.zeros(attn_contribs_pos.shape).to(\"cuda\")\n",
    "        attn_contribs_neg =  torch.zeros(attn_contribs_pos.shape).to(\"cuda\")\n",
    "    else:\n",
    "        attn_split_vals_neg = attn_module._split_heads(embeddings_neg['layers'][layer]['v_proj_out'], attn_module.num_heads, attn_module.head_dim)\n",
    "        attn_scores_neg = embeddings_neg['layers'][layer]['attn_out'][2]\n",
    "        attn_dots_neg = get_dots_per_head_and_token(token_idx, attn_module, attn_scores_neg, attn_split_weights, attn_split_vals_neg, range_normal)*c\n",
    "        attn_contribs_neg = attn_dots_neg * attn_scores_neg[0, :, token_idx, :]\n",
    "\n",
    "    attn_contribs = attn_contribs_pos - attn_contribs_neg\n",
    "    attn_contribs_list = []\n",
    "    for head, row in enumerate(attn_contribs):\n",
    "        for j, item in enumerate(row):\n",
    "            attn_contribs_list.append({\n",
    "                \"head\": head, \"token\": j, \"total_contrib\": item.item(), \"layer\": layer,\n",
    "                \"pos_contrib\": attn_contribs_pos[head,j].item(), \"pos_score\": attn_scores_pos[0,head,token_idx,j].item(), \"pos_dot\": attn_dots_pos[head,j].item(), \n",
    "                \"neg_contrib\": attn_contribs_neg[head,j].item(), \"neg_score\": attn_scores_neg[0,head,token_idx,j].item(), \"neg_dot\": attn_dots_neg[head,j].item()\n",
    "            })\n",
    "    attn_contribs_list = sorted(attn_contribs_list, key=lambda x: abs(x['total_contrib']), reverse=True)\n",
    "    return attn_contribs, attn_contribs_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "16aa69b2-4b11-43b0-87da-baa947787fab",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_LN_constant(model, embeddings_pos, embeddings_neg, layer, token_idx, range_normal, range_layer, use_ln_2=False):\n",
    "    good_score = decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal, model, range_layer, is_mlp=False, use_ln_2=use_ln_2)['score']\n",
    "    bad_score = decompose_layer_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal)['score']\n",
    "    return good_score/bad_score\n",
    "\n",
    "def get_LN_constant_across_tokens(model, embeddings_pos, embeddings_neg, layer, range_normal, range_layer, use_ln_2=False):\n",
    "    num_tokens = embeddings_pos['layers'][layer]['attn_in'].shape[1]\n",
    "    bad_scores = [decompose_layer_attn(layer, embeddings_pos, embeddings_neg, token_idx, range_normal)['score'] for token_idx in range(num_tokens)]\n",
    "    bad_score_idx = np.argmax(bad_scores)\n",
    "    bad_score = bad_scores[bad_score_idx]\n",
    "    good_score = decompose_layer_wrt_attn(layer, embeddings_pos, embeddings_neg, bad_score_idx, range_normal, model, range_layer, is_mlp=False, use_ln_2=use_ln_2)['score']\n",
    "    return good_score/bad_score\n",
    "\n",
    "def get_contribs_wrt_attn_naive(model, embeddings_pos, embeddings_neg, layer, token_idx, range_normal, range_layer, token_only=False, use_ln_2=False):\n",
    "    # we're naively assuming that locally, we can approximate layer-norm as just scaling our output by a constant\n",
    "    c = get_LN_constant(model, embeddings_pos, embeddings_neg, layer, token_idx, range_normal, range_layer, use_ln_2=use_ln_2)\n",
    "    \n",
    "    attn_module = model.transformer.h[layer].attn.attention\n",
    "    attn_split_weights = split_mat_heads(attn_module.out_proj.weight, attn_module.num_heads, attn_module.head_dim)\n",
    "    \n",
    "    attn_split_vals_pos = attn_module._split_heads(embeddings_pos['layers'][layer]['v_proj_out'], attn_module.num_heads, attn_module.head_dim)\n",
    "    attn_scores_pos = embeddings_pos['layers'][layer]['attn_out'][2]\n",
    "    attn_dots_pos = get_dots_per_head_and_token(token_idx, attn_module, attn_scores_pos, attn_split_weights, attn_split_vals_pos, range_normal)*c\n",
    "    attn_contribs_pos = attn_dots_pos * attn_scores_pos[0, :, token_idx, :]\n",
    "\n",
    "    if embeddings_neg is None:\n",
    "        # zero ablation\n",
    "        attn_split_vals_neg = torch.zeros(attn_split_vals_pos.shape).to(\"cuda\")\n",
    "        attn_scores_neg =  torch.zeros(attn_scores_pos.shape).to(\"cuda\")\n",
    "        attn_dots_neg =  torch.zeros(attn_contribs_pos.shape).to(\"cuda\")\n",
    "        attn_contribs_neg =  torch.zeros(attn_contribs_pos.shape).to(\"cuda\")\n",
    "    else:\n",
    "        attn_split_vals_neg = attn_module._split_heads(embeddings_neg['layers'][layer]['v_proj_out'], attn_module.num_heads, attn_module.head_dim)\n",
    "        attn_scores_neg = embeddings_neg['layers'][layer]['attn_out'][2]\n",
    "        attn_dots_neg = get_dots_per_head_and_token(token_idx, attn_module, attn_scores_neg, attn_split_weights, attn_split_vals_neg, range_normal)*c\n",
    "        attn_contribs_neg = attn_dots_neg * attn_scores_neg[0, :, token_idx, :]\n",
    "\n",
    "    attn_contribs_list = []\n",
    "    if not token_only:\n",
    "        attn_contribs = attn_contribs_pos - attn_contribs_neg\n",
    "        for head, row in enumerate(attn_contribs):\n",
    "            for j, item in enumerate(row):\n",
    "                attn_contribs_list.append({\n",
    "                    \"head\": head, \"token\": j, \"total_contrib\": item.item(), \"layer\": layer,\n",
    "                    \"pos_contrib\": attn_contribs_pos[head,j].item(), \"pos_score\": attn_scores_pos[0,head,token_idx,j].item(), \"pos_dot\": attn_dots_pos[head,j].item(), \n",
    "                    \"neg_contrib\": attn_contribs_neg[head,j].item(), \"neg_score\": attn_scores_neg[0,head,token_idx,j].item(), \"neg_dot\": attn_dots_neg[head,j].item()\n",
    "                })\n",
    "    else:\n",
    "        attn_contribs_pos = attn_contribs_pos.sum(axis=0) # sum over all heads\n",
    "        attn_contribs_neg = attn_contribs_neg.sum(axis=0)\n",
    "        attn_contribs = attn_contribs_pos - attn_contribs_neg\n",
    "        for j, item in enumerate(attn_contribs):\n",
    "            attn_contribs_list.append({\n",
    "                \"token\": j, \"total_contrib\": item.item(), \"layer\": layer,\n",
    "                \"pos_contrib\": attn_contribs_pos[j].item(), \"neg_contrib\": attn_contribs_neg[j].item()\n",
    "            })\n",
    "    attn_contribs_list = sorted(attn_contribs_list, key=lambda x: abs(x['total_contrib']), reverse=True)\n",
    "    return attn_contribs, attn_contribs_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4ab1e296-a5a3-4516-af5d-801f373a2662",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_all_head_token_contribs_for_attn_layer_per_token(model, embeddings_pos, embeddings_neg, token, normal, range_layer, token_only=False):\n",
    "    big_list = []\n",
    "    #cs = []\n",
    "    for layer in range(range_layer):\n",
    "        #cs.append(get_LN_constant(model, embeddings_pos, embeddings_neg, layer, token, normal, range_layer))\n",
    "        _, cur_list = get_contribs_wrt_attn_naive(model, embeddings_pos, embeddings_neg, layer, token, normal, range_layer, token_only=token_only)\n",
    "        big_list += cur_list\n",
    "    # get original embedding contribution\n",
    "    #c = sum(cs)/len(cs)\n",
    "    c = 1 # TODO: I think that there shouldn't be any LayerNorm constant for the original embeddings\n",
    "    embedding_contrib = c * (embeddings_pos['layers'][0]['ln_1_in'][0,token,:] - embeddings_neg['layers'][0]['ln_1_in'][0,token,:])@normal\n",
    "    print(c)\n",
    "    big_list.append({\n",
    "        \"layer\": \"embedding\", \"token\": token,\n",
    "        \"total_contrib\": embedding_contrib,\n",
    "    })\n",
    "    return sorted(big_list, key=lambda x: x['total_contrib'], reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "4699c337-bebb-4979-9f2e-52bd38e442ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_all_head_contribs_for_attn_layer_per_token(model, embeddings_pos, embeddings_neg, token, normal, range_layer=None):\n",
    "    big_mat_list = []\n",
    "    num_layers = range_layer\n",
    "    if num_layers is None:\n",
    "        num_layers = len(model.transformer.h)\n",
    "    for layer in range(num_layers):\n",
    "        cur_mat = get_contribs_per_head_token_naive(model, embeddings_pos, embeddings_neg, layer, token, normal, range_layer=range_layer)[0]\n",
    "        big_mat_list.append(cur_mat.sum(axis=1))\n",
    "    return torch.stack(big_mat_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b090c754-db4c-4edd-a6bb-b0e0507573be",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_all_head_contribs_for_output_per_token(model, embeddings_pos, embeddings_neg, token, normal):\n",
    "    big_mat_list = []\n",
    "    cs = []\n",
    "    for layer in range(len(model.transformer.h)):\n",
    "        cur_mat = get_contribs_per_head_token_naive(model, embeddings_pos, embeddings_neg, layer, token, normal)[0]\n",
    "        big_mat_list.append(cur_mat.sum(axis=1))\n",
    "    \"\"\"# get original embedding contribution\n",
    "    c = sum(cs)/len(cs)\n",
    "    embedding_contrib_mat = c * (embeddings_pos['layers'][0]['ln_1_in'][0,:,:] - embeddings_neg['layers'][0]['ln_1_in'][0,:,:])@normal\n",
    "    \n",
    "    print(c)\n",
    "    big_list.append({\n",
    "        \"layer\": \"embedding\",\n",
    "        \"total_contrib\": embedding_contrib,\n",
    "    })\"\"\"\n",
    "    return torch.stack(big_mat_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "87589119-831f-4cf6-ba26-1ee43a93c2b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_mediated_head_contrib(model, head_layer_list, embeddings_pos, embeddings_neg, range_normal):\n",
    "    num_tokens = embeddings_pos['layers'][head_layer_list[0][1]]['attn_in'].shape[1]\n",
    "    # head_layer_list: [ (head, layer) ] from latest layer head to earliest layer head\n",
    "    cs = []\n",
    "    normals = []\n",
    "    for i, head_layer in enumerate(head_layer_list):\n",
    "        if i == 0:\n",
    "            if head_layer[0] == -1:\n",
    "                normals.append(range_normal)\n",
    "            else:\n",
    "                normals.append(get_attn_normal(model, head_layer[1], head_layer[0], range_normal))\n",
    "            cs.append(1)\n",
    "            continue\n",
    "        if head_layer[0] == -1:\n",
    "            # original embedding\n",
    "            cs.append(1)\n",
    "            normals.append(normals[i-1])\n",
    "            continue\n",
    "        try:\n",
    "            with torch.no_grad():\n",
    "                c = get_LN_constant_across_tokens(model, embeddings_pos, embeddings_neg, head_layer[1], normals[i-1], head_layer_list[i-1][1])\n",
    "        except ZeroDivisionError:\n",
    "            return 0, torch.zeros(range_normal.shape).to(\"cuda\")\n",
    "        cs.append(c)\n",
    "        normals.append(get_attn_normal(model, head_layer[1], head_layer[0], c*normals[i-1]))\n",
    "    # now, build up Ys backwards\n",
    "    Ys_pos = []\n",
    "    Ys_neg = []\n",
    "    for i, head_layer in enumerate(reversed(head_layer_list)):\n",
    "        if i == 0:\n",
    "            if head_layer[0] == -1:\n",
    "                # get contribution of original embedding\n",
    "                prev_Y_pos =embeddings_pos['layers'][0]['ln_1_in'][0].T\n",
    "                prev_Y_neg = embeddings_neg['layers'][0]['ln_1_in'][0].T\n",
    "            else:\n",
    "                prev_Y_pos = embeddings_pos['layers'][head_layer[1]]['attn_in'][0].T # after [0].T: (neuron, token)\n",
    "                prev_Y_neg = embeddings_neg['layers'][head_layer[1]]['attn_in'][0].T # after [0].T: (neuron, token)\n",
    "        else:\n",
    "            prev_Y_pos = Ys_pos[i-1]\n",
    "            prev_Y_neg = Ys_neg[i-1]\n",
    "\n",
    "        with torch.no_grad():\n",
    "            Y_pos = prev_Y_pos @ embeddings_pos['layers'][head_layer[1]]['attn_out'][2][0,head_layer[0],:,:].T\n",
    "            Y_neg = prev_Y_neg @ embeddings_neg['layers'][head_layer[1]]['attn_out'][2][0,head_layer[0],:,:].T\n",
    "        \n",
    "        Ys_pos.append(Y_pos)\n",
    "        Ys_neg.append(Y_neg)\n",
    "    return torch.dot(normals[-1], (Ys_pos[-1]-Ys_neg[-1])[:,-1]).item(), normals[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0753ae90-d379-4a4b-9c52-00f3b22aad89",
   "metadata": {},
   "outputs": [],
   "source": [
    "# greedy heuristic\n",
    "# TODO: also account for embeddings\n",
    "def get_max_paths(model, embeddings_pos, embeddings_neg, range_normal, max_length, num_paths):\n",
    "    num_layers = len(model.transformer.h)\n",
    "    num_heads = model.transformer.h[0].attn.attention.num_heads\n",
    "    \n",
    "    my_list = []\n",
    "    embeddings_list = []\n",
    "    for head in range(num_heads):\n",
    "        for layer in range(num_layers):\n",
    "            contrib, _ = get_mediated_head_contrib(model, [(head,layer)], embeddings_pos, embeddings_neg, range_normal)\n",
    "            my_list.append({\"path\": [(head, layer)], \"contrib\": contrib})\n",
    "    contrib, _ = get_mediated_head_contrib(model, [(-1,-1)], embeddings_pos, embeddings_neg, range_normal)\n",
    "    embeddings_list.append({\"path\": [(-1,-1)], \"contrib\": contrib})\n",
    "    \n",
    "    prev_list = list(sorted(my_list, key=lambda x: x['contrib'], reverse=True))[:num_paths]\n",
    "    for cur_path_size in range(1, max_length):\n",
    "        cur_list = []\n",
    "        for list_item in prev_list:\n",
    "            base_path = list_item['path']\n",
    "            for head in range(num_heads):\n",
    "                for layer in range(base_path[-1][1]):\n",
    "                    # let's go, four nested loops!\n",
    "                    cur_path = base_path + [(head, layer)]\n",
    "                    contrib, _ = get_mediated_head_contrib(model, cur_path, embeddings_pos, embeddings_neg, range_normal)\n",
    "                    cur_list.append({'path': cur_path, 'contrib': contrib})\n",
    "            contrib, _ = get_mediated_head_contrib(model, base_path + [(-1,-1)], embeddings_pos, embeddings_neg, range_normal)\n",
    "            embeddings_list.append({'path': base_path + [(-1,-1)], 'contrib': contrib})\n",
    "        prev_list = list(sorted(cur_list, key=lambda x: x['contrib'], reverse=True))[:num_paths]\n",
    "    out_list = prev_list + embeddings_list\n",
    "    out_list = list(sorted(out_list, key=lambda x: x['contrib'], reverse=True))[:num_paths]\n",
    "    return out_list"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32b9bddb-6bb4-4c10-8815-0e0ec8afbc15",
   "metadata": {},
   "source": [
    "## Linear feature tracing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "65ff333b-b34d-43df-aefb-1760428f1e85",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_attn_normal(model, layer, head, range_normal):\n",
    "    attn_module = model.transformer.h[layer].attn.attention\n",
    "    W_out = split_mat_heads(attn_module.out_proj.weight, attn_module.num_heads, attn_module.head_dim)[head]\n",
    "    W_val = attn_module.v_proj.weight[head*attn_module.head_dim:(head+1)*attn_module.head_dim,:]\n",
    "    # attn_normal = (W_out W_V)^T range_normal = W_V^T W_out^T range_normal\n",
    "    return W_val.T @ W_out.T @ range_normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "91876f33-e985-4788-8603-e3c6087d6cb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_fake_mlp_normal(model, layer, range_normal):\n",
    "    return model.transformer.h[layer].mlp.c_fc.weight.T @ (model.transformer.h[layer].mlp.c_proj.weight.T @ range_normal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "b7b28938-6964-4dce-ac3b-69301c0dcdbc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def coupling_coeff(y1, y2): return torch.dot(y1, y2)/torch.linalg.norm(y1)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "30fa9e61-57b5-4538-8dfb-ae9f1d6a57e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def cossim(y1, y2): return torch.dot(y1, y2)/(torch.linalg.norm(y1)*torch.linalg.norm(y2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ac12250-a6aa-45cb-96f2-93c58954ed0d",
   "metadata": {},
   "source": [
    "## Prompt evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "43930dc2-bca6-49e7-b70c-cef707e65d2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def slice_tokenized_prompts_into_context_windows(prompts, size, max_tokens=None):\n",
    "    retlist = []\n",
    "    if max_tokens is not None:\n",
    "        num_tokens_seen = 0\n",
    "    for prompt in prompts:\n",
    "        prompt_len = prompt['input_ids'].shape[1]\n",
    "        for i in range(0, prompt_len, size):\n",
    "            input_ids = prompt['input_ids'][0,i:min(i+size, prompt_len)][None]\n",
    "            attention_mask = prompt['attention_mask'][0,i:min(i+size, prompt_len)][None]\n",
    "            retlist.append({'input_ids': input_ids, 'attention_mask': attention_mask})\n",
    "            if max_tokens is not None:\n",
    "                num_tokens_seen += input_ids.shape[1]\n",
    "                if num_tokens_seen > max_tokens: return retlist\n",
    "    return retlist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "9c3bcd71-d6f8-46e3-83a9-86b668bb0824",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tqdm\n",
    "def embeddings_from_prompt_list(model, prompts, return_np=True, use_tqdm=True, pre_tokenized=False, print_tensors_count=False):\n",
    "    outs_list = []\n",
    "    with torch.no_grad():\n",
    "        if use_tqdm: prompts_gen = tqdm.tqdm(prompts)\n",
    "        else: prompts_gen = prompts\n",
    "        for i, prompt in enumerate(prompts):\n",
    "            cur_embeddings, hooks = attach_hooks(model)\n",
    "            if pre_tokenized:\n",
    "                tokens = {\"input_ids\": prompt['input_ids'].to(\"cuda:0\"), 'attention_mask': prompt['attention_mask'].to(\"cuda:0\")}\n",
    "            else:\n",
    "                tokens = tokenizer(prompt, return_tensors=\"pt\").to(\"cuda:0\")\n",
    "            model(**tokens)\n",
    "            for hook in hooks: hook.remove()\n",
    "            if return_np:\n",
    "                cur_embeddings = embeddings_torch_to_np(cur_embeddings)\n",
    "            outs_list.append(cur_embeddings)\n",
    "            if print_tensors_count:\n",
    "                print(f\"After loading prompt {i}, number of tensors: {get_num_tensors()}\")\n",
    "    return outs_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "cb75954e-dca3-42b6-80d4-f5624ae03462",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_normal_scores_for_prompt(model, layer, sublayer, prompt, normal, use_tqdm=True, pre_tokenized=False):\n",
    "    embedding = embeddings_from_prompt_list(model, [prompt], return_np=False, use_tqdm=use_tqdm, pre_tokenized=pre_tokenized)[0]\n",
    "    if not (layer is None):\n",
    "        sublayer_embedding = embedding['layers'][layer][sublayer] # assuming that sublayer embedding has shape (1, tokens, neurons)\n",
    "    else:\n",
    "        sublayer_embedding = embedding[sublayer]\n",
    "    sublayer_embedding = sublayer_embedding[0]\n",
    "    # get dots: (tokens, neurons) . (neurons) = (tokens)\n",
    "    with torch.no_grad():\n",
    "        normal_scores = sublayer_embedding @ normal\n",
    "    normal_scores = normal_scores.detach().cpu().numpy()\n",
    "    free_embeddings(embedding)\n",
    "    del sublayer_embedding\n",
    "    do_free()\n",
    "    return normal_scores    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "995a91da-c73c-491c-a0fd-a5c1452fe64b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_normal_scores_for_prompt_list(model, layer, sublayer, prompts, normal, use_tqdm=True, pre_tokenized=False):\n",
    "    embeddings = embeddings_from_prompt_list(model, prompts, return_np=True, use_tqdm=use_tqdm, pre_tokenized=pre_tokenized)\n",
    "    ret_list = []\n",
    "    for i in range(len(embeddings)):\n",
    "        embedding = embeddings[i]\n",
    "        if not (layer is None):\n",
    "            sublayer_embedding = embedding['layers'][layer][sublayer] # assuming that sublayer embedding has shape (1, tokens, neurons)\n",
    "        else:\n",
    "            sublayer_embedding = embedding[sublayer]\n",
    "        sublayer_embedding = sublayer_embedding[0]\n",
    "        # get dots: (tokens, neurons) . (neurons) = (tokens)\n",
    "        normal_scores = sublayer_embedding @ normal\n",
    "        free_embeddings(embedding)\n",
    "        del sublayer_embedding\n",
    "        do_free()\n",
    "        ret_list.append(normal_scores)\n",
    "    return ret_list    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "57bdaeb9-1d3d-4df2-aeeb-1ffb05dc39be",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "def get_normal_list_scores_for_prompt_list(model, normals, prompts, use_tqdm=True, pre_tokenized=False, save_every=None, save_out=\"normal_list_scores.pkl\"):\n",
    "    #normals is a list of dicts: [{\"normal\", \"layer\", \"sublayer\", \"name\", \"token\"}]\n",
    "    retval = [ {\n",
    "        'info': {\n",
    "            'name': normal['name'],\n",
    "            'layer': normal['layer'],\n",
    "            'sublayer': normal['sublayer'],\n",
    "            'token': normal['token']\n",
    "        },\n",
    "        'scores': []\n",
    "    } for normal in normals ]\n",
    "    \n",
    "    with torch.no_grad():\n",
    "        if use_tqdm: tqdm_lambda = lambda x: tqdm.tqdm(x)\n",
    "        else: tqdm_lambda = lambda x: x\n",
    "        for i, prompt in tqdm_lambda(enumerate(prompts)):\n",
    "            embedding, hooks = attach_hooks(model)\n",
    "            if pre_tokenized:\n",
    "                tokens = {\"input_ids\": prompt['input_ids'].to(\"cuda:0\"), 'attention_mask': prompt['attention_mask'].to(\"cuda:0\")}\n",
    "            else:\n",
    "                tokens = tokenizer(prompt, return_tensors=\"pt\").to(\"cuda:0\")\n",
    "            model(**tokens)\n",
    "            for hook in hooks: hook.remove()\n",
    "            embedding = embeddings_torch_to_np(embedding)\n",
    "            for i, normal_info in enumerate(normals):\n",
    "                normal = normal_info['normal']\n",
    "                layer = normal_info['layer']\n",
    "                sublayer = normal_info['sublayer']\n",
    "                token = normal_info['token']\n",
    "                if not (layer is None):\n",
    "                    sublayer_embedding = embedding['layers'][layer][sublayer] # assuming that sublayer embedding has shape (1, tokens, neurons)\n",
    "                else:\n",
    "                    sublayer_embedding = embedding[sublayer]\n",
    "                sublayer_embedding = sublayer_embedding[0]\n",
    "                # get dots: (tokens, neurons) . (neurons) = (tokens)\n",
    "                normal_scores = sublayer_embedding @ normal\n",
    "                if token is not None:\n",
    "                    normal_scores = normal_scores[token]\n",
    "                retval[i]['scores'].append(normal_scores)\n",
    "            free_embeddings(embedding)\n",
    "            del sublayer_embedding\n",
    "            do_free()\n",
    "            if save_every is not None:\n",
    "                if i % save_every == 0 and i != 0:\n",
    "                    fp = open(save_out, \"wb\")\n",
    "                    pickle.dump(retval, fp)\n",
    "                    fp.close()\n",
    "    return retval    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "2f8a023a-5b50-4b3d-b16b-3206852688f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_top_normal_scores_for_prompt_list(model, layer, sublayer, prompts, normal, k=5, pre_tokenized=False, reverse=False, both=False):\n",
    "    scores_list = []\n",
    "    for prompt in tqdm.tqdm(prompts):\n",
    "        scores_list.append(get_normal_scores_for_prompt(model, layer, sublayer, prompt, normal, use_tqdm=False, pre_tokenized=pre_tokenized))\n",
    "    scores_arr = np.concatenate(scores_list)\n",
    "    scores_tensor = torch.from_numpy(scores_arr)\n",
    "    scores_topk = torch.topk(scores_tensor, k=k, largest=(not reverse), sorted=True)\n",
    "    # go from index to (prompt, token)\n",
    "    prompt_start_indices = np.cumsum([0]+[x.shape[0] for x in scores_list])[:-1]\n",
    "    retlist = []\n",
    "    for score, index in zip(scores_topk.values, scores_topk.indices):\n",
    "        score = score.item()\n",
    "        index = index.item()\n",
    "        prompt_idx = np.searchsorted(prompt_start_indices, index, side='right')-1\n",
    "        try:\n",
    "            token_idx = index-prompt_start_indices[prompt_idx]\n",
    "        except IndexError:\n",
    "            print(f\"prompt_idx: {prompt_idx}. prompt_start_indices: {prompt_start_indices}. index: {index}\")\n",
    "            raise IndexError\n",
    "        retlist.append({\"score\": score, \"prompt_idx\": prompt_idx, \"token_idx\": token_idx})\n",
    "    if both:\n",
    "        scores_topk = torch.topk(scores_tensor, k=k, largest=reverse, sorted=True)\n",
    "        new_retlist = []\n",
    "        for score, index in zip(scores_topk.values, scores_topk.indices):\n",
    "            score = score.item()\n",
    "            index = index.item()\n",
    "            prompt_idx = np.searchsorted(prompt_start_indices, index, side='right')-1\n",
    "            try:\n",
    "                token_idx = index-prompt_start_indices[prompt_idx]\n",
    "            except IndexError:\n",
    "                print(f\"prompt_idx: {prompt_idx}. prompt_start_indices: {prompt_start_indices}. index: {index}\")\n",
    "                raise IndexError\n",
    "            new_retlist.append({\"score\": score, \"prompt_idx\": prompt_idx, \"token_idx\": token_idx})\n",
    "        return retlist, new_retlist\n",
    "    return retlist   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "e7206825-43cf-43a6-ac25-6a53b296e5a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def logit_lens(model, tokenizer, v, k=5, reverse=False):\n",
    "    with torch.no_grad():\n",
    "        unembedded = model.lm_head.weight.data @ model.transformer.ln_f(v)\n",
    "        return tokenizer.batch_decode([ [x] for x in torch.topk(unembedded, k=k, largest=(not reverse)).indices ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "e85daa9a-65e3-4f15-81a6-7e4ce62195fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def logit_lens_layer0(model, tokenizer, v, k=5, reverse=False):\n",
    "    with torch.no_grad():\n",
    "        unembedded = torch.linalg.pinv(model.transformer.wte.weight).T @ v\n",
    "        return tokenizer.batch_decode([ [x] for x in torch.topk(unembedded, k=k, largest=(not reverse)).indices ])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4809e324-9259-490e-8493-5e0539d3467a",
   "metadata": {},
   "source": [
    "## Patching"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "ad39800d-ede1-4767-89ba-845958ed60d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_single_attn_head(model, layer, head, xs, qk_xs=None):\n",
    "\t# xs are \"attn_in\"\n",
    "\tattn_module = model.transformer.h[layer].attn.attention\n",
    "\tq_proj = attn_module.q_proj.weight[head*attn_module.head_dim:(head+1)*attn_module.head_dim]\n",
    "\tk_proj = attn_module.k_proj.weight[head*attn_module.head_dim:(head+1)*attn_module.head_dim]\n",
    "\tv_proj = attn_module.v_proj.weight[head*attn_module.head_dim:(head+1)*attn_module.head_dim]\n",
    "\n",
    "\tif qk_xs is None: qk_xs = xs\n",
    "\tquery = qk_xs @ q_proj.T\n",
    "\tkey = qk_xs @ k_proj.T\n",
    "\tvalue = xs @ v_proj.T\n",
    "\n",
    "\tquery = query.view(query.shape[0], 1, query.shape[1], query.shape[2])\n",
    "\tkey = key.view(key.shape[0], 1, key.shape[1], key.shape[2])\n",
    "\tvalue = value.view(value.shape[0], 1, value.shape[1], value.shape[2])\n",
    "\n",
    "\tattn_output, attn_weights = attn_module._attn(query, key, value)\n",
    "\n",
    "\to_proj = attn_module.out_proj.weight[:, head*attn_module.head_dim:(head+1)*attn_module.head_dim]\n",
    "\n",
    "\tattn_output = attn_output[:, 0, :, :] #(batch, token, feature)\n",
    "\tattn_output = attn_output @ o_proj.T\n",
    "\n",
    "\treturn attn_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "8c5fce25-81c4-4285-b3b5-8425ea77a6db",
   "metadata": {},
   "outputs": [],
   "source": [
    "def path_patching(model, embeddings_pos, embeddings_neg, path, only_patch_ov=False, no_ln_f=False):\n",
    "\t# path is a list like [(13, 'attn', 11), (16, 'mlp'), (17, 'attn', 14)]\n",
    "\tpos_layer = embeddings_pos['layers'][path[0][0]]\n",
    "\tif path[0][1] == 'attn':\n",
    "\t\t#if use_ln: sublayer = 'ln_1_in'\n",
    "\t\t#else: sublayer = 'attn_in'\n",
    "\t\tsublayer = 'ln_1_in'\n",
    "\telif path[0][1] == 'mlp':\n",
    "\t\t#if use_ln: sublayer = 'ln_2_in'\n",
    "\t\t#else: sublayer = 'mlp_in'\n",
    "\t\tsublayer = 'ln_2_in'\n",
    "\n",
    "\tclean = pos_layer[sublayer]\n",
    "\n",
    "\tif embeddings_neg is not None:\n",
    "\t\tneg_layer = embeddings_neg['layers'][path[0][0]]\n",
    "\t\tdirty = neg_layer[sublayer]\n",
    "\telse:\n",
    "\t\tdirty = torch.zeros(clean.shape).to(\"cuda\")\n",
    "\n",
    "\tfor component in path:\n",
    "\t\tlayer = component[0]\n",
    "\t\tmodel_layer = model.transformer.h[layer]\n",
    "\t\tbase = embeddings_pos['layers'][component[0]]\n",
    "\t\tbase_full_embed = base[sublayer]\n",
    "\t\tdirty_full_embed = base_full_embed - clean + dirty\n",
    "\t\tif component[1] == 'attn':\n",
    "\t\t\t#if use_ln:\n",
    "\t\t\t#\tdirty = model_layer.ln_1(dirty_full_embed)\n",
    "\t\t\tdirty = model_layer.ln_1(dirty_full_embed)\n",
    "\t\t\tif only_patch_ov:\n",
    "\t\t\t\tdirty = compute_single_attn_head(model, layer, component[2], dirty, qk_xs=base['attn_in'])\n",
    "\t\t\telse:\n",
    "\t\t\t\tdirty = compute_single_attn_head(model, layer, component[2], dirty)\n",
    "\t\t\t\t\n",
    "\t\t\tclean = model_layer.ln_1(base_full_embed)\n",
    "\t\t\tclean = compute_single_attn_head(model, layer, component[2], clean)\n",
    "\t\t\t#clean = base['attn_out'][0]\n",
    "\t\telif component[1] == 'mlp':\n",
    "\t\t\t#if use_ln:\n",
    "\t\t\t#\tdirty = model_layer.ln_2(dirty_full_embed)\n",
    "\t\t\tdirty = model_layer.ln_2(dirty_full_embed)\n",
    "\t\t\tdirty = model_layer.mlp(dirty)\n",
    "\t\t\tclean = base['mlp_out']\n",
    "\n",
    "\t# last step: patch ln_f\n",
    "\tbase_full_embed = embeddings_pos['ln_f_in']\n",
    "\tdirty_full_embed = base_full_embed - clean + dirty\n",
    "\tif no_ln_f:\n",
    "\t\treturn base_full_embed, dirty_full_embed\n",
    "\t\n",
    "\tdirty = model.lm_head(model.transformer.ln_f(dirty_full_embed))\n",
    "\tclean = model.lm_head(model.transformer.ln_f(base_full_embed))\n",
    "\treturn clean, dirty"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73824cb2-4d7c-4b80-b2de-45f98265f5ee",
   "metadata": {},
   "source": [
    "## Finding feature vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "90cf15ce-888d-4fe6-ae9f-fa05a7430fdf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_layer_subset(model, path, hidden_states):\n",
    "    for component in path:\n",
    "        residual = hidden_states\n",
    "        layer = component['layer']\n",
    "        model_layer = model.transformer.h[layer]\n",
    "        if component['sublayer'] == 'attn':\n",
    "            hidden_states = model_layer.ln_1(hidden_states)\n",
    "            if component['head'] == None:\n",
    "                attn_outputs = model.transformer.h[layer].attn(hidden_states)\n",
    "                attn_output = attn_outputs[0]\n",
    "            else:\n",
    "                attn_output = compute_single_attn_head(model, layer, component['head'], hidden_states)\n",
    "            hidden_states = residual + attn_output\n",
    "        elif component['sublayer'] == 'mlp':\n",
    "            hidden_states = model_layer.ln_2(hidden_states)\n",
    "            feed_forward_hidden_states = model_layer.mlp(hidden_states)\n",
    "            hidden_states = residual + feed_forward_hidden_states\n",
    "    return hidden_states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "9b5a3ba2-34ca-4aa9-93e5-95447900dbed",
   "metadata": {},
   "outputs": [],
   "source": [
    "def path_patching_per_token(model, embeddings_pos, embeddings_neg, path, only_patch_ov=False, no_ln_f=False, range_normal=None, only_return_path_diffs=False):\n",
    "    # path is a list like [{'layer': 6, 'head': 6, 'sublayer': 'attn', 'token': 3}, {'layer': 15, 'head': 13, 'sublayer': 'attn', 'token': 3}]\n",
    "    #print(path)\n",
    "    with torch.no_grad():\n",
    "        pos_layer = embeddings_pos['layers'][path[0]['layer']]\n",
    "        if path[0]['sublayer'] == 'attn' or path[0]['sublayer'] == 'embedding':\n",
    "            sublayer = 'ln_1_in'\n",
    "        elif path[0]['sublayer'] == 'mlp':\n",
    "            sublayer = 'ln_2_in'\n",
    "    \n",
    "        clean = pos_layer[sublayer]\n",
    "    \n",
    "        if embeddings_neg is not None:\n",
    "            neg_layer = embeddings_neg['layers'][path[0]['layer']]\n",
    "            dirty = neg_layer[sublayer]\n",
    "        else:\n",
    "            dirty = torch.zeros(clean.shape).to(\"cuda\")\n",
    "    \n",
    "        for component in path:\n",
    "            layer = component['layer']\n",
    "            model_layer = model.transformer.h[layer]\n",
    "            base = embeddings_pos['layers'][component['layer']]\n",
    "\n",
    "            if component['sublayer'] == 'attn' or component['sublayer'] == 'embedding':\n",
    "                sublayer = 'ln_1_in'\n",
    "            elif component['sublayer'] == 'mlp':\n",
    "                sublayer = 'ln_2_in'\n",
    "            base_full_embed = base[sublayer]\n",
    "            \n",
    "            if component['token'] is not None:\n",
    "                # TODO: this used to be dirty_full_embed = base_full_embed - clean[:, component['token'], :] + dirty[:, component['token'], :]\n",
    "                dirty_full_embed = base_full_embed.clone()\n",
    "                dirty_full_embed[:, component['token'], :] += dirty[:, component['token'], :] - clean[:, component['token'], :]\n",
    "            else:\n",
    "                dirty_full_embed = base_full_embed - clean + dirty\n",
    "\n",
    "            if range_normal is not None:\n",
    "                test_token = component['token'] if component['token'] is not None else -1\n",
    "                #print(f\"Before component {component}, dirty-clean diff: \", (range_normal @ (dirty_full_embed[0,test_token] - base_full_embed[0,test_token])).item())\n",
    "            \n",
    "            if component['sublayer'] == 'attn':\n",
    "                dirty = model_layer.ln_1(dirty_full_embed)\n",
    "                clean = model_layer.ln_1(base_full_embed)\n",
    "                \n",
    "                if component['head'] == None:\n",
    "                    clean_new = torch.zeros(dirty.shape).to(\"cuda\")\n",
    "                    dirty_new = torch.zeros(dirty.shape).to(\"cuda\")\n",
    "                    for head in range(16):\n",
    "                        if only_patch_ov:\n",
    "                            dirty_new += compute_single_attn_head(model, layer, head, dirty, qk_xs=base['attn_in'])\n",
    "                        else:\n",
    "                            dirty_new += compute_single_attn_head(model, layer, head, dirty)\n",
    "                        clean_new += compute_single_attn_head(model, layer, head, clean)\n",
    "                    dirty = dirty_new\n",
    "                    clean = clean_new\n",
    "                else:\n",
    "                    if only_patch_ov:\n",
    "                        dirty = compute_single_attn_head(model, layer, component['head'], dirty, qk_xs=base['attn_in'])\n",
    "                    else:\n",
    "                        dirty = compute_single_attn_head(model, layer, component['head'], dirty)\n",
    "                    clean = compute_single_attn_head(model, layer, component['head'], clean)\n",
    "            elif component['sublayer'] == 'mlp':\n",
    "                dirty = model_layer.ln_2(dirty_full_embed)\n",
    "                dirty = model_layer.mlp(dirty)\n",
    "\n",
    "                clean = base['mlp_out']\n",
    "            elif component['sublayer'] == 'embedding':\n",
    "                dirty = dirty_full_embed\n",
    "                clean = base_full_embed\n",
    "    \n",
    "        if only_return_path_diffs:\n",
    "            if component['sublayer'] != 'embedding':\n",
    "                return base_full_embed + clean, dirty_full_embed + dirty\n",
    "            return base_full_embed, dirty_full_embed\n",
    "        \n",
    "        # last step: patch ln_f\n",
    "        base_full_embed = embeddings_pos['ln_f_in']\n",
    "        dirty_full_embed = base_full_embed - clean[:, -1, :] + dirty[:, -1, :]\n",
    "        if no_ln_f:\n",
    "            return base_full_embed, dirty_full_embed\n",
    "        \n",
    "        dirty = model.lm_head(model.transformer.ln_f(dirty_full_embed))\n",
    "        clean = model.lm_head(model.transformer.ln_f(base_full_embed))\n",
    "    return clean, dirty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "692020f9-c932-449f-96d8-bbc598dddf4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def propagate_normal_through_LayerNorm(model, embeddings, layer, normal, ln_1=False, token=None, estimate_dot=False):\n",
    "    with torch.no_grad():\n",
    "        if ln_1:\n",
    "            W = model.transformer.h[layer].ln_1.weight\n",
    "            x = embeddings['layers'][layer]['ln_1_in'][0]\n",
    "        else:\n",
    "            W = model.transformer.h[layer].ln_2.weight\n",
    "            x = embeddings['layers'][layer]['ln_2_in'][0]\n",
    "        if estimate_dot:\n",
    "            x_bar = 1\n",
    "        else:\n",
    "            if token is None:\n",
    "                x_bar = torch.linalg.norm(x, axis=1).mean()\n",
    "            else:\n",
    "                x = x[token]\n",
    "                x_bar = torch.linalg.norm(x)\n",
    "        d = x.shape[-1]\n",
    "        return np.sqrt(d)/x_bar * W * normal\n",
    "\n",
    "def get_head_token_contribs_for_layer(model, embeddings_pos, embeddings_neg, layer, token_idx, range_normal):\n",
    "    with torch.no_grad():\n",
    "        attn_module = model.transformer.h[layer].attn.attention\n",
    "        attn_split_weights = split_mat_heads(attn_module.out_proj.weight, attn_module.num_heads, attn_module.head_dim)\n",
    "        attn_split_vals_pos = attn_module._split_heads(embeddings_pos['layers'][layer]['v_proj_out'], attn_module.num_heads, attn_module.head_dim)\n",
    "        attn_scores_pos = embeddings_pos['layers'][layer]['attn_out'][2]\n",
    "        attn_dots_pos = get_dots_per_head_and_token(token_idx, attn_module, attn_scores_pos, attn_split_weights, attn_split_vals_pos, range_normal)\n",
    "        attn_contribs_pos = attn_dots_pos * attn_scores_pos[0, :, token_idx, :]\n",
    "\n",
    "        if embeddings_neg is None:\n",
    "            # zero ablation\n",
    "            attn_split_vals_neg = torch.zeros(attn_split_vals_pos.shape).to(\"cuda\")\n",
    "            attn_scores_neg =  torch.zeros(attn_scores_pos.shape).to(\"cuda\")\n",
    "            attn_dots_neg =  torch.zeros(attn_contribs_pos.shape).to(\"cuda\")\n",
    "            attn_contribs_neg =  torch.zeros(attn_contribs_pos.shape).to(\"cuda\")\n",
    "        else:\n",
    "            attn_split_vals_neg = attn_module._split_heads(embeddings_neg['layers'][layer]['v_proj_out'], attn_module.num_heads, attn_module.head_dim)\n",
    "            attn_scores_neg = embeddings_neg['layers'][layer]['attn_out'][2]\n",
    "            attn_dots_neg = get_dots_per_head_and_token(token_idx, attn_module, attn_scores_neg, attn_split_weights, attn_split_vals_neg, range_normal)\n",
    "            attn_contribs_neg = attn_dots_neg * attn_scores_neg[0, :, token_idx, :]\n",
    "\n",
    "        attn_contribs = attn_contribs_pos - attn_contribs_neg\n",
    "        attn_contribs_list = []\n",
    "        for head, row in enumerate(attn_contribs):\n",
    "            for j, item in enumerate(row):\n",
    "                attn_contribs_list.append({\n",
    "                    \"path\": {\"head\": head, \"token\": j, \"layer\": layer, \"sublayer\": \"attn\"},\n",
    "                    \"contrib\": item.item()\n",
    "                })\n",
    "    attn_contribs_list = sorted(attn_contribs_list, key=lambda x: abs(x['contrib']), reverse=True)\n",
    "    return attn_contribs_list\n",
    "\n",
    "def get_head_token_contribs(model, embeddings_pos, embeddings_neg, token_idx, range_normal, num_layers=None):\n",
    "    if num_layers is None: num_layers = len(embeddings_pos['layers'])\n",
    "    retlist = []\n",
    "    for layer in range(num_layers):\n",
    "        retlist += get_head_token_contribs_for_layer(model, embeddings_pos, embeddings_neg, layer, token_idx, range_normal)\n",
    "    retlist = sorted(retlist, key=lambda x: abs(x['contrib']), reverse=True)\n",
    "    return retlist\n",
    "    \n",
    "def get_mlp_contribs(model, embeddings_pos, embeddings_neg, token_idx, range_normal, num_layers=None):\n",
    "    if num_layers is None: num_layers = len(embeddings_pos['layers'])\n",
    "    retlist = []\n",
    "    for layer in range(num_layers):\n",
    "        with torch.no_grad():\n",
    "            mlp_y_pos = embeddings_pos['layers'][layer]['mlp_out'][0, token_idx, :]\n",
    "            mlp_y_neg = embeddings_neg['layers'][layer]['mlp_out'][0, token_idx, :]\n",
    "            mlp_dot = range_normal @ mlp_y_pos - range_normal @ mlp_y_neg\n",
    "        retlist.append({\n",
    "            \"path\": {\"head\": -1, \"token\": token_idx, \"layer\": layer, \"sublayer\": \"mlp\"},\n",
    "            \"contrib\": mlp_dot.item()\n",
    "        })\n",
    "    retlist = sorted(retlist, key=lambda x: abs(x['contrib']), reverse=True)\n",
    "    return retlist\n",
    "\n",
    "def get_normal_for_path(model, embeddings_pos, embeddings_neg, range_normal, path, use_ln=True, normalize=False, estimate_dot=False):\n",
    "    normal = range_normal\n",
    "    for i, node in enumerate(path):\n",
    "        cur_token = node['token']\n",
    "        cur_layer = node['layer']\n",
    "        cur_sublayer = node['sublayer']\n",
    "        cur_head = node['head']\n",
    "        \n",
    "        use_ln_1 = False\n",
    "        if cur_sublayer == 'attn':\n",
    "            if cur_head != -1:\n",
    "                new_normal = get_attn_normal(model, cur_layer, cur_head, normal)\n",
    "            else:\n",
    "                attn_module = model.transformer.h[cur_layer].attn.attention\n",
    "                attn_module_v_proj = attn_module.v_proj.weight\n",
    "                attn_module_o_proj = attn_module.out_proj.weight\n",
    "                combined_WOV = torch.zeros(2048,2048).to(\"cuda\")\n",
    "                for head in range(attn_module.num_heads):\n",
    "                    combined_WOV += get_ov_mat_for_head(attn_module_v_proj, attn_module_o_proj, 16, 128, head)\n",
    "                new_normal = combined_WOV.T @ normal\n",
    "        elif cur_sublayer == 'mlp':\n",
    "            xpos = embeddings_pos['layers'][cur_layer]['mlp_in'][0,cur_token,:]\n",
    "            xneg = embeddings_neg['layers'][cur_layer]['mlp_in'][0,cur_token,:]\n",
    "            zeros = torch.zeros(normal.shape).to(\"cuda\")\n",
    "            affine = domain_boundary_intersection(xpos, xneg,\n",
    "                model.transformer.h[cur_layer].mlp, normal, zeros, lr=0.02, eps=0.0000001)\n",
    "            new_normal = get_tangent_plane_given_point(affine, model.transformer.h[cur_layer].mlp, normal, zeros)\n",
    "            use_ln_1 = True\n",
    "        else:\n",
    "            raise Exception(\"Invalid sublayer: \" + str(cur_sublayer))\n",
    "        if use_ln:\n",
    "            if i == len(path)-1:\n",
    "                new_normal = propagate_normal_through_LayerNorm(model, embeddings_pos, cur_layer, new_normal, ln_1=use_ln_1, token=cur_token, estimate_dot=estimate_dot)\n",
    "            else:\n",
    "                new_normal = propagate_normal_through_LayerNorm(model, embeddings_pos, cur_layer, new_normal, ln_1=use_ln_1, token=cur_token)\n",
    "        normal = new_normal\n",
    "    if normalize: normal = normal / torch.linalg.norm(normal)\n",
    "    return normal.detach()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "1e2865f0-20f5-47f3-b997-30157c9ca97f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def patch_get_max_paths(model, embeddings_pos, embeddings_neg, range_normal, max_length, num_paths, use_mlp=True, use_attn=True, starting_path=None, least_attrib=False, no_ln_f=True):\n",
    "    num_tokens = embeddings_pos['layers'][-1]['attn_in'].shape[1]\n",
    "    assert(num_tokens == embeddings_neg['layers'][-1]['attn_in'].shape[1])\n",
    "    \n",
    "    embedding_contribs_list = []\n",
    "    \n",
    "    paths = [starting_path]\n",
    "    if starting_path is None:\n",
    "        paths=[ [] ]                     \n",
    "    \n",
    "    for cur_length in range(0, max_length):\n",
    "        print(f\"Paths of length {cur_length+1}:\\n===================\")\n",
    "        cur_contribs_list = []\n",
    "        for path in paths:\n",
    "            try:\n",
    "                cur_token = path[0]['token']\n",
    "                cur_layer = path[0]['layer']\n",
    "                cur_sublayer = path[0]['sublayer']\n",
    "            except:\n",
    "                cur_token = -1\n",
    "                cur_layer = len(model.transformer.h)\n",
    "                cur_sublayer = \"\"\n",
    "            \n",
    "            # TODO: if (cur_layer, cur_sublayer) == (0, 'attn'), then treat this as an embedding\n",
    "            \n",
    "            # append contrib for each head-token, MLP to cur_contribs_list\n",
    "            # first, attention: loop through all layer-head-tokens\n",
    "            if use_attn:\n",
    "                attn_num_layers = cur_layer\n",
    "                if cur_sublayer == 'attn':\n",
    "                    attn_num_layers -= 1\n",
    "                for attn_layer in range(attn_num_layers):\n",
    "                    for head in range(model.transformer.h[0].attn.attention.num_heads):\n",
    "                        for token in range(num_tokens):\n",
    "                            new_path = [{'layer': attn_layer, 'sublayer': 'attn', 'token': token, 'head': head}] + path\n",
    "                            clean, dirty = path_patching_per_token(model, embeddings_pos, embeddings_neg, new_path, only_patch_ov=True, no_ln_f=no_ln_f)\n",
    "                            contrib = (range_normal @ clean[0,-1,:] - range_normal @ dirty[0,-1,:]).item()\n",
    "                            cur_contribs_list.append({'path': new_path, 'contrib': contrib})\n",
    "            # next, mlp\n",
    "            if use_mlp:\n",
    "                mlp_num_layers = cur_layer - 1\n",
    "                for mlp_layer in range(mlp_num_layers):\n",
    "                    new_path = [{'layer': mlp_layer, 'sublayer': 'mlp', 'token': cur_token, 'head': -1}] + path\n",
    "                    clean, dirty = path_patching_per_token(model, embeddings_pos, embeddings_neg, new_path, only_patch_ov=True, no_ln_f=no_ln_f)\n",
    "                    contrib = (range_normal @ clean[0,-1,:] - range_normal @ dirty[0,-1,:]).item()\n",
    "                    cur_contribs_list.append({'path': new_path, 'contrib': contrib})\n",
    "                    \n",
    "            # now, embeddings\n",
    "            new_path = [{'layer': 0, 'sublayer': 'embedding', 'token': cur_token, 'head': -1}] + path\n",
    "            clean, dirty = path_patching_per_token(model, embeddings_pos, embeddings_neg, new_path, only_patch_ov=True, no_ln_f=no_ln_f)\n",
    "            contrib = (range_normal @ clean[0,-1,:] - range_normal @ dirty[0,-1,:]).item()\n",
    "            embedding_contribs_list.append({'path': new_path, 'contrib': contrib})\n",
    "            \n",
    "        # sort cur_contribs_list, take the top num_paths entries\n",
    "        if type(num_paths) == list:\n",
    "            cur_num_paths = num_paths[cur_length-1]\n",
    "        elif type(num_paths) == int:\n",
    "            cur_num_paths = num_paths\n",
    "        else:\n",
    "            raise Exception(\"Invalid type for num_paths: \" + str(type(num_paths)))\n",
    "        \n",
    "        cur_contribs_list = list(sorted(cur_contribs_list, key=lambda x: x['contrib'], reverse=(not least_attrib)))[:cur_num_paths]\n",
    "        for contrib in cur_contribs_list:\n",
    "            print_path(list(reversed(contrib['path'])))\n",
    "            print(\":\", contrib['contrib'])\n",
    "        embedding_contribs_list = list(sorted(embedding_contribs_list, key=lambda x: x['contrib'], reverse=(not least_attrib)))[:cur_num_paths]\n",
    "        for contrib in embedding_contribs_list:\n",
    "            print_path(list(reversed(contrib['path'])))\n",
    "            print(\":\", contrib['contrib'])\n",
    "        print()\n",
    "        paths = [x['path'] for x in cur_contribs_list]\n",
    "    return cur_contribs_list, embedding_contribs_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "b85b27a2-4a51-49d3-8ce7-50dcc2ccf77f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def domain_boundary_intersection(x_pos, x_neg, f, range_normal, range_affine, lr=0.01, eps=0.000001):\n",
    "    with torch.enable_grad():\n",
    "        g = lambda t_: (range_normal.detach() @ ( f((1-t_)*x_neg.detach() + t_*x_pos.detach()) - range_affine.detach()))**2\n",
    "        t = torch.Tensor([0.5]).detach().to(\"cuda\")\n",
    "        t.requires_grad_(True)\n",
    "        \n",
    "        optimizer = torch.optim.Adam([t], lr=lr)\n",
    "        \n",
    "        loss = None\n",
    "        prev_loss = None\n",
    "        while loss is None or abs(loss.item()) > eps:\n",
    "            optimizer.zero_grad()\n",
    "            prev_loss = loss\n",
    "            loss = g(t)\n",
    "            if prev_loss is not None and abs(prev_loss.item() - loss.item()) < eps**2: break\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "            with torch.no_grad():\n",
    "                t[:] = torch.clamp(t, min=0, max=1)\n",
    "        #print(\"Final loss:\", loss.item())\n",
    "        #print(\"Final t:\", t)\n",
    "        \n",
    "        #if prev_loss is not None: print(abs(prev_loss.item() - loss.item()))\n",
    "        #if t.item() == 0 or t.item() == 1: t = 0.5\n",
    "        return (1-t)*x_neg + t*x_pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "2549581b-eb8a-421e-80aa-d449a06b497d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_path(path):\n",
    "    for i, node in enumerate(path):\n",
    "        if node['sublayer'] == 'attn':\n",
    "            print(f\"attn{node['layer']}.{node['head']}@{node['token']}\", end=\"\")\n",
    "        elif node['sublayer'] == 'mlp':\n",
    "            print(f\"mlp{node['layer']}@{node['token']}\", end=\"\")\n",
    "        elif node['sublayer'] == 'lm_out':\n",
    "            print(f\"lm_out@{node['token']}\", end=\"\")\n",
    "        elif node['sublayer'] == 'embedding':\n",
    "            print(f\"embedding@{node['token']}\", end=\"\")\n",
    "        if i != len(path)-1: print(\" <= \", end=\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "29356126-ed1f-4fee-abbe-3ff7f1aa79dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def token2embedding(token):\n",
    "    with torch.no_grad():\n",
    "        retval = model.transformer.wte(tokenizer(token, return_tensors=\"pt\")['input_ids'][0,0].to(\"cuda\"))\n",
    "    return retval"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0711b22a-cfe2-4d08-869e-509d22293480",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0085788f-7ab6-42b9-8752-01aa7ed3221e",
   "metadata": {},
   "source": [
    "## Model setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "7878740e-c72d-4bfb-80ef-469c6df9d10c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from transformers import AutoTokenizer, AutoModelForCausalLM, AutoConfig\n",
    "\n",
    "model_str = \"EleutherAI/gpt-neo-1.3b\"\n",
    "tokenizer = AutoTokenizer.from_pretrained(model_str)\n",
    "config = AutoConfig.from_pretrained(model_str, output_hidden_states=True, output_attentions=True, low_cpu_mem_usage=True)\n",
    "model = AutoModelForCausalLM.from_pretrained(model_str, config=config, low_cpu_mem_usage=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "42233a43-1b80-4f3e-85b0-8f0909892f2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = model.to(\"cuda:0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08f28afa-569f-44b1-bc83-8591c81b5c86",
   "metadata": {},
   "source": [
    "## Dataset setup"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1f900a6-f26a-4aef-9f2f-31d2073bbc37",
   "metadata": {},
   "source": [
    "### Get names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "64d4806b-dd4f-46f8-b460-6b540c23cb98",
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv\n",
    "\n",
    "male_names = []\n",
    "female_names = []\n",
    "\n",
    "# Gender by Name. (2020). UCI Machine Learning Repository. https://doi.org/10.24432/C55G7X.\n",
    "# get top 100 names of each gender from dataset that are one token long\n",
    "with open('name_gender_dataset.csv', newline='') as fp:\n",
    "    reader = csv.reader(fp, delimiter=',')\n",
    "    next(reader)\n",
    "    for row in reader:\n",
    "        name_with_space = ' ' + row[0]\n",
    "        gender = row[1]\n",
    "        name_tokens = tokenizer(name_with_space)['input_ids']\n",
    "        if len(name_tokens) != 1: continue\n",
    "        if gender == 'M' and len(male_names) < 100: male_names.append(row[0])\n",
    "        elif gender == 'F' and len(female_names) < 100: female_names.append(row[0])\n",
    "        if len(male_names) >= 100 and len(female_names) >= 100: break"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78f89ae4-6df5-485f-ac7d-d52a81c66846",
   "metadata": {},
   "source": [
    "### Make prompts\n",
    "\n",
    "The \"subject pronoun\" prompts are largely inspired by Mathwin et al. 2022."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "fd523c9b-6993-434d-93b3-21c09dba156a",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_prompt_templates = [\n",
    "    \"<|endoftext|>So, [NAME] really is a great friend, isn't\",\n",
    "    \"<|endoftext|>Man, [NAME] is so funny, isn't\",\n",
    "    \"<|endoftext|>Really, [NAME] always works so hard, doesn't\"\n",
    "]\n",
    "\n",
    "subj_prompts_male = []\n",
    "for template in subj_prompt_templates:\n",
    "    for name in male_names:\n",
    "        subj_prompts_male.append(template.replace(\"[NAME]\", name))\n",
    "subj_prompts_female = []\n",
    "for template in subj_prompt_templates:\n",
    "    for name in female_names:\n",
    "        subj_prompts_female.append(template.replace(\"[NAME]\", name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "55581920-fded-4551-806a-e96abc703c95",
   "metadata": {},
   "outputs": [],
   "source": [
    "obj_prompt_templates = [\n",
    "    \"<|endoftext|>What do I think about [NAME]? Well, to be honest, I love\",\n",
    "    \"<|endoftext|>When it comes to [NAME], I gotta say, I really hate\",\n",
    "    \"<|endoftext|>This is a present for [NAME]. Tomorrow, I'm gonna give it to\"\n",
    "]\n",
    "\n",
    "obj_prompts_male = []\n",
    "for template in obj_prompt_templates:\n",
    "    for name in male_names:\n",
    "        obj_prompts_male.append(template.replace(\"[NAME]\", name))\n",
    "obj_prompts_female = []\n",
    "for template in obj_prompt_templates:\n",
    "    for name in female_names:\n",
    "        obj_prompts_female.append(template.replace(\"[NAME]\", name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "d98dc1de-f862-4f0f-8a3d-0f8319d19945",
   "metadata": {},
   "outputs": [],
   "source": [
    "occu_prompt_templates = [\n",
    "    \"<|endoftext|>My friend [NAME] is an excellent\",\n",
    "    \"<|endoftext|>Recently, [NAME] has been recognized as a great\",\n",
    "    \"<|endoftext|>His cousin [NAME] works hard at being a great\",\n",
    "]\n",
    "\n",
    "occu_prompts_male = []\n",
    "for template in occu_prompt_templates:\n",
    "    for name in male_names:\n",
    "        occu_prompts_male.append(template.replace(\"[NAME]\", name))\n",
    "occu_prompts_female = []\n",
    "for template in occu_prompt_templates:\n",
    "    for name in female_names:\n",
    "        occu_prompts_female.append(template.replace(\"[NAME]\", name))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d028e33-55a4-4a03-9c8b-939b266bbe6f",
   "metadata": {},
   "source": [
    "## Get embeddings\n",
    "\n",
    "We'll be using embeddings to propagate our feature vectors through nonlinearities. However, we'll only use the embeddings from a single prompt of each gender (for both the occupation prediction and pronoun prediction observables)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "ae3227f1-ba44-455a-a53f-345a97f7ac60",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/1 [00:07<?, ?it/s]\n",
      "  0%|          | 0/1 [00:00<?, ?it/s]\n"
     ]
    }
   ],
   "source": [
    "occu_embeddings_male = embeddings_from_prompt_list(model, [occu_prompts_male[0]])\n",
    "occu_embeddings_female = embeddings_from_prompt_list(model, [occu_prompts_female[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "19010f8d-5d7e-453c-9424-fc46d42405e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/1 [00:00<?, ?it/s]\n",
      "  0%|          | 0/1 [00:00<?, ?it/s]\n"
     ]
    }
   ],
   "source": [
    "subj_embeddings_male = embeddings_from_prompt_list(model, [subj_prompts_male[0]])\n",
    "subj_embeddings_female = embeddings_from_prompt_list(model, [subj_prompts_female[0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d53fc74-42b3-47c0-af5d-41b1bd724e20",
   "metadata": {},
   "source": [
    "We'll also get embeddings for object pronouns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "1c989dfe-7c4b-43b0-bb18-38528db32e65",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/1 [00:00<?, ?it/s]\n",
      "  0%|          | 0/1 [00:00<?, ?it/s]\n"
     ]
    }
   ],
   "source": [
    "obj_embeddings_male = embeddings_from_prompt_list(model, [\"<|endoftext|>What do I think of John? Well, I love\"])\n",
    "obj_embeddings_female = embeddings_from_prompt_list(model, [\"<|endoftext|>What do I think of Jane? Well, I love\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29c075e1-0e1c-4106-9152-efc02689b537",
   "metadata": {},
   "source": [
    "## Propagate observable through `ln_f`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b31a695f-96d6-4d3a-bb78-bb49088f45a4",
   "metadata": {},
   "source": [
    "### Gendered occupations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "08aa436f-21b1-48d6-90a7-d5cff2c27807",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([50257])\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_54740/72145989.py:29: UserWarning: The use of `x.T` on tensors of dimension other than 2 to reverse their shape is deprecated and it will throw an error in a future release. Consider `x.mT` to transpose batches of matrices or `x.permute(*torch.arange(x.ndim - 1, -1, -1))` to reverse the dimensions of a tensor. (Triggered internally at /opt/conda/conda-bld/pytorch_1682343997789/work/aten/src/ATen/native/TensorShape.cpp:3571.)\n",
      "  n = n.T.to(\"cuda\", dtype=torch.float32)\n"
     ]
    }
   ],
   "source": [
    "occu_range_normal = make_range_normal([' nurse', ' teacher', ' secretary'], [' programmer', ' doctor', ' engineer'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "0590090c-d470-4d3e-abc8-7932e6af6ef9",
   "metadata": {},
   "outputs": [],
   "source": [
    "zeros = torch.zeros(occu_range_normal.shape).to(\"cuda\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "77c2527d-9ba5-401e-bf79-45ec00a309d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "occu_ln_f_x0 = torch.from_numpy(occu_embeddings_male[0]['ln_f_in'][:, -1, :]).to(\"cuda\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "ab38d587-66c6-4ca9-9864-2d29df3b5711",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final loss: 1.1125399396405555e-05\n",
      "9.999999999999998e-15\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "occu_ln_f_normal, occu_ln_f_affine = get_normal_and_affine(occu_ln_f_x0[0], model.transformer.ln_f, occu_range_normal,\n",
    "                                     zeros, lr=0.02, eps=0.0000001**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b545cd31-7c24-4d61-9bf1-92d5ecb43b8e",
   "metadata": {},
   "source": [
    "### Pronouns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "1ef898ac-5bf7-448b-897a-97764f1f8f07",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([50257])\n"
     ]
    }
   ],
   "source": [
    "subj_range_normal = make_range_normal([' she'], [' he'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "5c9c4988-bb9b-4572-abcf-2c20f9f7364c",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_ln_f_x0 = torch.from_numpy(subj_embeddings_male[0]['ln_f_in'][:, -1, :]).to(\"cuda\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "68f068f8-9488-4dd7-85c2-c6e15bb21604",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final loss: 1.757032066507236e-07\n",
      "9.999999999999998e-15\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "subj_ln_f_normal, subj_ln_f_affine = get_normal_and_affine(subj_ln_f_x0[0], model.transformer.ln_f, subj_range_normal,\n",
    "                                     zeros, lr=0.02, eps=0.0000001**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "81006a8b-8416-4d16-95b5-1617eb6e8dbd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([50257])\n"
     ]
    }
   ],
   "source": [
    "obj_range_normal = make_range_normal([' her'], [' him'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "79522bbf-cf38-4fb4-a6f7-95f0c709d6da",
   "metadata": {},
   "outputs": [],
   "source": [
    "obj_ln_f_x0 = torch.from_numpy(obj_embeddings_male[0]['ln_f_in'][:, -1, :]).to(\"cuda\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "d79e2a71-c920-44d0-a71c-52b8a889687f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final loss: 9.535579010844231e-07\n",
      "9.999999999999998e-15\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "obj_ln_f_normal, obj_ln_f_affine = get_normal_and_affine(obj_ln_f_x0[0], model.transformer.ln_f, obj_range_normal,\n",
    "                                     zeros, lr=0.02, eps=0.0000001**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9f2ff08-704b-4af9-8230-bbe71868a25f",
   "metadata": {},
   "source": [
    "# Embedding-less feature detection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "ab3affc0-4b4f-49b9-8177-3d82c15ace19",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([50257])\n",
      "torch.Size([50257])\n",
      "torch.Size([50257])\n",
      "torch.Size([50257])\n",
      "torch.Size([50257])\n",
      "torch.Size([50257])\n"
     ]
    }
   ],
   "source": [
    "ln_f_weight = model.transformer.ln_f.weight\n",
    "subj_range_normal = make_range_normal([' she'], [' he'])\n",
    "obj_range_normal = make_range_normal([' her'], [' him'])\n",
    "suffix_range_normal = make_range_normal(['woman'], ['man'])\n",
    "occupation_range_normal = make_range_normal([' nurse'], [' engineer'])\n",
    "ctrl_range_normal = make_range_normal([' car'], [' angel'])\n",
    "case_range_normal = make_range_normal([' him', ' them', ' me'], [' he', ' they', ' I'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "57912557-a5be-4c79-92a7-d6accfbe8bc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_layers = len(model.transformer.h)\n",
    "n_heads = model.transformer.h[0].attn.attention.num_heads"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "515d2758-281d-42d3-9892-9e8fcb8b110d",
   "metadata": {},
   "source": [
    "## Feature norms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b3032425-d94c-4802-ba57-f603b01c7094",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_head_features = [ [ \n",
    "    get_normal_for_path(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal,\n",
    "        [\n",
    "            {'layer': i, 'sublayer': 'attn', 'token': 3, 'head': j}\n",
    "        ], estimate_dot=True\n",
    "    ).detach().cpu().numpy()\n",
    "for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "\n",
    "obj_head_features = [ [ \n",
    "    get_normal_for_path(model, cur_obj_embeddings_female, cur_obj_embeddings_male, obj_ln_f_normal,\n",
    "        [\n",
    "            {'layer': i, 'sublayer': 'attn', 'token': 3, 'head': j}\n",
    "        ], estimate_dot=True\n",
    "    ).detach().cpu().numpy()\n",
    "for j in range(n_heads) ] for i in range(n_layers) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "c8d418af-6f3b-40fb-b3f9-fedf9e0c2a21",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_feature_sizes = [ [ torch.linalg.norm(get_attn_normal(model, i, j, subj_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "obj_feature_sizes = [ [ torch.linalg.norm(get_attn_normal(model, i, j, obj_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fefc015e-797b-4ff2-adae-d57c30d37d47",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_attn_normal.detach().cpu().numpy() @ subj_embeddings_female[0]['layers'][17]['ln_1_in'][0,-1,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "7b46a68f-05e2-4f90-8d91-2d0eb444276d",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_ln_norm = np.mean([np.linalg.norm(x['ln_f_in'][0,-1,:]) for x in subj_embeddings_female+subj_embeddings_male])\n",
    "obj_ln_norm = np.mean([np.linalg.norm(x['ln_f_in'][0,-1,:]) for x in obj_embeddings_female+obj_embeddings_male])\n",
    "\n",
    "subj_ln_f_weight = model.transformer.ln_f.weight * np.sqrt(2048) / subj_ln_norm\n",
    "obj_ln_f_weight = model.transformer.ln_f.weight * np.sqrt(2048) / obj_ln_norm\n",
    "\n",
    "subj_feature_sizes_ln = [\n",
    "    [ torch.linalg.norm(\n",
    "        (get_attn_normal(model, i, j, subj_range_normal)) * model.transformer.h[i].ln_1.weight * np.sqrt(2048) * subj_ln_f_weight\n",
    "    ).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers)\n",
    "]\n",
    "\n",
    "obj_feature_sizes_ln = [\n",
    "    [ torch.linalg.norm(\n",
    "        (get_attn_normal(model, i, j, obj_range_normal)) * model.transformer.h[i].ln_1.weight * np.sqrt(2048) * obj_ln_f_weight\n",
    "    ).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers)\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "abc0ffaa-cc28-4168-91a5-4175c48c5617",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.matshow(subj_feature_sizes)\n",
    "plt.xlabel(\"Attention head\")\n",
    "plt.ylabel(\"Layer\")\n",
    "plt.title(\"Subject pronoun feature norms\")\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "7a33081d-0161-416d-b540-efebc7264839",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1471c0278af0>"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "subj_feature_sizes_ln_matshow = ax.matshow(subj_feature_sizes_ln)\n",
    "ax.set_xlabel(\"Attention head\")\n",
    "ax.set_ylabel(\"Layer\")\n",
    "ax.set_title(\"Subject pronoun feature norms w/ LayerNorm\", fontsize=10)\n",
    "fig.colorbar(subj_feature_sizes_ln_matshow, ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "12f58116-8475-435c-9d44-fe52f0db1129",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x148d8ccc6880>"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "obj_feature_sizes_ln_matshow = ax.matshow(obj_feature_sizes_ln)\n",
    "ax.set_xlabel(\"Attention head\")\n",
    "ax.set_ylabel(\"Layer\")\n",
    "ax.set_title(\"Object pronoun feature norms w/ LayerNorm\", fontsize=10)\n",
    "fig.colorbar(obj_feature_sizes_ln_matshow, ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "b4d50e58-31af-4245-a950-24cdc50b2922",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([26.3397, 26.3397, 27.5772,  ..., 26.6933, 24.9255, 27.5772],\n",
       "       device='cuda:0', grad_fn=<MulBackward0>)"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.transformer.h[17].ln_1.weight * np.sqrt(2048)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "717d40ca-8044-49f6-b230-18f7ca17313d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top heads:\n",
      "[[18 11]\n",
      " [17 14]\n",
      " [13 11]\n",
      " [15 13]\n",
      " [18  0]]\n",
      "\n",
      "Top heads' respective values:\n",
      "tensor([72.2168, 70.7219, 45.9200, 39.4049, 17.4824])\n"
     ]
    }
   ],
   "source": [
    "subj_feature_sizes_tensor = torch.from_numpy(np.array(subj_feature_sizes))\n",
    "top_subj_feature_sizes, top_subj_feature_sizes_indices = torch.topk(subj_feature_sizes_tensor.flatten(), 5)\n",
    "print(\"Top heads:\")\n",
    "print(np.array(np.unravel_index(top_subj_feature_sizes_indices.numpy(), subj_feature_sizes_tensor.shape)).T)\n",
    "print()\n",
    "print(\"Top heads' respective values:\")\n",
    "print(top_subj_feature_sizes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "650004ad-40c3-4833-9e20-096993bb992e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top heads:\n",
      "[[18 11]\n",
      " [17 14]\n",
      " [13 11]\n",
      " [15 13]\n",
      " [ 9  1]]\n",
      "\n",
      "Top heads' respective values:\n",
      "tensor([237.3204, 236.2457, 186.3744, 145.4124,  73.2155])\n"
     ]
    }
   ],
   "source": [
    "subj_feature_sizes_tensor = torch.from_numpy(np.array(subj_feature_sizes_ln))\n",
    "top_subj_feature_sizes, top_subj_feature_sizes_indices = torch.topk(subj_feature_sizes_tensor.flatten(), 5)\n",
    "print(\"Top heads:\")\n",
    "print(np.array(np.unravel_index(top_subj_feature_sizes_indices.numpy(), subj_feature_sizes_tensor.shape)).T)\n",
    "print()\n",
    "print(\"Top heads' respective values:\")\n",
    "print(top_subj_feature_sizes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "4e6042e3-ab49-438d-bf83-31d3eb99c787",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x149f20759670>"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(obj_feature_sizes)\n",
    "plt.xlabel(\"Attention head\")\n",
    "plt.ylabel(\"Layer\")\n",
    "plt.title(\"Object pronoun feature norms\")\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "38f6071d-ce7e-4fc2-b493-265ffdc683c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x14c9a07d49d0>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(obj_feature_sizes_ln)\n",
    "plt.xlabel(\"Attention head\")\n",
    "plt.ylabel(\"Layer\")\n",
    "plt.title(\"Object pronoun feature norms\")\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "6b5e85ac-219c-486a-9535-6334b2974941",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top heads:\n",
      "[[18 11]\n",
      " [17 14]\n",
      " [13 11]\n",
      " [15 13]\n",
      " [14 10]]\n",
      "\n",
      "Top heads' respective values:\n",
      "tensor([69.2137, 68.9342, 51.8211, 44.0450, 19.5974])\n"
     ]
    }
   ],
   "source": [
    "obj_feature_sizes_tensor = torch.from_numpy(np.array(obj_feature_sizes))\n",
    "top_obj_feature_sizes, top_obj_feature_sizes_indices = torch.topk(obj_feature_sizes_tensor.flatten(), 5)\n",
    "print(\"Top heads:\")\n",
    "print(np.array(np.unravel_index(top_obj_feature_sizes_indices.numpy(), obj_feature_sizes_tensor.shape)).T)\n",
    "print()\n",
    "print(\"Top heads' respective values:\")\n",
    "print(top_obj_feature_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7f7fc95-9aa5-44e9-b905-46bfe59db214",
   "metadata": {},
   "source": [
    "## Cosine similarities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "311f1273-1bbc-4ba3-8503-300811dc8a5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    subj_obj_cossims = [ [ cossim(get_attn_normal(model, i, j, subj_range_normal), get_attn_normal(model, i, j, obj_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "    subj_ctrl_cossims = [ [ cossim(get_attn_normal(model, i, j, subj_range_normal), get_attn_normal(model, i, j, ctrl_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "    obj_ctrl_cossims = [ [ cossim(get_attn_normal(model, i, j, obj_range_normal), get_attn_normal(model, i, j, ctrl_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "    suffix_subj_cossims = [ [ cossim(get_attn_normal(model, i, j, suffix_range_normal), get_attn_normal(model, i, j, subj_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "    suffix_obj_cossims = [ [ cossim(get_attn_normal(model, i, j, suffix_range_normal), get_attn_normal(model, i, j, obj_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "    occupation_subj_cossims = [ [ cossim(get_attn_normal(model, i, j, occupation_range_normal), get_attn_normal(model, i, j, subj_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "    occupation_obj_cossims = [ [ cossim(get_attn_normal(model, i, j, occupation_range_normal), get_attn_normal(model, i, j, obj_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed9c9591-fb75-4b20-b99d-271eb888c1c7",
   "metadata": {},
   "source": [
    "### Subject-object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "43d31b80-bb99-4d12-a7be-28d6f56f52d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x1531a14a8250>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CsmXLTK5bUFCQUKVKFSEiIkJYtmyZ0L59e6F+/fpCixYthM8//7zYOfHQ3VOCIAgXL14UBg4cKNSvX18IDg4WQkNDTe4sK6LT6YTevXsLvr6+QlBQkNCnT59i1+Lo0aNCq1athNatWwtt27Y1uTvoUZ+xTZs2Qnh4uPDll18WO27ZsmVCq1athObNmwu+vr7CiBEjhNTUVPH9pKQk4ZVXXhFat24tBAUFCYGBgULPnj2Fo0ePCoJQeCtv0bWqUqWKEBQUJPzxxx/CM888I9SpU0f87hw6dEjYtm2b+N3x9fUVJkyYYPG1etiaNWuEbt26CYGBgUJwcLDQunVrYebMmeItuK+//rrQpEkTAYDQpEkTITY2Vvj222+FoKAgAYBQp04dYdCgQUJGRkaxz5GRkSEMGjTI5HPs3r37kdekrBXdPXXlQl3h1tX6Vt2uXKhrl3dPqQTBTof47cDatWsxYsQIXLlyxaSf3N6oVCrMmTOn2AN+RLaWkZEBb29vXL7gA08rz3KbmWlEkxapSE9PN3tTSGXF7qkK5rPPPhP/v6ifumjg1V4cOHBAHDwv6uYqbWCcyNZ4y610bDQqmKKpKARBwDfffIOIiAiT2y7twYYNG7BlyxYAhTccODs7o2fPnuVcKyKSgrfcVjD9+vVDhw4dUKVKFfj7+9v01sfy0qNHD7z11ltYsWIFNBoNPvvsMzRv3ry8q0UOzPi/zdrntEcc0yAih1U0pnHhfB2bjGm0aHnD7sY0mGkQkcMruk3W2ue0RxzTICIiyZhpEJHDKxAKN2uf0x4x0yAiIskcutHYsWMH2rdvjy5duiAiIqLM5r757LPP0KtXL/To0QOhoaEYOHCguFpaWVq2bJnJqmxl4c8//8S//vUvdO/eHW3atEFISIjiaeal0Ov1mDJlCoKDgxEREYHw8HCbrvNuMBgwY8YMODk5mV39ceXKlWjXrh06deqEfv36KZqyXmrs/Px8rFq1Ct26dUP37t0REhKCl19+GTdv3rR57IdNnTrV7KqU5cVoo80eOWyjkZiYiGHDhmHjxo04fPgwRo4cid69e0ueFlqJoUOHIjY2FgcOHMDx48fh6emJPn36iFObl4Vr167hvffeK7N4QOE03t26dcPo0aPx/fff48yZM2jatGmZNNbz58/HV199hcOHD+OHH37AihUrMHjwYJtMzpecnIyIiAhcu3bNZBrzIl988QXmzJmDb7/9FkeOHEF4eDj69+9f6hoj1oidmpqKCRMm4IMPPsD333+Po0ePIiUlBc8995ziuI+K/aDTp08/csndsmaECgVW3owwv9RzZeewjcbChQvRt29fcSrmoUOHIj8/H+vWrbN57Keffhq9evUCUDg99fjx43Hp0iWcOnXK5rGLTJgwATNmzCizeADw7rvvIiwsDD169ABQOH3IokWL0L9/f5vHPn36NEJDQ+Hp6QkAaNu2Lby9vcWFq6wpKysLGzZswIgRI8y+v2DBAkRHR4vT6k+aNAlnz57Fnj17bBrbxcUFL7/8srjAlFarxZgxY3D48GFxok1bxS5iNBoxbtw4zJkzR3E8Kh8O22gcOHAAoaGh4mu1Wo2QkJBSp822lm3btpm8Lpot12Aw2Dw2AHz99ddwdnZGnz59yiReke3btyMiIsJkX8OGDctkXq2BAwfi8OHD4my3e/fuRVpaGurUqWP1WIGBgWjatKnZ9+7evYtTp06ZfPe8vb3RvHlzq3z3Sotdu3Zt/Oc//zHZZ83vXmmxi3z44Yfo0qULAgMDFcezJqNgm80eOeTdU7dv30Z6ejp8fHxM9vv4+IhTXZelY8eOoV69eujUqZPNY2VnZ+ONN97A3r17odfrbR7vwbhJSUkwGo148cUXkZycDHd3d4wZM8Zq3SOlGT58OLKyshAYGIi6devi999/x8CBA/H888/bPPaDisauzH33ymNc69ixY2jfvn2ZNNxXr17F6tWrcezYsWJrvVDl4ZCNRtE6CVqt1mS/Vqs1WTSoLOj1eixatAhLly4ttta1LcyaNQsxMTGoW7dumQ5C3rt3DwAwc+ZMHDhwAO3atUNiYiIiIiJQUFCAf/3rXzaNv3LlSrz77rs4efIkmjRpgjNnzuDgwYNwcirbfwIV6bt369YtrFq1Cjt37iyTeBMmTEB8fLzJuvEVRdE4hLXPaY8csnuq6Ev78F/aer2+zL/QRX9pDxw40Oaxfv75Zxw/fhwxMTE2j/WwopX6+vfvj3bt2gEAwsLCMGDAALz//vs2jS0IAuLi4jBmzBg0adIEABAUFISvv/4a8fHxNo39sIry3cvPz8fgwYPx5ptvlsniRzt37oSTkxP69u1r81hkWw6ZadSoUQPe3t5ITU012Z+amlps9TlbiouLg5OTExYsWFAm8Xbt2oX79++je/fuACDerTV58mRUrVoVq1atemSftFy1atWCVqtFgwYNTPb7+fnhwIEDNolZJC0tDffu3SvWBdO4cWN8/vnneP31120a/0FF3y9z372ymunXaDQiOjoaERERGDNmTJnE3L17N5KTkxEZGQngn8xz8ODBcHV1xa5du8p1NmdmGtI5ZKMBFC7PWrQUKlD41+ipU6fwxhtvlEn8hQsXIjk5GZs2bYJKpcLJkycBACEhITaLOWvWLMyaNUt8nZycjMaNG2PJkiXiP2ZbcXJywuOPP47r16+b7L9x4wYaNmxo09g1a9aEVqstFvv69etwc3OzaeyHVatWDW3btoVOpxPHcjIyMnDx4kUsXLiwTOowbtw41K9fX/wu7N+/H/7+/jb9g2nlypUmrxMSEtCtWzds2bLFrhcYs0cO2T0FFP6Vv2fPHly8eBEAsHHjRmg0GkRHR9s89ooVK7BhwwZMmjQJp06dgk6nw9dff13qmuL24LXXXsOXX36JK1euACh80G/Hjh2YOHGiTeOq1WpER0dj1apVuHv3LgDg1KlT+O677zBo0CCbxjZn5syZWLduHdLS0gAAS5cuRWBgYJl03cTFxeH8+fMYNGgQdDoddDodPvvsM/z11182j12RGQWVTTZ75NBTo+/YsQMLFiyAm5sb1Go1PvroI7Ru3dqmMTMzM1G1alWzD3KtWbMGw4cPt2n8IpMnT8ZPP/2E48ePIygoCC1atBAXRrKlTz/9FIsXL4a7uzvy8/MxevRovPzyyzaPm5OTg7lz52L//v1wd3dHZmYmoqOjMWXKFKhU1v3HbTAY0KtXL9y7dw9nzpxBeHg4fH19TW61XrFiBf773//C1dUV1apVw8qVK4t13Vk79rlz50q81fXgwYOKs00pnxso7JK6cOGCeEyHDh2wZMkSRbHlKpoa/cez9eBh5anRszKN6Bx4ze6mRnfoRoOIHFtRo/HD2fo2aTQiAq/aXaPhsGMaRERFCqBGgZV760ueSKVyc9gxDSIishwzDSJyeIINBq4FOx0IZ6ZBRESSMdMgIofHh/ukY6ZBRESSOXyjodfrMXfu3DKd8ZWxGZuxK5YCQW2TzR45/HMaRfdpl8e91IzN2Ixdvorq9s0vjVHFys9pZGca8USbKxXycyvBMQ0icnhGqGC0cseLEfb59zgbDSJyeBwIl87uGw2j0Yhr167B09PT7BxDGRkZJv8tS4zN2IytjCAIyMzMRL169cQ1W8i27H5M4++//4avr295V4OIbCglJUXWhI9FYxo7zjRDFU+NVeuUnVmAAUGXOKZR2Xh6egIABuwcBOcqLhaX//1OHUXxO/tcll32eq63otg1XLJll71foGzp2b+zq8oum6F3VRT7TnoV2WUb1r6jKLaHs/w7hNQqZX+/uajlz3akNPaF27Vll21VM/XRB5UgL9uAHU99Jv47J9uz+0ajqEvKuYqLrEZDk6t99EGl0HrI/+XrrLG8vg9y0Rpkly0oUBbbCfKvm8ZJ2TVX58lvdJyqKIvt7Cz/l6/SX9zO5dhoaO7Lv25y/l0+TOn09oUD4dYdg5BzPkuWaxAEAQsWLMC2bdtQtWpVZGdnY/To0Rg9erTSqpeqUjQa5bHuBRFRWUpMTMSwYcOg0+kQEBCA9evXo3fv3jh//rzZTOqTTz7BokWL8Ntvv6F+/fpISUlBYGAg6tevj379+tmsnhV+5KjoQm7cuBGHDx/GyJEj0bt3b2RmZpZ31YjIThj/NzW6NTdLb+FduHAh+vbti4CAAADA0KFDkZ+fj3Xr1pk9/vTp02jRogXq168PAPD19UVAQAD27dun7GI8QoVvNCy9kEREFUlGRobJVtKT8QcOHEBoaKj4Wq1WIyQkBPv37zd7/NNPP43z58+Ly0SfOXMGZ8+eRZ06ysZhH6XCNxqWXki9Xl/sh0REVBpbTiPi6+sLb29vcYuPjy8W//bt20hPT4ePj4/Jfh8fHyQlJZmtc1RUFNasWYPu3bujVatWaNeuHcLCwvDKK69Y/wI9oEKPaZR2IU+cOGG2THx8PObNm1cW1SMiO2GU0Z306HMW3lyQkpJicsutVlv8poGcnByz72m1WvG9h+3atQujR4/Gvn37EBISgqSkJHz22Wdwd3e31kcwq0JnGnIu5IwZM5Ceni5uKSkpNq8nEVFJvLy8TDZzjUbRL/qHu670en2JjcAbb7yBZ599FiEhIQAAf39/XLp0CePHj7fyJzBVoRsNORdSq9UW+yEREZWmQFDZZJOqRo0a8Pb2Rmqq6TMrqamp8Pf3N1vm0qVLaNSokcm+xo0b4/PPP7f481uiQjcaci4kEVFl1L17d+h0OvG1IAg4deoUoqKizB5fv359XL9+3WTf9evX4ebmZtN6VuhGA7D8QhIRWcrat9sWbZaIi4vDnj17cPHiRQDAxo0bodFoEB0dDQAYMWIEXnrpJfH4l19+GVu3bsVff/0FAPjzzz+xZcsWDBo0yEpXxbwKPRAOFF7IqKgoXLx4Ec2bNy92IYmI7EFYWBjWrVuHIUOGiA8y7927V3ywLzc3F3l5eeLx06ZNg0qlwjPPPAN3d3dkZGRg7NixmDlzpk3rWeEbjUddSCIipYyCGkYrr7RnlDEX7IABAzBgwACz723evNnktZOTE+Li4hAXFyerfnJV+EYDKP1CSmUwOkEwWv5xH/e5oiiu0YLBsIfl5Cubk+fXnHqyy2Z/Kr8sAAjP35Zdtq6nsmdrGnnLn3TQx1VZ7Ft6D9ll0zreUxRb9X192WWd1EZFset5yb9uVZ3vyy5rcMp79EFkVZWi0SAisiU5YxCPPqd9rjpR4QfCiYio4mCmQUQOzwhY9FyF1HPaIzYaROTwbDONiH125NjnpyIiIptgpkFEDu/BWWmteU57ZJ+fioiIbIKZBhE5vIqyRnhlwEyDiIgkY6ZBRA6PYxrS2eenIiIim2CmQUQOzzbTiNjn3+RsNIjI4RkFlaLJRUs6pz2yz6aQiIhsgpkGETk8ow26p+x1GhGHaTQ8NHq4OFk+VfFf2dUVxV3g96XsskvylS1p6+Gsl132eCtl62lE1roqu2wtl0xFsY/daiy7rLeCtR0AQK2SP03d3d3NFMUuyJbfHRLu85ei2NdyvGWX/fWu/O9afrb87zjJ4zCNBhFRSWyzcp99Zhr2+amIiMgmmGkQkcMrgAoFVp72w9rnqyiYaRARkWTMNIjI4XFMQzr7/FRERGQTzDSIyOEVwPpjEAVWPVvFwUaDiBweu6eks89PRURENsFMg4gcHtfTkM4+PxUREdkEMw0icniCDdYIF/hwHxEROTpmGkTk8DimIZ3DNBpadQFc1PkWl+ta45KiuBvvhssuO6vuXkWx513rI7vsEz10imKfSGsou2wddw9FsQ0FGtll/VzvKIr9sa6L/MKWz9xv4smgM7LLemiUTTGe4ewqu2wt1yzZZQ1qA47KLk1yOEyjQURUEi73Kh0bDSJyeAU2WLnP2uerKOzzUxERkU0w0yAih8fuKemYaRARkWTMNIjI4RmhhtHKf0Nb+3wVhX1+KiIisglmGkTk8AoEFQqsPAZh7fNVFMw0iIhIMmYaROTwePeUdMw0iIhIMmYaROTwBBss9ypwwkIiIvtUABUKrLz+hbXPV1HYZ1NIRFQJ7dixA+3bt0eXLl0QERGBc+fOlXr8rVu3MGrUKERGRqJ9+/YIDAzE1q1bbVpHNhpE5PCMwj+D4dbbLKtDYmIihg0bho0bN+Lw4cMYOXIkevfujczMTLPHGwwGREVFoWvXrkhISIBOp8MTTzyBEydOWOGKlMxhuqeSs6vBCVqLyx1L9VMU977eRXbZe/nuymIXOMsum6ewPzaweqrssmm5CtfTyJf/tfbU5CqK/ULbRNllv7vaQlFsJWq7ZCgqr1bJXwzkXp7877lKXSC7bEWzcOFC9O3bFwEBAQCAoUOHYvr06Vi3bh3Gjx9f7PhVq1bB1dUVw4YNE/e99tprSEtLs2k9mWkQkcMz/m8g3NobAGRkZJhser35Ba8OHDiA0NBQ8bVarUZISAj2799v9vjt27cjIiLCZF/NmjXRsmVLK10V89hoEBHZkK+vL7y9vcUtPj6+2DG3b99Geno6fHx8TPb7+PggKSnJ7Hl//fVXuLm5YezYsejUqRO6deuGFStWQBAULgH5CA7TPUVEVBIjVDBa+W6novOlpKTAy8tL3K/VFu8mz8nJMfueVqsV33vY3bt3ER8fjy+//BLLly/HpUuX0KVLF6Snp+O1116z1scohpkGEZENeXl5mWzmGg1398JxnYe7rvR6vfjew9RqNcLCwvDEE08AAJo1a4aXX34Z77//vpU/gSlmGkTk8Mp7wsIaNWrA29sbqammN5CkpqbC39/fbBlfX180aNDAZJ+fnx9u3LiB+/fvw83NzfJKS8BMg4gcni0HwqXq3r07dDqd+FoQBJw6dQpRUVFmj+/SpQuuX79usu/GjRuoWbOmzRoMgI0GEVGFEBcXhz179uDixYsAgI0bN0Kj0SA6OhoAMGLECLz00kvi8VOmTEFiYqL4XMadO3ewfv16TJw40ab1ZPcUETk8I2wwy62FA+thYWFYt24dhgwZAjc3N6jVauzduxeenp4AgNzcXOTl5YnHt2nTBjt27MC4cePg7OyM/Px8jB49GlOnTrXq53gYGw0iogpiwIABGDBggNn3Nm/eXGxf79690bt3b1tXywQbDSJyeIINbrkVOGEhERE5OmYaROTwuHKfdMw0iIhIMmYaROTw5DxXIeWc9shhGo08owaCUWNxuch6fyiK6+t6R3bZ728pmyrb3+OW7LJKU+vMfFfZZZt53lQU+8KN2rLLXrovvywAeDnJn1o9uNZVRbG16nzZZbMK5P+8AOBilvzrZiiQ/2so775BdlmSx2EaDSKiknBMQzo2GkTk8Gw5y629sc9ONyIisokKn2nMnTsXX375JapWrSru8/b2xldffVV+lSIiu8LuKekqfKMBAEuWLEFkZGR5V4OIyOFVikaDiMiWmGlIxzENIiKSrFI0Gp988gkiIyPRqVMnREdH4/LlyyUeq9frkZGRYbIREZWmKNOw9maPKnyj0bBhQ7Rt2xb79+/H4cOH0bhxY4SEhODqVfMPQsXHx8Pb21vcfH19y7jGRET2q8I3Gi+//DKmTJkCJycnqNVqzJo1C66urvjoo4/MHj9jxgykp6eLW0pKShnXmIgqG2Ya0lW6gXCNRoNGjRqV2EWl1Wqh1WrLuFZEVJkJsP7DeIJVz1ZxVPhMY9KkScX2Xbt2jd1ORETloMI3Gjt37sTOnTvF16tWrcLNmzfx8ssvl2OtiMiesHtKugrfPbVgwQIsWbIE77//PvR6PVxcXPDdd9+hZcuW5V01IiKHU+EbjSFDhmDIkCHlXQ0ismN8uE+6Ct9oWEsTz1tw8XCxuFyawUNRXCXllayHAQBJWTVll800KLuZIKzmn7LLpuRUUxS7fQP5d8z5u6Upin0rz1N22cx8Zdf8foGz7LK/5tZTFNvDWS+7bMMq8tecMQh5ssuSPA7TaBARlYSZhnQVfiCciIgqDmYaROTwmGlIx0aDiByeIKggWPmXvLXPV1Gwe4qIiCRjpkFEDo9rhEvHTIOIiCRjpkFEDo8D4dIx0yAiIsmYaRCRw+PdU9Ix0yAiIsmYaRCRw+OYhnTMNIiISDJmGkTk8DimIZ3DNBrVnHOgdbZ8GuUChT/43+/VkV9Y/izbAIC6bumyy3o4uSqKnZkvv/xIn0OKYm9Ke1x22a+uBSmKnW2wfPr9Io285U8RDgB/pMufCr9DnWRFsZ1VBbLLnr7bQHbZ/Gz5U7I/SLBB95S9NhrsniIiIskcJtMgIiqJAEAQrH9Oe8RMg4iIJGOmQUQOzwgVVJywUBJmGkREJBkzDSJyeLzlVjpmGkREJBkbDSJyeEXTiFh7s9SOHTvQvn17dOnSBRERETh37pykcrt27YJKpcLatWstjmkpdk8RkcMTBBvccmvh+RITEzFs2DDodDoEBARg/fr16N27N86fPw9Pz5Kf9M3OzsbMmTMV1lY6ZhpERBXAwoUL0bdvXwQEBAAAhg4divz8fKxbt67UcrNnz8bYsWPLoooA2GgQEYkD4dbeLHHgwAGEhoaKr9VqNUJCQrB///4Sy/z8889ITEzE6NGjZX92S7F7iojIhjIyMkxea7VaaLVak323b99Geno6fHx8TPb7+PjgxIkTZs9rNBoxbtw4rFixAipV2d2pxUyDiByeLTMNX19feHt7i1t8fHyx+Dk5OQBQrDHRarXiew/78MMP0blzZ7Rp08bKV6N0zDSIiGwoJSUFXl5e4uuHGwYAcHd3BwDo9aaz9ur1evG9B129ehWrVq3CsWPHrFzbR2OjQUQOzyiooLLRyn1eXl4mjYY5NWrUgLe3N1JTU032p6amwt/fv9jx+/btAwD069fPZP8777yDtWvXYv78+ejcubOS6pfIYRqNX9Lrwznf8rUOarlmKYobWvNP2WWVrDMAAJn64n/RSNWpTpKi2Df0pf8jKc2UXwcpil2jivl0XopOtZR97rPp9WSXDa2arCh2jozvdxEPjbJ1KZSsRRFR65LssrlueVC2+krF0b17d+h0OvG1IAg4deoU3njjjWLHjhgxAiNGjDDZp1KpEBcXh+HDh9u0nhzTICKHV/SchrU3S8TFxWHPnj24ePEiAGDjxo3QaDSIjo4GUNhQvPTSS9b+6BZzmEyDiKgiCwsLw7p16zBkyBC4ublBrVZj79694oN9ubm5yMsrvvroO++8g2+//Vb8/7Vr1yIhIcFm9WSjQUQOrzAzsPaEhZaXGTBgAAYMGGD2vc2bN5vdHxcXh7i4OMuDycRGg4gcHme5lY5jGkREJBkzDSJyeAKsv6Y31wgnIiKHx0yDiBwexzSkY6ZBRESSMdMgIuKghmTMNIiISDJmGkRENhjTgJ2OabDRICKHVxHWCK8s2D1FRESSOUymkW1wgZOz5VOFT2/4jaK4n98JffRBJRhY95Si2HvSHpNd9nJWLUWxL9yoLbtso5p3FMXONMifEj45p4ai2AajRnbZNRceVxTbv+Zt2WV1dxoqiu3uZJBd9tJt+d+1ghw9gL2yyxfhLbfSMdMgIiLJHCbTICIqkaCy/sA1Mw0iInJ0zDSIyOHx7inpmGkQEZFkzDSIiDiNiGTMNIiISDJmGkTk8PichnRsNIiIALvtTrI2dk8REZFkzDSIyOGxe0o6ZhpERCQZMw0iIt5yKxkzDSIikoyZBhERVP/brH1O++MwjUamXguNxvJ1Fib9OlhR3H5+52SXTbgboCj2vVw32WWv3fZWFLtm1SzZZXPznRXFdnfOk132eo6Xoti3sqrILhve4E9Fsb2d78su+0emsvVTku9Vl13Ww1Uvu2xBgfyyJI/DNBpERCXimIZkbDSIiNhoSMaBcCIikqzcGw2DwYAZM2bAyckJycnJxd5fuXIl2rVrh06dOqFfv364evVq2VeSiOxb0cp91t7sULk2GsnJyYiIiMC1a9dQUFBQ7P0vvvgCc+bMwbfffosjR44gPDwc/fv3h9FoLIfaEhFRuTYaWVlZ2LBhA0aMGGH2/QULFiA6Ohq1a9cGAEyaNAlnz57Fnj17yrKaRGTnilbus/Zmj8q10QgMDETTpk3Nvnf37l2cOnUKoaGh4j5vb280b94c+/fvL/Gcer0eGRkZJhsREVlHuY9plCQpKQkA4OPjY7Lfx8dHfM+c+Ph4eHt7i5uvr69N60lEdkCw0WaHKmyjkZOTAwDQak0fyNNqteJ75syYMQPp6enilpKSYtN6EhE5kgr7nIa7uzuAwu6mB+n1elSpUvJTt1qttlhDQ0RUKlvc7cS7p8qWv78/ACA1NdVkf2pqqvgeERGVrQrbaFSrVg1t27aFTqcT92VkZODixYuIiooqx5oRkb1RCbbZ7FGFbTQAYObMmVi3bh3S0tIAAEuXLkVgYCD69u1bzjUjIrvCgXDJZI1pLF26FFqtFmPGjFEU3GAwoFevXrh37x4AYPDgwfD19cW2bdsAAM8++yxu3ryJ3r17w9XVFdWqVcPXX38NtbpCt3VERHZLVqPx+uuvY/ny5YqDu7i4ICEhodRjYmJiEBMTozhWzn0XqFWWD5B39LuiKG5CajPZZe9my5/aHABcXeRPEV7dO1tR7AlNDsou+1VasKLYF27Vll12UoD8egPAjhttZZc9nNREUewW9W7ILpt8R/7U5gBQxytTdtmcPGVT4VsFB8Ilk/Une+fOnfHSSy+Zfa+0ZyiIiKhyk9VoREVF4ZtvvjH73qhRoxRViIiozHFMQzJZ3VO7d+/GW2+9hZo1a6JBgwbQaDTie6dPn7ZW3YiIHMqOHTuwYMECuLm5Qa1W46OPPkLr1q3NHrt//34sXboUWVlZuH//Pjw9PbFw4UK0bSu/i1QKWY1GcnIyXn311RLfIyKqVCrAIkyJiYkYNmwYdDodAgICsH79evTu3Rvnz5+Hp6dnseNjYmLw2muv4d///jcAYPbs2ejZsyd+++03cZJXW5DVaAwdOhRz5swx+56rq6uiChEROaKFCxeib9++CAgIAFD4e3b69OlYt24dxo8fX+z49u3bY+TIkeLriRMn4q233sL+/fsxZMgQm9VT1pjGW2+9Jf7/w+tgvPbaa8pqRERU1irAmMaBAwdMZvVWq9UICQkpcVbvLVu2mDx+UPQHu8FgsCywhWQ1GoIg4N1330XDhg3RokULAMCECRPw1ltvQbDXSeSJyH7ZcOW+h5dqeHg+PQC4ffs20tPTLZ7V+0HHjh2Dm5sb+vfvr/x6lEJWo7FgwQJs2bIFkyZNQrVq1QAU9qelpaVh1qxZVq0gEVFl5uvra7JcQ3x8fLFj5M7qXUQQBMyfP1+8QcmWZI1pfPPNN/jxxx/h7u6O3bt3AwBq1aqFDz74AJGRkdasHxGRzdlirqii86WkpMDLy0vcb24W7tJm9S56rzRz585F/fr1MXXqVAU1lkZWo6FSqcx+EJVKhexsZU8SExHZEy8vL5NGw5waNWrA29tb1qzeK1euxIkTJ/Dll18qraoksrqn1Go19u3bV2z/qlWrJLWKREQVSgUYCO/evbvJrN6CIODUqVOlzuq9efNmbN26Fdu3b4eLiwuSkpJKXQ7bGmRlGu+++y769OmDhg0b4vr16+jWrRsuXbqEnJwcfPfdd9auIxGR3YuLi0NUVBQuXryI5s2bY+PGjdBoNIiOjgYAjBgxAvn5+diwYQMAYNeuXYiLi8PatWtx7tw5AMDJkydx/fp1my4fIavR6NChAy5evIgPP/xQrOyoUaMwfvx4mw/CEBHZo7CwMKxbtw5DhgwRnwjfu3ev+GBfbm4u8vL+mYR0xIgRuHXrFrp3725ynpKeobMWWY3Gxo0b8eKLL+LNN9+0dn2IiBzWgAEDMGDAALPvbd682eR10TpDZU1WozF9+nTk5eXh+eefL3W9biKiykAFG9w9Zd3TVRiyGo169eohKysLTzzxBJo2bYoRI0agS5cu1q6bVQlGFQSj5T9G3XVfRXFre2bJLhtSL0VR7JSsarLL/nm9hqLYWz1CH31QCS7fUha7XtUM2WWbaVMffVApsgyWr9lSpCBb2boSl9Pkdw0rfSb3yt+1ZJdt4Xdddtn8guIPypFtybp7av369Rg/fjwOHTqESZMm4fPPP0eHDh3w9ttv4++//7Z2HYmIbMuGT4TbG1mNRsuWLcX/DwoKwgsvvIAWLVpg5syZaNOmDfr27Ytt27ZxShEiqhwqwC23lYWsRqNfv364efMm3nvvPbRu3RqdO3fG1atX8emnn+LatWtYvXo1fvvtN5vOtEhERGVP1phGQkICGjRogAYNGiA6OhrDhw+Hn5+f+H7dunUxZ84ctGvXzmoVJSKymQqwnkZlIavRqF27NlavXl3s/uAHxcfHw83NTXbFiIio4pHVPfXxxx+X2GAUPew3Y8YMHDlyRH7NiIjKSNGEhdbe7JGsTKPoEXW9Xo+bN2+aDHj/+9//xtGjR61TOyIiqlBkNRrXrl3DSy+9hB9++IF3SBFR5ccxDclkNRoTJkxAt27d8NFHH2H48OHYsmUL9Ho9tm/fjowM+Q9WERFRxSar0bh58yZmzpwJoHBd2qI7p2bMmFHivClERBUWMw3JZDUaDy5mnpeXh5ycHLi7u6OgoAC///671SpHRFQWbLlyn72RdfeUh4cHYmNjkZWVhbCwMPTs2RMLFixAnz59ODU6EZEdk9VovP3222jcuDEMBgNmzpyJqlWrYuHChcjKysLKlSutXUciItvi3FOSyeqeCgoKQlBQkPh69+7dGDx4MI4fP47+/fvj8uXLVqsgERFVHLIaDXO2bNkCAHj88cetdUqreqnVcbh6WD71dJDbX4rifnS1m+yyJ/72e/RBpSjIl5VIAgDeCN2jKPaq5E6yy/bwu6go9sWM2rLL7st4TFHsxl63ZZf9vM9GRbGfO/+i7LLDGyp7turtn5+QXdao4C9yJWVNcCBcMvm/VUqgUtlnSkZERFbMNIiIKivePSWd5Exj3rx5tqwHERFVApIzja1bt8Lf3/+R04aU12LnRESycUxDMsmNxoULFxAdHf3I4zimQUSVji1mpbXTRkNy91RERASMRuMjt7CwMFvWl4iIypHkTOPdd9+VdNySJUvk1oWIqHywe0oyyZlGaGiopOPCw8NlV4aIiCo23nJLRMRMQzKrP9xHRET2i5kGETk8PtwnHTMNIiKSjI0GERFJxkaDiIgk45gGERHvnpLMYRqNr1KCoHHXWlxuuypYUdw79zxkl3Vz1yuK/V7bbbLLvnWxv6LYNy/XkF12142qimK/1PYn2WX3Xw9QFHtO069ll92a2UJR7Dyj/I6DL2+0VRTb1c0gu+zvF+vLLmu8nyu77IM4EC4du6eIiEgyh8k0iIhKZaeZgbUx0yAiIsmYaRARcSBcMmYaREQkGTMNInJ4vHtKOmYaREQkGTMNIiKOaUjGRoOIHB67p6Rj9xQREUnGTIOIiN1TkjHTICIiydhoEBEJNtostGPHDrRv3x5dunRBREQEzp07V+rxP/74Izp06ICIiAh06NABhw8ftjyohdg9RURUASQmJmLYsGHQ6XQICAjA+vXr0bt3b5w/fx6enp7Fjv/zzz/Rr18/fPXVV4iMjMQPP/yA/v3745dffoGfn5/N6ukwjUaPer9D6+Fscbk8QaMo7gutjssuO+TkSEWxz973lV3WU6tsWvYbLkbZZYcpmNocAK7kyJ+WPe1UHUWxkxrWll02ObemothP1PtNdtkZNeSXBYBuZwfKLru5zyeyy2ZlGtFRdul/VIS7pxYuXIi+ffsiIKBwev6hQ4di+vTpWLduHcaPH1/s+KVLl6JFixaIjIwEAERERCAgIADLli3De++9p7T6JWL3FBGRDWVkZJhser35P8gOHDiA0NBQ8bVarUZISAj2799v9vj9+/ebHA8AoaGhJR5vLWw0iIhsOKbh6+sLb29vcYuPjy8W/vbt20hPT4ePj4/Jfh8fHyQlJZmtclJSkkXHW4vDdE8REZWHlJQUeHl5ia+12uIriObk5Jh9T6vViu+ZK2PJ8dZS7o2GwWDAnDlzsGjRIvzxxx9o1KiR+N7w4cNx4cIFuLq6ivsCAgKwcuXKcqgpEdktGz6n4eXlZdJomOPu7g4Axbqu9Hq9+J65MpYcby3l2mgkJyfjhRdeQPPmzVFQUGD2mC1btpg0JERE1lbeA+E1atSAt7c3UlNTTfanpqbC39/fbBl/f3+LjreWch3TyMrKwoYNGzBixIjyrAYRUbnr3r07dDqd+FoQBJw6dQpRUVFmj+/Ro4fJ8QCg0+lKPN5ayrXRCAwMRNOmTcuzCkREFeLhvri4OOzZswcXL14EAGzcuBEajQbR0dEAgBEjRuCll14Sj580aRLOnz+PQ4cOAQAOHz6M8+fPY8KECRZ/fEuU+5jGo8THx+P3339Hfn4+goKCMHv2bNSpU/K99Hq93qSfLyMjoyyqSUSkSFhYGNatW4chQ4bAzc0NarUae/fuFR/sy83NRV5enni8n58fdu3ahWnTpsHFxQV6vR67d++26YN9QAVvNJo3bw4/Pz8sX74c+fn5eOWVV9ChQwf8+uuv8PDwMFsmPj4e8+bNK+OaElFlVt5jGkUGDBiAAQMGmH1v8+bNxfZ16dIFP/2k7GFYS1Xo5zRef/11vPjii1Cr1XBxccHixYvx119/mb14RWbMmIH09HRxS0lJKcMaExHZtwqdaTzMy8sLtWrVwuXLl0s8RqvVmr0PmoioRJwaXbIKnWlMmjTJ5LVer8ft27fh6yt/TiUiIpKvQjcaK1asMLmlbP78+fD29sbzzz9fjrUiIrtTAe6eqizKtXvKYDCgV69euHfvHgBg8ODB8PX1xbZt2wAA7733HqZMmQInJyfk5OSgZs2aOHjwIGrXlj+TKBHRw1T/26x9TntUro2Gi4sLEhISSnx/woQJNr/nmIiIpKtUA+FKuKkNcFVbni8qXU/jxVMvyy7bsPpdRbFP3JN/v3bSdWVrO3jUzpZd9vjtRopi/32vqvzCjZVN9vbJFfmrO+TmKfvn6Okqfw2UTRfbK4pdUCC/p3vQyVHy4+boAbwju7yIA+GSVegxDSIiqlgcJtMgIipJRXm4rzJgpkFERJIx0yAi4piGZMw0iIhIMmYaRESA3WYG1sZMg4iIJGOmQUQOj3dPScdGg4iIA+GSsXuKiIgkY6ZBRA6P3VPSMdMgIiLJmGkQEXFMQzJmGkREJJnDZBrNtDfg7mr5NOevffWioriCT67ssn8J1RTFjmr0u/zY1ZTFzs51kV3W3cmgKHZOpvw14r+M+EhR7J0ZwbLL/pJRX1Hs3276yC7bovYNRbG/aPqd7LKRZ5+RXTZfrccl2aX/wTEN6ZhpEBGRZA6TaRARlYhjGpKx0SAiYqMhGbuniIhIMmYaROTwOBAuHTMNIiKSjJkGERHHNCRjpkFERJIx0yAih6cSBKgE66YG1j5fRcFMg4iIJGOmQUTEMQ3JmGkQEZFkzDSIyOHxOQ3p2GgQEbF7SjJ2TxERkWQOk2n8ct8XWo2zxeV8g68pipuW6SG7bPYdN0Wx9Ub5P97MHFdFsWt4Zssum1tg+c/pQW4eetllnz0yVlFs1d/yr9ull5Yriv145kDZZc9eracodssbL8ku6+qSJ7tsQa5KdtkHsXtKOmYaREQkmcNkGkREJeKYhmTMNIiISDJmGkTk8DimIR0zDSIikoyZBhERxzQkY6NBRAT77U6yNnZPERFVMgaDAZMmTUJISAhCQkIwceJEGAyGEo/PycnB4sWL0bVrV3Tr1g3t2rXDq6++iqysLItjM9MgIhKEws3a57SR2NhY/Pbbb0hMTAQA9OnTB9OmTcMHH3xg9vhTp05h4cKFOHnyJBo0aID09HR07twZt27dwvr16y2KzUyDiKgSuX37NlasWIGpU6dCo9FAo9FgypQpWL58Oe7cuWO2jKenJyZOnIgGDRoAALy9vREdHY1t27ahoKDAovjMNIjI4dnyltuMjAyT/VqtFlqtVvZ5Dx06hLy8PISGhor7QkNDkZeXh0OHDuGZZ54pViYoKAhBQUEm+1xdXVFQUACj0QiNRiM5PjMNIiIb8vX1hbe3t7jFx8crOl9SUhKcnJxQs2ZNcV+tWrWg0WiQlJQk+TzHjh3D008/DWdny+Z6Y6ZBRGTDW25TUlLg5eUl7laSZQCFg9ouLi7F9ru4uCAnJ0fSOS5cuIC9e/dCp9NZHJ+ZBhGRDXl5eZlsJTUac+fOhUqlKnXT6XRwd3c3e6eUwWCAu7v7I+uTmZmJF154AevXr0ejRo0s/jwOk2kk5dSEs6p46/wot7KqKIpb1f2+7LK9/c4riv17Zh3ZZfPzpPdxmlPbPVN22Vv35U8nDwC1FEzLvqDtBkWxF6b0lV028uwzimJ39bksu6zGx6go9qm7vrLLXsvwevRBJSgQrDQ1urFwsyZLzxcbG4uYmJhSj6lZsyZSUlKQn5+PW7duiV1UaWlpKCgogL+/f6nlc3Nz8cwzz2Dy5Mno21fed9VhGg0iohJVgCfCPTw84OHx6D+YunbtCmdnZ+h0OvTp0wcAoNPp4OzsjK5du5ZYLj8/H4MGDcKzzz6L6OhoAMC2bdsQFRWFatWqSa4nu6eIiCqRGjVqICYmBosXLxbvflqyZAliYmJQvXp1AIWZh6+vL3bv3g0AMBqNiI6ORpUqVRAeHg6dTgedTof169cjPT3dovjMNIjI4VW2WW4XLVqEadOmISwsDADQsWNHLFq0SHzfaDTi/v37yMsrXBXxm2++waZNmwAAW7ZsMTnXsmXLLIrNRoOIqJLRarVYunRpie/XqVMHt27dEl/369cPgpWeUGejQURUyaYRKU8c0yAiIsmYaRCRw6tsYxrliZkGERFJxkyDiKgCPKdRWTDTICIiyZhpEJHD45iGdGw0iIh4y61k7J4iIiLJmGkQkcNj95R0zDSIiEgyh8k0zu5vDo3W1eJy9xvmKYor1JA/3//Bq80UxQ6qfU122Rtenopi/3yuseyyLneUreWR3zBXdtmhl0tfz+BR/Julyi6bft/y7+eDLmXWkl329BX562EAwPTQvbLLfnC7u+yyBXn5ssua4C23kjHTICIiyRwm0yAiKgnHNKRjpkFERJKVa6Px2WefoVevXujRowdCQ0MxcOBAJCUlmRyzcuVKtGvXDp06dUK/fv1w9erVcqotEdkto2CbzQ6Va6MxdOhQxMbG4sCBAzh+/Dg8PT3Rp08f5OYWDmR+8cUXmDNnDr799lscOXIE4eHh6N+/P4xGK68AT0SOTbDRZofKtdF4+umn0atXr8KKqNUYP348Ll26hFOnTgEAFixYgOjoaNSuXRsAMGnSJJw9exZ79uwptzoTETmycm00tm3bZvLa1bXwlkODwYC7d+/i1KlTCA0NFd/39vZG8+bNsX///hLPqdfrkZGRYbIREZVGhX8Gw622lfeHspEKNRB+7Ngx1KtXD506dRLHNnx8fEyO8fHxKTbu8aD4+Hh4e3uLm6+vsvvPiYjoHxWm0dDr9Vi0aBGWLl0KZ2dn5OTkAChcQP1BWq1WfM+cGTNmID09XdxSUlJsWm8isgNFExZae7NDFeY5jTFjxuC5557DwIEDAQDu7u4AChuTB+n1elSpUqXE82i12mINDRERWUeFyDTi4uLg5OSEBQsWiPv8/f0BAKmpptMypKamiu8REVmD1cczbPCwYEVR7o3GwoULkZycjP/+979QqVQ4efIkTp48iWrVqqFt27bQ6XTisRkZGbh48SKioqLKscZERI6rXBuNFStWYMOGDZg0aRJOnToFnU6Hr7/+Gr/++isAYObMmVi3bh3S0tIAAEuXLkVgYCD69u1bntUmInvD5zQkK7cxjczMTIwbNw5GoxEdO3Y0eW/NmjUAgGeffRY3b95E79694erqimrVquHrr7+GWl3uCRIRkUMqt0bD09MTBQUFjzwuJiYGMTHKpqsGAG3bu9C4Wz5AXrdKyXdqSWEU5N+t7aRW9uT7sb8ayS77dLNfFcU+51FXdll/j1uKYidn15Bd9rerPo8+qBRX/pY/PXnf1mcVxT55q4HssnFh3yqKvf1aO9ll61VLl10230WPy7JL/0MlCFBZ+W4na5+voqgwd08REZUb4/82a5/TDrGfh4iIJGOmQUQOj91T0jHTICIiyZhpEBHZ4hZZ+0w0mGkQEZF0zDSIiGwxwSDHNIiIyNEx0yAih2eLCQbtdcJCNhpEROyekozdU0REJBkzDSJyeCpj4Wbtc9ojZhpERCQZMw0iIo5pSMZMg4iIJHOYTCOvQANjgcbicmqF982tab5Jdtlun8cqii1Uz5Nddtuv8tdHAIDG9eSviXFL76EodqbB8nVTinhWyVUU+162p+yyTupHry9TGndn+T/vdX92UBTbz/Ou7LK6FF/ZZY05yn5eIk4jIhkzDSIikoyNBhE5vKKp0a292YrBYMCkSZMQEhKCkJAQTJw4EQaDQXL5gQMHQqWSt6ooGw0iokomNjYW586dQ2JiIhITE3H+/HlMmzZNUtldu3bh+++/lx2bjQYRUdHdU9bebOD27dtYsWIFpk6dCo1GA41GgylTpmD58uW4c+dOqWWzs7Pxxhtv4LXXXpMdn40GEZGAf9YJt9Zmo96pQ4cOIS8vD6GhoeK+0NBQ5OXl4dChQ6WWnTVrFsaOHQsfHx/Z8dloEBHZUEZGhsmm1+sVnS8pKQlOTk6oWbOmuK9WrVrQaDRISkoqsdzPP/+MxMREjB49WlF8NhpE5PBsORDu6+sLb29vcYuPj1dU15ycHLi4uBTb7+LigpycHLNljEYjxo0bh48++ghqtbJf+w7znAYRUXlISUmBl5eX+FqrNf8c0dy5czFv3rxSz3XixAm4u7ubvVPKYDDA3d3dbLlly5ahU6dOaNOmjQU1N4+NBhGRABtMI1L4Hy8vL5NGoySxsbGIiYkp9ZiaNWsiJSUF+fn5uHXrlthFlZaWhoKCAvj7+5stt2/fPty9exeRkZEAgNTUVABAZGQkPDw8sGvXLokfio0GEVGF4OHhAQ+PR8+G0LVrVzg7O0On06FPnz4AAJ1OB2dnZ3Tt2tVsmd27d5u8Xrt2LUaMGIGEhASL68kxDSKiSnTLbY0aNRATE4PFixejoKAARqMRS5YsQUxMDKpXrw6gMPPw9fUt1lhYAxsNIqJKZtGiRWjRogXCwsIQGhqK5s2bY9GiReL7RqMR9+/fR15e8fnIIiMj8c477xT7f6nYPUVEZAQgb1aN0s9pI1qtFkuXLi3x/Tp16uDWLfOThsrpknoQGw0icni2mCvKlnNPlSeHaTQ+arMRVTwt740bduJlRXE3124ru+ycvp8rij3/dF/ZZV1d5U+zDQB3c9xklw2vkawo9sU1LWSXvReWryi2ykX+n5ffXm6pKLYhp/i9+2Ul7a78KeFVavm/XGXOuUcKOEyjQURUIq7cJxkHwomISDJmGkREzDQkY6ZBRESSMdMgImKmIRkzDSIikoyZBhFRJXu4rzwx0yAiIsmYaRCRw+MT4dKx0SAi4kC4ZOyeIiIiyZhpEBEZBUBl5czAyEyDiIgcHDMNIiKOaUjGTIOIiCSz+0xD+F9rH1D1KLy8vCwur+tl7RqVnWf7lHcNysfr75V3DaisZGRkwBdvi//O5bPFmt72mWnYfaORmZkJAPD19S3nmhCRrWRmZsLb27u8q+EQ7L7RqFevHlJSUuDp6QmVmWW+MjIy4Ovri5SUFFmZiBKMzdiMrYwgCMjMzES9evWUnohjGhLZfaOhVqvRoEGDRx7n5eVV5v+YGJuxGVs5q2QYRgFW707iLbdEROTo7D7TICJ6JMFYuFn7nHbI4TMNrVaLOXPmQKvVMjZjM7adxSbrUwnK71UjIqqUMjIy4O3tjSjfsXBSW7dRyzfqsT9lOdLT08ttHMkWHD7TICIi6TimQUTEu6ckY6ZBRESSMdMgIuLDfZIx0yCzunbtiqioqGL7165di4SEBJN9ycnJmDt3rk3qkZCQgLVr15rs0+v18PX1xYkTJ2wSs8jMmTPRqFEjREZG2jRORYnr0AT803BYbSvvD2UbbDSomJSUFBw7dgwHDx7E9evXTd4rqdGYN2+eTepirtHQaDQICAiAp6enTWIWmT9/PoYPH27TGBUpLpEUbDSomM2bN2P69OkQBAFbtmwp7+oU4+TkhP3796NFixblXRWyF1bPMmwxa27FwEaDivn8888xdepUPP7449i0aZO4f9iwYTh9+jTWrl2LyMhIjBkzBt9//z0mT54MAIiMjERkZCSOHTsGALh+/Tqee+45tG/fHp07d0Z0dDTu3LkjxggODoZKpcKuXbvw1FNPoVmzZpgwYYIYb/HixVi7di1Onz4tnvv+/fvo1asXqlatatIllp+fj7i4OAQGBiI0NBTdunXDmTNnAABZWVmIjIyEq6sr3n33Xbz00ksIDQ3F448/jitXrki6JosWLUJUVBSaNWuG9evXm7xX2ucEgG3btqFjx47o1q0bwsLC8Oqrr0Kv15uc4+OPP4a/vz86d+6MMWPGICcnR1K9iMoaGw0ycf78efj4+KB69ep44YUXoNPpcOnSJQDA+vXrERwcjOHDhyMhIQErV65E9+7dsWTJEgCFXUkJCQl4/PHHAQDPPvssmjZtCp1Oh8OHD0Or1WLIkCEAgOeee04s99tvv2Hnzp04cuQIPv74Yxw8eBAA8Oqrr2L48OEIDg4Wz+3m5oZ9+/YhODjYpN6zZ8/G3r178dNPP+HEiRN44YUX0LNnT6Snp8PDwwMJCQnw8fHB559/juXLl+PEiROoW7eupLGYkydPIiQkBPv378f777+PV155RZxy/1GfEwC2bt2KuLg4HDx4EEeOHMH58+excOFC8f2jR49i7Nix2LJlC3788UdMnz4dGzZssOjnRgoZjbbZ7BAbDTKxceNGvPDCCwCAQYMGwcnJySTbkOr777/HTz/9hNjYWACASqXC6NGjsXfvXly+fNnk2KJfsLVr10arVq1w+vRpi2Ldv38f77//PsaNGwcPDw8AwMiRI2E0GvHf//7X5NinnnpKPCYyMlJSrDp16qB79+4ACm8QyM7Oxh9//CH5c7733nvo378/AMDZ2RnPPPMMvvnmG/H8y5YtQ6dOnRAWFgYAaNKkidmbEIgqAt5ySyZ27tyJGTNmACj8Jd6jRw9s2rQJc+bMseg8Z8+ehVqtxnPPPSfuy8/Ph5+fH65fv44mTZqI++vWrSv+v6enJzIyMiyK9ccffyA3NxfNmjUT92k0GjRq1Ahnz541OVZOrAfLFE0HUVROyufMzs7Giy++iD///BMuLi5ITU016Z66cOFCscypYcOGSElJkfDpySp4y61kbDRIdOzYMdy8eRP9+vUT9924cQMXL16ETqdD+/btLT7ngQMHoNFoSj3mwfdVKpXFS3eWdvzDC2/JiWWu/g+XK+lzZmVloXv37vjXv/6FjRs3Qq1WY+3atSbdYoIgmF0gjKgiYvcUiTZt2oT169eL4wcJCQlITEyEm5ub2EWlVv/zlcnKyoIgCCb78vPzcf/+fTz22GMwGo3ieEiRsWPH4vbt25Lr9OC5c3NzkZeXV+yYZs2awdXV1SRWQUEBkpOTERgYKDmWHI/6nBcuXMDNmzfx/PPPi5/FYDCYHNuqVatiXXZ//fWXTetND+HdU5Kx0SAAhb9kDx06hB49epjs9/T0xFNPPYWtW7fCaDSiVq1auHv3LgAgPDwcWVlZqFWrFgDg7t27+OKLLzB79mx069YNHTt2xPz582H834Dgtm3bcOHCBdSoUUNyvR6M9+qrr2Lfvn3FjnFzc8OUKVPw0UcfITs7GwCwevVqqNVq/Pvf/7b8YljgUZ/T398fbm5u2L9/P4DC6/zVV1+ZnGPChAk4cuQIEhMTAQBXrlzBnj17bFpvIrnYaBDS09PRsWNHXL16Vbx9tsjq1atx8uRJXLt2DR07dsT48eOxd+9edOrUCU899RQ8PT3RsmVLDBkyRLyTatSoUQCAL774Avn5+QgMDES3bt2wfft2bN26FQDw7bffmtyqe+fOHYwYMUK8pXfRokUAgIEDB0Kr1aJz5874888/ERUVhV69eonHzZw5EwDw5ptvolevXggPD0doaCg2bdqEffv2iUuBRkZGIjU1Fe+88w42bdqErVu34p133kFqamqxhrLIO++8I97yO2zYMKSnp4tPaU+ePBnffffdIz9n9erVsWnTJmzZsgXh4eF47rnnUKdOHZO4jz/+OFasWIHBgwejU6dOmDlzJoYOHYrTp0+LA+hkY0bBNpsd4noaROSwitbT6FEtGk5qF6ueO99owIG767ieBhEROS7ePUVEJNigO8lOO3GYaRARkWTMNIiIBBus3MdMg4iIKgKDwYBJkyYhJCQEISEhmDhxYrHnf8xJSEhAz5490a1bNzRv3hxRUVHFlj94FGYaRERGI6Cy8gSDgu0mLIyNjcVvv/0mPtvTp08fTJs2DR988EGJZX788UeMGjUKCQkJaNCgATIzMxEUFITbt2+bTJXzKMw0iIgqkdu3b2PFihWYOnUqNBoNNBoNpkyZguXLl5tMyf+wV199FbGxsWjQoAGAwgd3t2/fDj8/P4vis9EgIqpE04gcOnQIeXl5CA0NFfeFhoYiLy8Phw4dMlsmJSUFJ06cQEREhMn+tm3bWrwCJruniMjhCUYjBCt3Twn/6556eCZlrVYLrVYr+7xJSUlwcnJCzZo1xX21atWCRqNBUlKS2TK//vorgMIpal599VWkp6ejbt26mDNnDtq0aWNRfGYaREQ25OvrC29vb3GLj49XdL6cnBy4uBR/et3FxaXEFR+L5m+bNWsW1q9fj6NHjyIyMhIdOnSQvHplETYaREQ27J5KSUlBenq6uBWtV/OwuXPnQqVSlbrpdDq4u7ubvVPKYDDA3d3d7LmLZlh+5ZVXxAlGx48fj2rVqmHlypUWXSp2TxER2ZCXl5ekuadiY2MRExNT6jE1a9ZESkoK8vPzcevWLbGLKi0tDQUFBfD39zdbztfXFwDEQXCgcD2Zhg0bWpxpsNEgIjIKgKp8H+7z8PAQlyIuTdeuXeHs7AydToc+ffoAAHQ6HZydndG1a1ezZdq1awd3d/diz2TcuHEDnTt3tqie7J4iIqpEatSogZiYGCxevBgFBQUwGo1YsmQJYmJiUL16dQCFmYevry92794NAHB3d8fEiROxYsUK3L9/HwDw1Vdf4fr16xavOcNMg4hIEABY++E+200jsmjRIkybNg1hYWEAgI4dO4pr0ACA0WjE/fv3TVa6nD9/PmbOnInw8HBUrVoVGo0GBw4cQPPmzS2KzfU0iMhhFa2n0d3leTipnK167nwhD98bttndehrMNIjI4QlGAYKVxzTs9e9xjmkQEZFkzDSIiAQjrD+mYbsJC8sTGw0icnjsnpKO3VNERCQZMw0iInZPScZGg4gcXj7yrL7aaz7yHn1QJcRGg4gclouLC3x8fPBj6h6bnN/Hx8fsjLSVGR/uIyKHlpubK2l9bTlcXFzg6upqk3OXFzYaREQkGe+eIiIiydhoEBGRZGw0iIhIMjYaREQkGRsNIiKSjI0GERFJxkaDiIgk+3+z91k/bfRJGwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 400x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(subj_obj_cossims)\n",
    "plt.xlabel(\"Attention head\")\n",
    "plt.ylabel(\"Layer\")\n",
    "plt.title(\"Subject-object cosine sims\")\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb70b7f5-7c1d-4637-8b5a-30818159de7b",
   "metadata": {},
   "source": [
    "Get heads with highest cosine similarities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "16202228-bd4b-48a5-ba33-5849c9d3a83b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top heads:\n",
      "[[17 14]\n",
      " [18 11]\n",
      " [15 13]\n",
      " [13 11]\n",
      " [22  2]]\n",
      "\n",
      "Top heads' respective values:\n",
      "tensor([0.9882, 0.9831, 0.9816, 0.9352, 0.9102])\n"
     ]
    }
   ],
   "source": [
    "subj_obj_cossims_tensor = torch.from_numpy(np.array(subj_obj_cossims))\n",
    "top_subj_obj_cossims, top_subj_obj_cossim_indices = torch.topk(subj_obj_cossims_tensor.flatten(), 5)\n",
    "print(\"Top heads:\")\n",
    "print(np.array(np.unravel_index(top_subj_obj_cossim_indices.numpy(), subj_obj_cossims_tensor.shape)).T)\n",
    "print()\n",
    "print(\"Top heads' respective values:\")\n",
    "print(top_subj_obj_cossims)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5e4c956-00ee-4bb3-a63c-a398b7c404f5",
   "metadata": {},
   "source": [
    "What's the cosine similarities between our range vectors?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "ba4984d3-b654-4146-b6f5-2a61866088de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.5685, device='cuda:0', grad_fn=<DivBackward0>)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cossim(subj_range_normal, obj_range_normal)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "383148f4-9566-46b6-aa24-f3648fb18315",
   "metadata": {},
   "source": [
    "Relatively high, but much lower than those of these attention heads' features. This indicates that these attention heads in particular are performing specific computations relevant to both the subject pronoun case and the object pronoun case. It's not just that the two range normals were similarly-aligned to begin with."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8be1bbc8-8ffc-4b28-a674-91da4beb288f",
   "metadata": {},
   "source": [
    "Now, look at cosine similarities with the control range normal."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7763573e-6529-4168-89d1-2f773aa635d6",
   "metadata": {},
   "source": [
    "## Coupling coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "be583ac4-0584-4f33-8950-c698b2adbf94",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_obj_couplings = [ [ coupling_coeff(get_attn_normal(model, i, j, subj_range_normal), get_attn_normal(model, i, j, obj_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "subj_ctrl_couplings = [ [ coupling_coeff(get_attn_normal(model, i, j, subj_range_normal), get_attn_normal(model, i, j, ctrl_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "obj_ctrl_couplings = [ [ coupling_coeff(get_attn_normal(model, i, j, obj_range_normal), get_attn_normal(model, i, j, ctrl_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]\n",
    "subj_occupation_couplings = [ [ coupling_coeff(get_attn_normal(model, i, j, subj_range_normal), get_attn_normal(model, i, j, occupation_range_normal)).detach().cpu().numpy() for j in range(n_heads) ] for i in range(n_layers) ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "b8df5fb8-b9ef-4bc6-a361-7edd96effc70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x14c7eb91aa30>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.matshow(subj_obj_couplings)\n",
    "plt.xlabel(\"Attention head\")\n",
    "plt.ylabel(\"Layer\")\n",
    "plt.title(\"Subject-object coupling coeffs\")\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "3739d7c0-7a7d-4756-a9ca-4b364e6595c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(0.67086416, dtype=float32),\n",
       " array(0.7730598, dtype=float32),\n",
       " array(0.73551905, dtype=float32))"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subj_obj_couplings[17][14], subj_obj_couplings[15][13], subj_obj_couplings[13][11]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38522c65-5d30-4470-b9f6-1b925c7c8869",
   "metadata": {},
   "source": [
    "# Patching head attribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "0c1ff831-6bc2-4fc4-ab85-7344bd234405",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_layer_head_patching_scores(model, embeddings_pos_np, embeddings_neg_np, range_normal, only_patch_ov=False, no_ln_f=False):\n",
    "    with torch.no_grad():\n",
    "        token_idx = -1\n",
    "        num_layers = len(model.transformer.h)\n",
    "        num_heads = model.transformer.h[0].attn.attention.num_heads\n",
    "        out_mat = torch.zeros(num_layers, num_heads).to(\"cuda\")\n",
    "        embeddings_pos = embeddings_np_to_torch(embeddings_pos_np, free=False)\n",
    "        if embeddings_neg_np is not None:\n",
    "            embeddings_neg = embeddings_np_to_torch(embeddings_neg_np, free=False)\n",
    "        for layer in range(num_layers):\n",
    "            for head in range(num_heads):    \n",
    "                if embeddings_neg_np is not None:\n",
    "                    pos_out, neg_out = path_patching(model, embeddings_pos, embeddings_neg, [(layer, 'attn', head)], only_patch_ov=only_patch_ov, no_ln_f=no_ln_f)\n",
    "                else:\n",
    "                    pos_out, neg_out = path_patching(model, embeddings_pos, None, [(layer, 'attn', head)], only_patch_ov=only_patch_ov, no_ln_f=no_ln_f)\n",
    "                out_mat[layer, head] = (range_normal @ pos_out[0, token_idx]) - (range_normal @ neg_out[0, token_idx]) \n",
    "        free_embeddings(embeddings_pos)\n",
    "        if embeddings_neg_np is not None:\n",
    "            free_embeddings(embeddings_neg)\n",
    "    return out_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "9dd7256a-6d57-4632-9227-677196e32f54",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tqdm\n",
    "def get_mean_layer_head_patchings_for_embeddings(model, embeddings_pos_list, embeddings_neg_list, range_normal, only_patch_ov=False, no_ln_f=False):\n",
    "    out_mat = 0\n",
    "    if embeddings_neg_list is not None:\n",
    "        for embeddings_pos_np, embeddings_neg_np in tqdm.tqdm(zip(embeddings_pos_list, embeddings_neg_list)):\n",
    "            out_mat = out_mat + get_layer_head_patching_scores(model, embeddings_pos_np, embeddings_neg_np, range_normal, only_patch_ov=only_patch_ov, no_ln_f=no_ln_f)\n",
    "    else:\n",
    "        for embeddings_pos_np in tqdm.tqdm(embeddings_pos_list):\n",
    "            out_mat = out_mat + get_layer_head_patching_scores(model, embeddings_pos_np, None, range_normal, only_patch_ov=only_patch_ov, no_ln_f=no_ln_f)\n",
    "    out_mat /= len(embeddings_pos_list)\n",
    "    return out_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "b86b4e53-537a-45b5-8837-c7932fca9273",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tqdm\n",
    "def get_mean_layer_head_patchings_for_prompts(model, prompts_pos, prompts_neg, range_normal, only_patch_ov=False, no_ln_f=False, use_tqdm=True, pre_tokenized=False):\n",
    "    out_mat = 0\n",
    "    with torch.no_grad():\n",
    "        if use_tqdm: tqdm_lambda = lambda x: tqdm.tqdm(x)\n",
    "        else: tqdm_lambda = lambda x: x\n",
    "        for i, tuple in tqdm_lambda(enumerate(zip(prompts_pos, prompts_neg))):\n",
    "            prompt_pos, prompt_neg = tuple\n",
    "            embedding_pos, hooks = attach_hooks(model)\n",
    "            if pre_tokenized:\n",
    "                tokens = {\"input_ids\": prompt_pos['input_ids'].to(\"cuda:0\"), 'attention_mask': prompt_pos['attention_mask'].to(\"cuda:0\")}\n",
    "            else:\n",
    "                tokens = tokenizer(prompt_pos, return_tensors=\"pt\").to(\"cuda:0\")\n",
    "            model(**tokens)\n",
    "            for hook in hooks: hook.remove()\n",
    "            embedding_pos = embeddings_torch_to_np(embedding_pos)\n",
    "\n",
    "            embedding_neg, hooks = attach_hooks(model)\n",
    "            if pre_tokenized:\n",
    "                tokens = {\"input_ids\": prompt_neg['input_ids'].to(\"cuda:0\"), 'attention_mask': prompt_neg['attention_mask'].to(\"cuda:0\")}\n",
    "            else:\n",
    "                tokens = tokenizer(prompt_neg, return_tensors=\"pt\").to(\"cuda:0\")\n",
    "            model(**tokens)\n",
    "            for hook in hooks: hook.remove()\n",
    "            embedding_neg = embeddings_torch_to_np(embedding_neg)\n",
    "            \n",
    "            out_mat = out_mat + get_layer_head_patching_scores(model, embedding_pos, embedding_neg, range_normal, only_patch_ov=only_patch_ov, no_ln_f=no_ln_f)\n",
    "            \n",
    "            free_embeddings(embedding_pos)\n",
    "            free_embeddings(embedding_neg)\n",
    "            do_free()\n",
    "        out_mat /= len(prompts_pos)\n",
    "    return out_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "3f645ad3-40db-4dd5-9c10-b4173f1d5ed8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_top_for_matrix(matrix, largest=True, k=5):\n",
    "    obj_feature_sizes_tensor = torch.from_numpy(np.array(matrix))\n",
    "    top_obj_feature_sizes, top_obj_feature_sizes_indices = torch.topk(obj_feature_sizes_tensor.flatten(), k, largest=largest)\n",
    "    print(\"Top heads:\")\n",
    "    print(np.array(np.unravel_index(top_obj_feature_sizes_indices.numpy(), obj_feature_sizes_tensor.shape)).T)\n",
    "    print()\n",
    "    print(\"Top heads' respective values:\")\n",
    "    print(top_obj_feature_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "faf3189e-c1a9-4c86-b7f3-aadfa95de344",
   "metadata": {},
   "source": [
    "## Subject pronouns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "a2f56715-f155-4d24-98fe-b522ddc89fc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_lm_normal = make_lm_head_normal([' she'], [' he']).to(\"cuda\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "f3c6ed7c-91d2-4e88-bdd1-fb36d70b98f4",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "300it [14:51,  2.97s/it]\n"
     ]
    }
   ],
   "source": [
    "subj_head_patchings = get_mean_layer_head_patchings_for_prompts(model, subj_prompts_female, subj_prompts_male, subj_lm_normal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "3ab49b6a-a847-4818-b3ff-45b8cb507e69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title(\"Subject pronoun head patching\")\n",
    "ax.set_xlabel(\"Attention head\")\n",
    "ax.set_ylabel(\"Layer\")\n",
    "matshow = ax.matshow(subj_head_patchings.detach().cpu().numpy())\n",
    "fig.colorbar(matshow, ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "9ebb6dee-11e4-4e0a-b5bb-3a5c2fef849f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top heads:\n",
      "[[17 14]\n",
      " [13 11]\n",
      " [15 13]\n",
      " [13  3]\n",
      " [22  2]]\n",
      "\n",
      "Top heads' respective values:\n",
      "tensor([5.0037, 3.0501, 1.1985, 0.5844, 0.4263])\n"
     ]
    }
   ],
   "source": [
    "get_top_for_matrix(subj_head_patchings.detach().cpu())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "d34105ee-1e97-4d49-8484-74ccbc6fff6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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K7dq15eGHH7bqXXD//fcr3e5iY2Nl9OjR5Y5VWloqU6dOlebNm0t0dLQ0btxYxo8fL8XFxco2TzzxhERGRirdCVesWCHbt2+X2NhYASD169eXgQMHKtsXFhbKyJEjJTIyUlq0aCExMTEyb968cmVX5bv697//bVWOpXdLz549pXbt2lKtWjWJjY2Vn376qcJz9e677yrfdWRkpEycOFGMRqPExsZKzZo1pWbNmhIbG6t0wystLZXMzExp1qyZxMTESGxsrDz++ONW51VEZPbs2dK0aVNp0aKFJCYmyttvv63U8f7771e2++GHHyQxMVHCw8Olffv28sQTT0h6erryGd9///1Kv2eRq71lJk+eLOnp6dKxY0e5+eabJTExsdx19u2330r37t0lIiJC7rzzTnn00UelX79+yvmxbH/y5Enp0aOHNG/eXGJiYqx6hV37vbVt21Y6deqkdMG05zo4evRoufN78ODBctfjV199JdnZ2VbfT1pamlLetm3bJD4+XurXry8JCQny6quvSmpqqjRu3NjmOfMHOpHrEprkkMWLF2PkyJE4fPgwGjdu7OnqYNu2bejRowe2bt1q9ZAIaY9Op0NmZiamTp3q6ap4hfvuuw+HDx/26C88b6CZtIwnXPt0n+WnruWGGxG51tGjR/H0009brZP/5tzbtWvnoVp5DwZ3FUaNGoWTJ09CRPDZZ58hMTGxXFc8InKNS5cu4a233rK69/Tqq6/i2LFj5YK+P2JwV6F///7o3Lkz2rRpg4CAACxbtszTVQJw9SbdtWPRpKene7hG5AqWsWUA4J133rHqZeQPIiIiMGrUKIwcORKxsbGIiorCunXrsGnTJuW8+DPm3ImINIgtdyIiDWJwJyLSIAZ3IiIN8uvg/umnn6JDhw644447kJiY6LbHlleuXInevXujZ8+e6NixIwYOHIjff//dLWVbzJs3DzqdrsqDRjnLkSNHMHjwYCQnJ6Nt27aIj493+YQKRqMREyZMQFxcHBITE9GpUyeXTr1YWlqKjIwMBAYGVjiBzPz589G+fXt069YN/fv3d8ron7bKLSsrw8KFC9GjRw8kJycjPj4ejzzyCE6dOuWUcm2Vfb1nnnmGk2e7iyefoPKknTt3Sq1ateTAgQMiIrJkyRK59dZbrZ66dJVq1arJxo0bRUTEZDJJamqq3HbbbeWeSHWV48ePS1RUlF3jwzvD6dOnpUmTJrJp0yYRuTr29kMPPVThk6nONHnyZGnSpIny3e7Zs0eCgoLKjSfvDIcPH5bOnTvL8OHDK3xi+eOPP5b69evLyZMnRUTkpZdekri4OGWyCVeUm5+fL8HBwco47CUlJdKrVy+54447VJVZlbKv9f3330udOnVsbkPO47fB/YEHHpCHHnpIeW0ymaR+/fouDzQiV2fyudZ3330nAGT79u0uL1vk6me3PArvzuD+7LPPyuDBg63WHTlyxOX/0O+55x6r71pEpG7duvLaa685vawff/xRfvvtN2X4h+s/W/v27eW5555TXp87d04CAwNl7dq1Liv35MmT8sQTT1htn52dLQDk+PHjqsq9UdkWJpNJunbtKvPmzWNwdxO/Tcts3rwZHTt2VF7r9XrEx8ermiiiqrKzs61eWwY1Ky0tdXnZa9euRbVq1dC3b1+Xl3W9jz/+GImJiVbroqKiXD5cw8CBA/H1118rg65t3LgRp0+fdnjoW1tat26N5s2bV/je2bNnsWfPHqvrLiwsDC1atFB93dkqt169evjHP/5htc6Z15ytsi3efPNN3HHHHZxIw400MZ67vc6cOYOioiJERERYrY+IiMB3333n9vrs2LEDDRo0QLdu3VxazsWLF/HCCy9g48aNVhNGuMPFixfx+++/w2w2Y+jQocjLy0ONGjUwevRoDBo0yKVljxgxAhcuXEDr1q1xyy234Ndff8XAgQPx4IMPurTc61nuq1R03bn7nsuOHTvQoUMHt4yDdPz4cSxatAg7duywe7RLcpxfBnfLcKUGg8FqvcFgUN5zF6PRiNmzZ2Pu3LnKmO2uMmXKFIwZMwa33HKL229oWSZQmDx5MjZv3oz27dtj165dSExMhMlkwuDBg11W9vz58zFr1izs3r0bzZo1w759+7B161YEBrr38veW6+6PP/7AwoULsWbNGreUl5aWhqysLNSoUcMt5dFVfpmWsVxk17dejUaj2y9AS8t14MCBLi3n+++/x86dOzFmzBiXllMZyyQR99xzjzI1WkJCAgYMGIDXX3/dZeWKCNLT0zF69Gg0a9YMABAbG4u1a9ciKyvLZeVWxBuuu7KyMgwZMgQvv/xyuXlxXWHNmjUIDAxEv379XF4WWfPLlnt4eDjCwsLKTdZbWFhoNVGEq6WnpyMwMBAzZsxweVnr1q3D5cuXlUk6LHO4jh8/HjfddBMWLlx4w7ypGnXr1oXBYEDDhg2t1jdq1KjCCSOc5fTp0zh37ly59EOTJk3wr3/9C88//7zLyr6e5dqq6Lq76667XF6+2WxGamoqEhMTMXr0aJeXBwDr169HXl6eMuy05RfckCFDEBwcjHXr1nGwPRfxy+AOXJ3hxzLzEXC1hbdnzx688MILbil/5syZyMvLwwcffACdTofdu3cDAOLj411S3pQpUzBlyhTldV5eHpo0aYI5c+a4Zbz3wMBAdOnSpdy0bidPnkRUVJTLyq1Tpw4MBkO5ck+cOIHq1au7rNyK1K5dG+3atUNOTo5yn6G4uBi5ubmYOXOmy8sfO3Ysbr31VuU62LRpE5o2berSBs38+fOtXlvmGVixYoVXzHugZX6ZlgGutpo3bNigTEG3fPlyBAQEIDU11eVlv/POO1i2bBnGjRuHPXv2ICcnB2vXrtX85AKTJk3CqlWrcPjwYQBXH2j69NNP8dRTT7msTL1ej9TUVCxcuBBnz54FAOzZswdffPEFHnroIZeVW5nJkydjyZIlOH36NABg7ty5aN26tcvTFunp6fjll1/w0EMPIScnBzk5OVi5ciWOHj3q0nLJgzzdF9OTPvnkE4mPj5fu3bvLnXfeKfv373d5mcXFxaLX6wVAueW9995zefkiIuPGjZNOnTopU5ld3/fclZYtWybt2rWTbt26SadOnaymcHOVixcvyrPPPquU27ZtW3n11VfFbDY7vSyj0SiJiYnKtHKdOnUq91zD22+/Le3atZMuXbpIv379JD8/36Xl7t+/v8LrDU56zqEqn1lEZPDgwVbbjBs3TnXZVDkO+UtEpEF+m5YhItIyBnciIg1icCci0iAGdyIiDWJwJyLSIAZ3IiINYnAnItIgvw/uRqMRU6dOdfsQuJ4s2x8/M8v2r+uMAL9/iKm4uBhhYWEoKipCaGioX5Ttj5+ZZfvXdUZsuRMRaRKDOxGRBml+yF+z2YyCggKEhIRAp9OVe7+4uNjqv+7kqbL98TOzbG1dZyKC8+fPo0GDBspEMK5QUlLitLmNg4KClLlr3UHzOfdjx44hMjLS09UgIhfIz88vNwGMs5SUlKBJo1ooPGVyyvEiIiJw+PBhtwV4zbfcQ0JCAABJkY8hUB/k4doQkTOUmUuxLX+B8u/bFUpLS1F4yoTDuxshNETdr4Pi82Y0iT+C0tJSBvdrffrpp5gxYwaqV68OvV6Pt956C61atarSvpZUTKA+CIF6ww22JiJfUlGq1dlCQ/Sqg7sneH1w37VrF4YPH46cnBxER0dj6dKl6NOnD3755ReX/tUmIgIAk5hhUpm8NonZOZWxg9f/OZo5cyb69euH6OhoAMDDDz+MsrIyLFmyxMM1IyJ/YIY4ZXE3rw/umzdvRseOHZXXer0e8fHx2LRpkwdrRUTk3bw6LXPmzBkUFRUhIiLCan1ERAS+++47D9WKiPyJGWaoTaqoP4L9vDq4X7p0CQBgMFjfCDUYDMp71zMajVZjWXiiXzERaYdJBCaVPcbV7u8Ir07L1KhRAwDKDTxkNBqV966XlZWFsLAwZWEfdyLyR14d3MPDwxEWFobCwkKr9YWFhWjatGmF+2RkZKCoqEhZ8vPz3VFVItIoX72h6tVpGQBITk5GTk6O8lpEsGfPHrzwwgsVbm8wGMqlcYiIHGWGwKQyOLO3TAXS09OxYcMG5ObmAgCWL1+OgIAApKamerhmRETey+tb7gkJCViyZAlSUlKUJ1Q3btzIB5iIyC2ckVZhWqYSAwYMwIABAzxdDSLyQ77aW8YngjsRkaeY/7uoPYa7Mbh7M7WDIml7NGfXcMNAVJXi90VOxOBORGSDyQm9ZdTu7wgGdyIiG0wCJ4wK6Zy62MPru0ISEZH92HInIrKBN1SJiDTIDB1MUHej3axyf0cwLUNEpEFsuRMR2WCWq4vaY7gbgzsRkQ0mJ6Rl1O7vCKZliIg0iC13IiIbfLXlzuBORGSDWXQwi8reMir3dwSDOxGRDb7acmfOnYhIg9hyJyKywQQ9TCrbwSYn1cUeDO5ERDaIE3Luwpw7EdSNqa52THRPjqmuV9E6NHti9BLyZgzuREQ2+OoNVQZ3IiIbTKKHSVTm3DmeOxEROQNb7kRENpihg1llO9jMafaIiLyLr+bcmZYhItIgttyJiGxwzg1VpmWIiLzK1Zy7702zx+BORGSD2QnDD3jihipz7kREGsSWOxGRDcy5ExFpkBl6n+znzrQMEZEGseVORGSDSXQwqRyyV+3+jmBw92aeHH5WLU8O26uGvw437EmOnHM135OdnDNZB9MyRETkBGy5ExHZYBY9zCp7y5g98KuMLXciIhssaRm1i6PmzZsHnU6Hbdu22bUfgzsRkZcqKCjAK6+84tC+DO5ERDaY8b8eM44ujs5wm5aWhoyMDIf2Zc6diMgG5zzEZP/+a9euRbVq1dC3b1+HymRwJyKywTnDD9i3/8WLF/HCCy9g48aNMBqNDpXJ4E5E5CbFxcVWrw0GAwwGQ7ntpkyZgjFjxuCWW25BXl6eQ2Ux505EZINlPHe1CwBERkYiLCxMWbKyssqV9/3332Pnzp0YM2aMqnqz5U5EZIMz0zL5+fkIDQ1V1lfUal+3bh0uX76M5ORkAEBJSQkAYPz48bjpppuwcOFCNG/e/IZlMrgTEblJaGioVXCvyJQpUzBlyhTldV5eHpo0aYI5c+YgKSmpymUxuBMR2eCcsWXcnwFncCcissEsOphVjuro6P7jx4/Ht99+q/z/7bffjhUrVlRpXwZ3IiIvNWfOHIf3ZXAnIrLBORNkMy3jfdSOG+2vY3T76uf2ZL19dRx7jXPOqJDuD+7s505EpEFsuRMR2WCCDiaonGZP5f6OYHAnIrLBV9MyDO5ERDaYoL7lbXJOVezCnDsRkQax5U5EZAPTMkREGuSJ8dydgWkZIiINYsudiMgGuWY8djXHcDcGdyIiG5iWISIir8GWOxGRDZ4c8lcNBnciIht8dbIOpmWIiDSILfcbUTsMq17F30+zWV3ZvsqTw8/66rC7vjrEMuBY3d34eZmWISLSIDP0qifb4GQdFZg6dSpWrVqFm266SVkXFhaG1atXe65SROQ3TKKDSWXLW+3+jvD64A5cnUcwKSnJ09UgIvIZPhHciYg8hTl3IiINEieMCil8QrVi7777LpKSktCtWzekpqbi0KFDnq4SEZFX8/rgHhUVhXbt2mHTpk34+uuv0aRJE8THx+P48eMVbm80GlFcXGy1EBE5yjKHqtrF3bw+uD/yyCOYMGECAgMDodfrMWXKFAQHB+Ott96qcPusrCyEhYUpS2RkpJtrTERaYpb/5d0dX9xfb68P7tcLCAhA48aNK03NZGRkoKioSFny8/PdXEMiIs/z+uA+bty4cusKCgoqbZEbDAaEhoZaLUREjrJMs6d2cTevD+5r1qzBmjVrlNcLFy7EqVOn8Mgjj3iwVkTkL8z/naxD7eJuXt8VcsaMGZgzZw5ef/11GI1GBAUF4YsvvkBMTIynq0ZEfoBPqLpISkoKUlJSPF0NIiKf4vXBnYjIk5yRM/dEzp3B3dU8OWyvrw4h68vD16rhr+fckevUjcNCm+GE4QfYz52IiJyBLXciIhvECb1dhL1liIi8i6+OCsm0DBGRBrHlTkRkA3vLEBFpENMyRETkNdhyJyKywRljw3BsGSIiL+OraRkGdyIiG3w1uDPnTkSkQWy5ExHZ4KstdwZ3IiIbfDW4My1DRKRBbLkTEdkgUN+V0RMDKjO434jacaP9dYxuFcQQ5PC+OmOpusJ9dQx8T3Lj2OqewLQMERF5DbbciYhs8NWWO4M7EZENvhrcmZYhItIgttyJiGzw1ZY7gzsRkQ0iOojK4Kx2f0cwuBMR2eCrQ/4y505EpEFsuRMR2cCcOxGRBvlqzp1pGSIiDWLLnYjIBnenZVavXo0FCxbAaDTi8uXLuHz5MiZNmoSHHnrIrjIZ3ImIbHB3Wubtt99GSkoKhg8fDgBYu3Yt7r//fsTExKBNmzZVPg7TMkREXmTGjBlISUlRXiclJcFsNuPgwYN2HYctd1dTMwys3oN/ez04fK2qYXs9OUSz2rLV7G82e67sMpO6sgMcuM7deH2KE9Iy9rTc4+Pjlf+/cuUKZs+ejZYtW+Kuu+6yq0y23ImIbBBc/VuiavnvsYqLi60Wo9FYabljx45F3bp1sXnzZmzcuBG1atWyq94M7kREbhIZGYmwsDBlycrKqnTbf/zjHzhz5gx69uyJbt264cSJE3aVxeBORGSDZfgBtQsA5Ofno6ioSFkyMjJslh0QEICpU6dCRPDaa6/ZVW/m3ImIbHBmb5nQ0FCEhoba3La0tBRBQf+balKv1+O2227Dzz//bFeZbLkTEdlg6eeudqmq9u3bl1t34sQJNGjQwK56M7gTEXmRn3/+GevXr1dev//++/j111+Rmppq13GYliEissHS40XtMarqjTfewIwZM/D3v/8dJpMJOp0Oa9asQffu3e0qk8GdiMgGdz+hmpaWhrS0NFXlAUzLEBFpElvuREQ2+OqQvwzuREQ2mEUHnQ9O1sG0DBGRBrHlTkRkg7t7yzgLgzsRkQ1Xg7vanLuTKmMHpmWIiDTIf1ruOp1DY1abbrJvmM3rBRRddHhfcWSc62vorpSp2NlHx0VX20TyZNkeHENfVdkqr1OHzrna69MO7C1DRKRBgv+Nx67mGO7G4E5EZIOvttyZcyci0iC23ImIbPHRvAyDOxGRLU5Iy4BpGSIicga23ImIbOATqkREGsTeMkRE5DXYciciskV06m+I8glVIiLv4qs5d6ZliIg0iC13IiJb+BATEZH2+GpvGf8J7g4mzgLOnldXroqhSVUN2auSBAao2l9XUur4zmqHkFXDk8Pu+itHzrm7vycfvCyYcyci0iCPB/fS0lJkZGQgMDAQeXl55d6fP38+2rdvj27duqF///44fvy4+ytJRH7LkpZRu7ibR4N7Xl4eEhMTUVBQAJPJVO79Tz75BJmZmfj3v/+N7du3o1OnTrjnnntgNps9UFsi8kvipMXNPBrcL1y4gGXLlmHkyJEVvj9jxgykpqaiXr16AIBx48Zh//792LBhgzurSUTkczwa3Fu3bo3mzZtX+N7Zs2exZ88edOzYUVkXFhaGFi1aYNOmTe6qIhH5PZ2TFvfy2t4yv//+OwAgIiLCan1ERITyHhGRy7Gfu3NdunQJAGAwGKzWGwwG5b2KGI1GGI1G5XVxcbFrKkhE5MU83lumMjVq1AAAq0BteW15ryJZWVkICwtTlsjISJfWk4g0jjdUnatp06YAgMLCQqv1hYWFynsVycjIQFFRkbLk5+e7tJ5EpHGWUSHVLm7mtcG9du3aaNeuHXJycpR1xcXFyM3NRa9evSrdz2AwIDQ01GohIvI3XhvcAWDy5MlYsmQJTp8+DQCYO3cuWrdujX79+nm4ZkTkLywjl6hd3M2hG6pz586FwWDA6NGjVRVeWlqK3r1749y5cwCAIUOGIDIyEtnZ2QCABx54AKdOnUKfPn0QHByM2rVrY+3atdDrvfpvEhFpiT/1lnn++efx9ttvqy48KCgI27Zts7nNmDFjMGbMGNVlERE5xEdnYnKoCdy9e3cMGzaswvfYB52IyPMcCu69evXCZ599VuF7jz76qKoKERF5E504Z3E3h9Iy69evx7Rp01CnTh00bNgQAQH/G/t77969zqqbJqgZF11XesWJNbGzbJVjyUtI5c8i3JCKz60rKz8AnT2kmuPP9akawx4A1Iyhr/aOnYp5Bzwywag771D6U849Ly8PTz/9dKXvERGRZzkU3B9++GFkZmZW+F5wcLCqChEReRUfvaHqUHCfNm2a8v8mk8kqLTNp0iT1tSIi8hY+mpZx6IaqiGDWrFmIiorC7bffDgBIS0vDtGnTIJyDkojI4xwK7jNmzMCKFSswbtw41K5dGwDw4osv4vTp05gyZYpTK0hE5FE+OnCYQ2mZzz77DP/5z39Qo0YNrF+/HgBQt25dvPHGG0hKSnJm/YiIPMuf0jI6na7CYXd1Oh0uXryoulJERKSOQ8Fdr9fj888/L7d+4cKFNsdaJyLyOT465K9DaZlZs2ahb9++iIqKwokTJ9CjRw/89ttvuHTpEr744gtn15GIyGOc8YSpJ55Qdajl3rlzZ+Tm5uL+++/HnXfeiZtvvhmPPvoocnNzER8f7+w6EhF5jj/dUF2+fDmGDh2Kl19+2dn1ISIiJ3AouD/33HO4cuUKHnzwQdSsWdPZdSIiIpUcSss0aNAAFy5cwN13341HHnkEX3/9tbPrRUTkFXRwwqiQHqi3Q8F96dKlePLJJ/HVV19h3Lhx+Ne//oXOnTvjb3/7G44dO+bsOhIRkZ0cSsvExMQo/x8bG4u//vWvKCoqwuTJk/HKK6+gc+fOGDlyJAYNGgSdmqFENUDV0Llqz50nh3H14LC9aqj6vgJUTv/oyaE7PFm22YGyHdnHUT46cJhDV2P//v1x6tQpvPLKK2jVqhW6d++O48eP4/3330dBQQEWLVqEn3/+GSkpKc6uLxGRe/lTb5lt27ahYcOGaNiwIVJTUzFixAg0atRIef+WW25BZmYm2rdv77SKEhFR1TkU3OvVq4dFixYhOTm50m2ysrJQvXp1hytGROQV/GlsmQULFlQa2H/66ScAQEZGBrZv3+54zYiIvIBfzaHaq1cvAIDRaMSpU6esxnB/7LHH8M033zindkREfmjlypVYuHAhTCYTiouLERUVhdmzZ6Np06ZVPoZDwb2goADDhg3Dl19+yck5iEjbPJCWefjhh7Fu3Tr07t0bZrMZjzzyCPr27YsffvihylOZOpSWSUtLQ48ePfDTTz8hISEBv//+O3755RdMnz4dzz33nCOHJCLyTh7oLfOXv/wFvXv3BnB1FN4nn3wSv/32G/bs2VPlYzjUcj916hQmT54M4OqE2JaeMhkZGRgwYIAjhyQi8kqeGBUyOzvb6rWltV5aWlrlYzgU3PX6/zX4r1y5gkuXLqFGjRowmUz49ddfHTkkEZHmFRcXW702GAwwGAw33G/Hjh1o0KABunXrVuWyHErL1KpVCxMnTsSFCxeQkJCAu+66CzNmzEDfvn1Rp04dRw5JROSdnDhZR2RkJMLCwpQlKyvrhsUbjUbMnj0bc+fORbVq1apcbYda7n/729/wn//8B6WlpZg8eTKGDRuGmTNnolWrVnj33XcdOSQRkXdy4g3V/Px8hIaGKqur0mofPXo0Bg0ahIEDB9pVpEPBPTY2FrGxscrr9evXY8iQIdi5cyfuueceHDp0yJHDEhFpWmhoqFVwv5H09HQEBgZixowZdpflUHCvyIoVKwAAXbp0cdYhiYg8zlPT7M2cORN5eXn44IMPoNPpsHv3bgCo8mx3TgvuFv4+CiQRaYwH+rm/8847WLZsGRYsWKB0f1y3bh0aN27sueDutcpMgN7+oWTLjh1XVWxgk0Y33qgSF2+vp6rsmr+cdHhfCQxQVbZOxZCspuOFDu8bEKHunKkatlflUMXrd613eN/+Xe9TVbaquldTGUYceRBSww9Pnj9/HmPHjoXZbEbXrl2t3nvvvfeqfJwqX8kvvfRS1WtHRKQVzhhXxo6/RSEhITCZTBCRcsuIESOqfJwq/8n96KOP0LRp0xsON3D69OkqF05E5PV8dFTIKgf3AwcOIDU19YbbMedOROR5VU7LJCYmwmw233BJSEhwZX2JiNxL6zMxzZo1q0rbzZkzx9G6EBF5HU91hVSryi33jh07Vmm7Tp06OVwZIiJyDpXTtRMRkTfyn37uRESO0HpvGSIif6T5nDsREfkOttyJiG7EB0c7YHAnIrLFR3PuTMsQEWkQW+5ERDb46g1VBnciIlt8NC3jP8E9MADQ2z9GeWDjKHXlqhh3Ws147AAAFYO46VSOTa6m7IBbIxzeV6rfeE5KW3QlpY7vrHIM/H53DlBRtqqi1Q34p3ZsdUfOm1ndufYH/hPciYgcwLQMEZEWMS1DRKRBPhrc2RWSiEiD2HInIrKBOXciIi1iWoaIiLwFW+5ERLb4aMudwZ2IyAZfzbkzLUNEpEFsuRMR2cK0DBGR9jAtQ0REXoMtdyIiW5iW8XI6nWPD0JrNqoo1h9V0eF998SVVZaP0iuP7VvPgpaFiuGHdZaMTK2IfUXnOdCYV15pJ3RDNZ7rf6vC+4dsLVJVtOmH/0NYmUXFt24vBnYhIe3T/XdQew908HtxLS0uRmZmJ2bNn4+DBg2jcuLHy3ogRI3DgwAEEBwcr66KjozF//nwP1JSIyHd4NLjn5eXhr3/9K1q0aAFTJT8rV6xYYRXwiYjcykfTMh7tLXPhwgUsW7YMI0eO9GQ1iIgqZekKqXZxN4+23Fu3bg0AOHbsmCerQUSkOR7Pud9IVlYWfv31V5SVlSE2NhYvvvgi6tev7+lqEZG/YFrG+Vq0aIE777wTW7ZswZYtW2A0GtG5c2dcuHCh0n2MRiOKi4utFiIiVUTl4gFeHdyff/55DB06FHq9HkFBQXjttddw9OhRfPjhh5Xuk5WVhbCwMGWJjIx0Y42JiLyDVwf364WGhqJu3bo4dOhQpdtkZGSgqKhIWfLz891YQyLSGl+9oerVwX3cuHFWr41GI86cOWOzNW4wGBAaGmq1EBE5TG1KxkOpGa8O7u+88w5ycnKU19OnT0dYWBgefPBBD9aKiMj7ebS3TGlpKXr37o1z584BAIYMGYLIyEhkZ2cDAF555RVMmDABgYGBuHTpEurUqYOtW7eiXr16Hqw1EfkTXx3y16PBPSgoCNu2bav0/bS0NKSlpbmvQkRE1/PRrpBe38+diMiTfLXl7tU5dyIicoz/tNxFri72cmQM+GuoGpNdZdkIDFC3vxqOnGsLT9ZbxTnXXSlTV7aac6byWlE7JrsaAbfY/8S5mI3AERdUpsLCwLQMEZHm+GhwZ1qGiEiD2HInIrLBV2+oMrgTEdnCtAwREXkLttyJiGzQiUCnpifTf4/hbgzuRES2MC1DRETegi13IiIb2FuGiEiLfDQtw+BORGSDr7bcmXMnItIgBnciIls8NM1eaWkpMjIyEBgYiLy8PLv3Z3AnIrLBExNk5+XlITExEQUFBTCZTA7V239y7iYzIGb79wvw4N8/lQ8+SFA1h/dVPXytp6gdJlnN/mofVNGruNbUlq3ic3/w9QpVRad0H6xqfy26cOECli1bhmPHjmHp0qUOHcN/gjsRkSM80FumdevWAIBjx445XCSDOxHRDTirt0txcbHVa4PBAIPB4JyDX4c5dyIiN4mMjERYWJiyZGVluawsttyJiGxxdIrO648BID8/H6GhocpqV7XaAQZ3IiKbnPkQU2hoqFVwdyWmZYiINIgtdyIiWzi2DBGR9ujMVxe1x7BHaWkpevfujXPnzgEAhgwZgsjISGRnZ1f5GAzuRES2eKDlHhQUhG3btqkqkjl3IiINYsudiMgGXx3yl8GdiMgWJ/ZzdyemZYiINIgtdyIiG5iW8XbVAgG9Ax/XrLIPlJqfYyqHr/XZYXvV8MGfzxZldR1/cjHwVJG6wlV8bs0P2euj/dyZliEi0iD/abkTETmAaRkiIi1ibxkiIvIWbLkTEdnAtAwRkRb5aG8ZBnciIht8teXOnDsRkQax5U5EZItZri5qj+FmDO5ERLb4aM6daRkiIg1iy52IyAYdnHBD1Sk1sQ+DOxGRLXxClYiIvAVb7kRENvhqP3f/Ce5mMwAHxmZX+3NK5ZjsPkvNedOr+EHpyZ/PKr9r1WOyk2uwtwwREXkL/2m5ExE5QCcCncpfhGr3dwSDOxGRLQ5mdMsdw80Y3ImIbPDVljtz7kREGsSWOxGRLT7aW4bBnYjIFj6hSkRE3oItdyIiG/iEKhGRFjEtQ0RE3oItdyIiG3Tmq4vaY7gbgzsRkS1MyxARkbdgy/1G/HXIXrV89bz5ar3JdfgQExGR9nBsGQesXLkSvXv3Rs+ePdGxY0cMHDgQv//+u9U28+fPR/v27dGtWzf0798fx48f91BticgvWXLuahc382hwf/jhhzFx4kRs3rwZO3fuREhICPr27YuSkhIAwCeffILMzEz8+9//xvbt29GpUyfcc889MJs9cOuZiMiHeDS4/+Uvf0Hv3r2vVkSvx5NPPonffvsNe/bsAQDMmDEDqampqFevHgBg3Lhx2L9/PzZs2OCxOhORnxH8b0x3Rxd/m2YvOzvb6nVwcDAAoLS0FGfPnsWePXvQsWNH5f2wsDC0aNECmzZtcms9ich/WXLuahd386qukDt27ECDBg3QrVs3JfceERFhtU1ERES5vDwREVnzmt4yRqMRs2fPxty5c1GtWjVcunQJAGAwGKy2MxgMynuVHcdoNCqvi4uLXVNhIvIPAic8xOSUmtjFa1ruo0ePxqBBgzBw4EAAQI0aNQDAKlBbXlveq0hWVhbCwsKUJTIy0nWVJiLtY28Zx6WnpyMwMBAzZsxQ1jVt2hQAUFhYaLVtYWGh8l5FMjIyUFRUpCz5+fmuqTQRkRfzeHCfOXMm8vLy8M9//hM6nQ67d+/G7t27Ubt2bbRr1w45OTnKtsXFxcjNzUWvXr0qPZ7BYEBoaKjVQkTkMLU9ZSyLm3k0uL/zzjtYtmwZxo0bhz179iAnJwdr167Fjz/+CACYPHkylixZgtOnTwMA5s6di9atW6Nfv36erDYR+RFf7S3jsRuq58+fx9ixY2E2m9G1a1er99577z0AwAMPPIBTp06hT58+CA4ORu3atbF27Vro9R7/wUFE/sJHR4X0WHAPCQmByWS64XZjxozBmDFj3FAjIiLt8JqukEREXoktdyIiDWJwJ6+jZmxytRejmrLVDAzH8dgdo+Y+ltqB/Bz5zvg93xCDOxGRLWYAav+WcA5VIiLvwsk6iIjIa7DlTkRkC2+oEhFpkFkAncrgbGZahoiIAHz66afo0KED7rjjDiQmJuKnn36ya3+23ImIbPFAWmbXrl0YPnw4cnJyEB0djaVLl6JPnz745ZdfEBISUqVjsOVORGSTM8Zyty+4z5w5E/369UN0dDQA4OGHH0ZZWRmWLFlS5WMwuBMR2eKByTo2b95sNX+0Xq9HfHy8XfNHMy1DROQm10/7aTAYyk0leubMGRQVFVU4f/R3331X5bLYcicissUszlkAREZGWk0DmpWVVa44R+ePvh5b7kREtoj56qL2GADy8/OtZoe7PoADjs8ffT0GdyIiN6nK1J/h4eEICwuze/7o6zEtQ0RkiwduqCYnJ1vNHy0i2LNnj835o6/HlvuNqBxa1Bxa9Z9R19MXVz2/ViEPPPLsFJ4cztWDwyRLNRX/HIOqqSpbd/Gyqv1VceS8ufPaNtvflbHiY1Rdeno6evXqhdzcXLRo0QLLly9HQEAAUlNTq3wMBnciIi+TkJCAJUuWICUlBdWrV4der8fGjRur/AATwOBORGSbhwYOGzBgAAYMGOBwkQzuRES2CJwQ3J1SE7vwhioRkQax5U5EZAvHcyci0iCzGaonQVU7ibgDGNyJiGzx0ZY7c+5ERBrEljsRkS0+2nJncCcissUDT6g6A9MyREQaxJY7EZENImaIyiF/1e7vCAZ3IiJbRNSnVdhbhoiInIEtdyIiW8QJN1TZW8Z1pHowJKD8lFY3onaca33RRVX7k530Kn+MeuBJQgvdlTLHdzZ5rt6qx9/39nkHzGZA55xp9tyJaRkiIg3ym5Y7EZFDmJYhItIeMZshKtMy7ApJRORtfLTlzpw7EZEGseVORGSLWQCd77XcGdyJiGwRgerJOpiWISIiZ2DLnYjIBjELRGVaRpiWISLyMuKEOVT5hCoRETkDW+5ERDYwLUNEpEU+mpbRfHC3/MUsMxkd2l9ndmy//x1A5Yh5vkrN51bVyvHdUSHV8eDn9sCokGXm0v/u6voWcRmuqH5AtQxXnFMZO2g+uJ8/fx4A8OVvb3q4JkTkbOfPn0dYWJhLjh0UFISIiAj8p3CDU44XERGBoKAgpxyrKnTiiWSQG5nNZhQUFCAkJAS6CloYxcXFiIyMRH5+PkJDQ91aN0+V7Y+fmWVr6zoTEZw/fx4NGjSAXu0Y/jaUlJSgtLTUKccKCgpCcHCwU45VFZpvuev1ejRs2PCG24WGhrr9H52ny/bHz8yytXOduarFfq3g4GC3BmRnYldIIiINYnAnItIgvw/uBoMBmZmZMBjsn1/VV8v2x8/Msv3rOiM/uKFKROSP/L7lTkSkRQzuREQaxOBORKRBDO5Uzp133olevXqVW7948WJs27bNal1eXh6mTp3qknps27YNixcvtlpnNBoRGRmJ7777ziVlWkyePBmNGzdGUlKSS8vxlnJJexjcyUp+fj527NiBrVu34sSJE1bvVRbcX3rpJZfUpaLgHhAQgOjoaISEhLikTIvp06djxIgRLi3Dm8ol7WFwJysffvghnnvuOYgIVqxY4enqlBMYGIhNmzbh9ttv93RViLwagztZ+de//oVnnnkGXbp0wQcffKCsHz58OPbu3YvFixcjKSkJo0ePxpYtWzB+/HgAQFJSEpKSkrBjxw4AwIkTJzBo0CB06NAB3bt3R2pqKv7880+ljLi4OOh0Oqxbtw733XcfbrvtNqSlpSnlvfbaa1i8eDH27t2rHPvy5cvo3bs3brrpJqtUUFlZGdLT09G6dWt07NgRPXr0wL59+wAAFy5cQFJSEoKDgzFr1iwMGzYMHTt2RJcuXXD48OEqnZPZs2ejV69euO2227B06VKr92x9TgDIzs5G165d0aNHDyQkJODpp5+G0Wg90uiCBQvQtGlTdO/eHaNHj8alS5eqVC8im4Tov37++We59957RURk3rx5AkByc3OV9xMTEyUzM9Nqn61bt0pFl1Hnzp1l0qRJIiJiNpvlsccekz59+pTbb+bMmSIicvLkSTEYDLJlyxZlm8zMTElMTCx37OvrkZGRIXFxcXL+/HkREZk/f77UrVtXzp07p2zTqFEj6dixo7LNgAEDZPjw4TbPR2ZmptSqVUs2b94sIiJr166VmjVrSnFxcZU/58CBA2X16tUiIlJaWip9+/aVl156SXl/+/btEhAQIDt37hQRkYMHD0pERESFn5vIHmy5k2L58uX461//CgB46KGHEBgYaNV6r6otW7bg22+/xcSJEwEAOp0O//d//4eNGzfi0KFDVtumpKQAAOrVq4eWLVti7969dpV1+fJlvP766xg7dixq1aoFABg1ahTMZjP++c9/Wm173333KdskJSVVqaz69esjOTkZwNUbzRcvXsTBgwer/DlfeeUV3HPPPQCAatWq4f7778dnn32mHH/evHno1q0bEhISAADNmjWr8GY2kb00PyokVd2aNWuQkZEB4Gqw7dmzJz744ANkZmbadZz9+/dDr9dj0KBByrqysjI0atQIJ06cQLNmzZT1t9xyi/L/ISEhKC4utqusgwcPoqSkBLfddpuyLiAgAI0bN8b+/futtnWkrGv3sYxsaNmvKp/z4sWLGDp0KI4cOYKgoCAUFhZapWUOHDiAuLg4qzKjoqKQn59fhU9PVDkGdwIA7NixA6dOnUL//v2VdSdPnkRubi5ycnLQoUMHu4+5efNmBAQE2Nzm2vd1Op3dM+vY2v768fsdKaui+l+/X2Wf88KFC0hOTsbgwYOxfPly6PV6LF682Op+gYhUOM8AkVpMyxAA4IMPPsDSpUuxbds2Zdm1axeqV6+upGaunRThwoULEBGrdWVlZbh8+TLatGkDs9mM3377zaqMxx9/HGfOnKlyna49dklJCa5cKT9V2W233Ybg4GCrskwmE/Ly8tC6desql+WIG33OAwcO4NSpU3jwwQeVz3L9xA8tW7Ysl6o6evSoS+tN/oHBnWAymfDVV1+hZ8+eVutDQkJw33334aOPPoLZbEbdunVx9uxZAECnTp1w4cIF1K1bFwBw9uxZfPLJJ3jxxRfRo0cPdO3aFdOnT4f5v3NzZmdn48CBAwgPD69yva4t7+mnn8bnn39ebpvq1atjwoQJeOutt3Dx4kUAwKJFi6DX6/HYY4/ZfzLscKPP2bRpU1SvXh2bNm0CcPU8r1692uoYaWlp2L59O3bt2gUAOHz4MDZscM60buTnPHk3lzzv3LlzkpCQIOHh4fLkk09avbdw4UJp3ry5AJBOnTrJV199JdHR0dK1a1dJT09XtktJSZG4uDjp0qWLHDhwQERECgsLZfDgwRITEyNJSUkyePBgOXnypIiIfPbZZxIbGysAJDExUc6cOSMjRoyQsLAwadSokcyaNUtErvag6dixo3Tr1k369esnJSUlctdddynbvfDCCyIicuXKFZk0aZK0atVKOnToIImJifL9998r9UtMTBSDwSDR0dGyfPlyWbFihURHR4vBYJDk5OQKz0tWVpY0atRIwsLCZNiwYXLu3DlJTEwUABIbGyuff/75DT+niMinn34qLVq0kISEBLn//vtl5MiR5cpdsGCBNGnSRLp27SopKSny1FNPSVhYmPTv39/Rr5VIOOQvEZEGMS1DRKRBDO5ERBrE4E5EpEEM7kREGsTgTkSkQQzuREQaxOBORKRBDO5ERBrE4E5EpEEM7kREGsTgTkSkQQzuREQa9P83HjNRZ6W2BQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title(\"Subject pronoun head patching\")\n",
    "ax.set_xlabel(\"Attention head\")\n",
    "ax.set_ylabel(\"Layer\")\n",
    "matshow = ax.matshow(subj_head_patchings.detach().cpu().numpy())\n",
    "fig.colorbar(matshow, ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "6d9a33ef-a886-4a4a-bed6-027a429f7da8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top heads:\n",
      "[[17 14]\n",
      " [13 11]\n",
      " [15 13]\n",
      " [13  3]\n",
      " [18 11]]\n",
      "\n",
      "Top heads' respective values:\n",
      "tensor([4.7859, 4.5473, 1.0804, 0.6352, 0.4049])\n"
     ]
    }
   ],
   "source": [
    "get_top_for_matrix(subj_head_patchings.detach().cpu())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03665832-3b7b-4439-a023-d288ce17fe49",
   "metadata": {},
   "source": [
    "## Obj pronouns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "5b0d2682-f1ed-4fca-9cec-8a70759c6a5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "obj_lm_normal = make_lm_head_normal([' her'], [' him']).to(\"cuda\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "16f792ba-814d-4473-88ea-5b400c557486",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "300it [14:57,  2.99s/it]\n"
     ]
    }
   ],
   "source": [
    "obj_head_patchings = get_mean_layer_head_patchings_for_prompts(model, obj_prompts_female, obj_prompts_male, obj_lm_normal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "5de553e1-9d0c-4ab4-b0e7-a297c2bcecdd",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "10it [00:15,  1.52s/it]\n"
     ]
    }
   ],
   "source": [
    "obj_head_patchings = get_mean_layer_head_patchings_for_embeddings(model, obj_embeddings_female, obj_embeddings_male, obj_lm_normal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "ffd24cd8-ac93-4003-82a3-327f79e25dda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title(\"Object pronoun head patching\")\n",
    "ax.set_xlabel(\"Attention head\")\n",
    "ax.set_ylabel(\"Layer\")\n",
    "matshow = ax.matshow(obj_head_patchings.detach().cpu().numpy())\n",
    "fig.colorbar(matshow, ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "0589507e-7cbd-4a50-a5a0-00898c879329",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top heads:\n",
      "[[17 14]\n",
      " [13 11]\n",
      " [15 13]\n",
      " [22  2]\n",
      " [23  0]]\n",
      "\n",
      "Top heads' respective values:\n",
      "tensor([2.9491, 1.8853, 1.8634, 0.3653, 0.2359])\n"
     ]
    }
   ],
   "source": [
    "get_top_for_matrix(obj_head_patchings.detach().cpu())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "6a06f19e-009a-4075-a52e-0914f5d6de52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.set_title(\"Object pronoun head patching\")\n",
    "ax.set_xlabel(\"Attention head\")\n",
    "ax.set_ylabel(\"Layer\")\n",
    "matshow = ax.matshow(obj_head_patchings.detach().cpu().numpy())\n",
    "fig.colorbar(matshow, ax=ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "b39d51a9-977c-444c-8f53-880984cd6e21",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top heads:\n",
      "[[17 14]\n",
      " [15 13]\n",
      " [13 11]\n",
      " [22  2]\n",
      " [15  0]]\n",
      "\n",
      "Top heads' respective values:\n",
      "tensor([3.5636, 3.0652, 2.1328, 0.5218, 0.2863])\n"
     ]
    }
   ],
   "source": [
    "get_top_for_matrix(obj_head_patchings.detach().cpu())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5aab67b2-b240-4017-a2fb-01b1f9d319dc",
   "metadata": {},
   "source": [
    "# Finding feature vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38d3d7c9-60f1-476c-8777-c1d927f9b86b",
   "metadata": {},
   "source": [
    "## Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "40e1dea9-d213-4bb2-9afc-44ee87756bed",
   "metadata": {},
   "outputs": [],
   "source": [
    "cur_occu_embeddings_female = embeddings_np_to_torch(occu_embeddings_female[0], free=False)\n",
    "cur_occu_embeddings_male = embeddings_np_to_torch(occu_embeddings_male[0], free=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "9b1b0b59-c483-4bde-a074-a31b197d9fd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "cur_subj_embeddings_female = embeddings_np_to_torch(subj_embeddings_female[0], free=False)\n",
    "cur_subj_embeddings_male = embeddings_np_to_torch(subj_embeddings_male[0], free=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "f5c16665-811a-47a2-b227-7fb6825a8039",
   "metadata": {},
   "outputs": [],
   "source": [
    "cur_obj_embeddings_female = embeddings_np_to_torch(obj_embeddings_female[0], free=False)\n",
    "cur_obj_embeddings_male = embeddings_np_to_torch(obj_embeddings_male[0], free=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fea1143-2e26-4a64-9a27-86501d6607df",
   "metadata": {},
   "source": [
    "## Path patching recursion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b29b4fa2-3f30-4964-9c28-b323d7ff1e0e",
   "metadata": {},
   "source": [
    "### Subject pronouns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "454e18ab-d974-4d56-969e-57eed0b3474c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paths of length 1:\n",
      "===================\n",
      "attn13.11@5: 3.4273200035095215\n",
      "mlp18@-1: 2.334465503692627\n",
      "attn17.14@4: 1.6758766174316406\n",
      "mlp16@-1: 1.5480985641479492\n",
      "mlp19@-1: 1.0288758277893066\n",
      "attn17.14@9: 0.8834829330444336\n",
      "attn17.14@10: 0.829963207244873\n",
      "mlp17@-1: 0.6939783096313477\n",
      "attn13.11@4: 0.6556925773620605\n",
      "attn17.14@5: 0.6509819030761719\n",
      "embedding@-1: -4.76837158203125e-07\n",
      "\n",
      "Paths of length 2:\n",
      "===================\n",
      "attn13.11@5 <= attn9.1@3: 1.336902141571045\n",
      "attn13.11@5 <= attn6.6@3: 0.809196949005127\n",
      "attn17.14@4 <= attn13.3@3: 0.4383583068847656\n",
      "mlp16@-1 <= attn13.3@3: 0.375551700592041\n",
      "attn17.14@4 <= attn9.1@3: 0.3448495864868164\n",
      "mlp17@-1 <= attn13.11@5: 0.3383798599243164\n",
      "attn13.11@4 <= attn9.1@3: 0.3243856430053711\n",
      "attn17.14@10 <= attn9.1@3: 0.3155651092529297\n",
      "attn13.11@5 <= attn10.5@5: 0.307647705078125\n",
      "attn17.14@4 <= attn15.13@3: 0.25746870040893555\n",
      "attn13.11@5 <= embedding@5: 0.0\n",
      "attn17.14@4 <= embedding@4: 0.0\n",
      "mlp16@-1 <= embedding@-1: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "attn17.14@9 <= embedding@9: 0.0\n",
      "attn17.14@10 <= embedding@10: 0.0\n",
      "mlp17@-1 <= embedding@-1: 0.0\n",
      "attn13.11@4 <= embedding@4: 0.0\n",
      "attn17.14@5 <= embedding@5: 0.0\n",
      "embedding@-1: -4.76837158203125e-07\n",
      "\n",
      "Paths of length 3:\n",
      "===================\n",
      "attn13.11@5 <= attn6.6@3 <= mlp1@3: 0.4477052688598633\n",
      "attn13.11@5 <= attn6.6@3 <= mlp0@3: 0.4235038757324219\n",
      "attn13.11@5 <= attn9.1@3 <= mlp1@3: 0.3361673355102539\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3: 0.3288264274597168\n",
      "attn13.11@5 <= attn9.1@3 <= mlp0@3: 0.30481815338134766\n",
      "mlp17@-1 <= attn13.11@5 <= attn9.1@3: 0.18024253845214844\n",
      "attn13.11@5 <= attn10.5@5 <= attn6.6@3: 0.15015697479248047\n",
      "mlp17@-1 <= attn13.11@5 <= attn6.6@3: 0.12578773498535156\n",
      "attn17.14@4 <= attn15.13@3 <= mlp12@3: 0.09822511672973633\n",
      "attn13.11@5 <= attn9.1@3 <= mlp6@3: 0.09788036346435547\n",
      "attn17.14@4 <= attn15.13@3 <= embedding@3: 1.9550323486328125e-05\n",
      "attn13.11@5 <= embedding@5: 0.0\n",
      "attn17.14@4 <= embedding@4: 0.0\n",
      "mlp16@-1 <= embedding@-1: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "attn17.14@9 <= embedding@9: 0.0\n",
      "attn17.14@10 <= embedding@10: 0.0\n",
      "mlp17@-1 <= embedding@-1: 0.0\n",
      "attn13.11@4 <= embedding@4: 0.0\n",
      "attn17.14@5 <= embedding@5: 0.0\n",
      "\n",
      "Paths of length 4:\n",
      "===================\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3: 0.18532800674438477\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp0@3: 0.17064619064331055\n",
      "attn13.11@5 <= attn10.5@5 <= attn6.6@3 <= mlp1@3: 0.08254194259643555\n",
      "attn13.11@5 <= attn10.5@5 <= attn6.6@3 <= mlp0@3: 0.08019638061523438\n",
      "mlp17@-1 <= attn13.11@5 <= attn6.6@3 <= mlp1@3: 0.07691574096679688\n",
      "mlp17@-1 <= attn13.11@5 <= attn6.6@3 <= mlp0@3: 0.062066078186035156\n",
      "mlp17@-1 <= attn13.11@5 <= attn9.1@3 <= mlp0@3: 0.058825016021728516\n",
      "mlp17@-1 <= attn13.11@5 <= attn9.1@3 <= mlp1@3: 0.05578804016113281\n",
      "mlp17@-1 <= attn13.11@5 <= attn9.1@3 <= attn6.6@3: 0.045482635498046875\n",
      "attn13.11@5 <= attn9.1@3 <= mlp6@3 <= mlp4@3: 0.04052591323852539\n",
      "attn13.11@5 <= attn9.1@3 <= mlp6@3 <= embedding@3: 0.004731178283691406\n",
      "attn17.14@4 <= attn15.13@3 <= embedding@3: 1.9550323486328125e-05\n",
      "attn13.11@5 <= embedding@5: 0.0\n",
      "attn17.14@4 <= embedding@4: 0.0\n",
      "mlp16@-1 <= embedding@-1: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "attn17.14@9 <= embedding@9: 0.0\n",
      "attn17.14@10 <= embedding@10: 0.0\n",
      "mlp17@-1 <= embedding@-1: 0.0\n",
      "attn13.11@4 <= embedding@4: 0.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = patch_get_max_paths(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal, 4, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86061301-a330-4906-a1ac-ba070efc6630",
   "metadata": {},
   "source": [
    "### Object pronouns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "3ec0e5a5-4347-4586-a9ed-4b2c4d3bb55a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paths of length 1:\n",
      "===================\n",
      "mlp18@-1: 3.437502145767212\n",
      "attn15.13@6: 2.464179039001465\n",
      "attn17.14@7: 1.8911547660827637\n",
      "attn13.11@6: 1.5276784896850586\n",
      "attn13.11@7: 0.9481534957885742\n",
      "attn17.14@11: 0.8216190338134766\n",
      "attn17.14@9: 0.7756085395812988\n",
      "attn17.14@8: 0.5406274795532227\n",
      "attn18.11@6: 0.5189943313598633\n",
      "attn23.8@11: 0.3799419403076172\n",
      "embedding@-1: 0.0\n",
      "\n",
      "Paths of length 2:\n",
      "===================\n",
      "attn15.13@6 <= mlp12@6: 0.9650425910949707\n",
      "mlp18@-1 <= attn15.13@6: 0.4858846664428711\n",
      "attn13.11@6 <= attn6.6@6: 0.39538097381591797\n",
      "attn17.14@7 <= attn13.3@6: 0.39145851135253906\n",
      "attn17.14@7 <= attn15.13@6: 0.36108875274658203\n",
      "attn17.14@11 <= attn15.13@6: 0.3336629867553711\n",
      "attn17.14@7 <= mlp12@7: 0.32725000381469727\n",
      "attn17.14@7 <= attn13.11@7: 0.3150959014892578\n",
      "attn15.13@6 <= mlp0@6: 0.3031148910522461\n",
      "attn15.13@6 <= attn6.6@6: 0.2721385955810547\n",
      "attn15.13@6 <= embedding@6: 0.002132415771484375\n",
      "attn18.11@6 <= embedding@6: 0.00024175643920898438\n",
      "embedding@-1: 0.0\n",
      "mlp18@-1 <= embedding@-1: 0.0\n",
      "attn17.14@7 <= embedding@7: 0.0\n",
      "attn17.14@11 <= embedding@11: 0.0\n",
      "attn17.14@9 <= embedding@9: 0.0\n",
      "attn17.14@8 <= embedding@8: 0.0\n",
      "attn23.8@11 <= embedding@11: 0.0\n",
      "attn13.11@7 <= embedding@7: -4.76837158203125e-07\n",
      "\n",
      "Paths of length 3:\n",
      "===================\n",
      "attn15.13@6 <= mlp12@6 <= attn6.6@6: 0.3005671501159668\n",
      "attn15.13@6 <= mlp12@6 <= mlp1@6: 0.21135520935058594\n",
      "attn13.11@6 <= attn6.6@6 <= mlp0@6: 0.19423198699951172\n",
      "attn15.13@6 <= mlp12@6 <= mlp0@6: 0.1908726692199707\n",
      "attn17.14@7 <= mlp12@7 <= attn6.6@6: 0.1840672492980957\n",
      "attn17.14@7 <= mlp12@7 <= attn9.1@6: 0.1816411018371582\n",
      "attn13.11@6 <= attn6.6@6 <= mlp1@6: 0.17979907989501953\n",
      "mlp18@-1 <= attn15.13@6 <= mlp12@6: 0.1562662124633789\n",
      "attn17.14@7 <= attn15.13@6 <= mlp12@6: 0.14171361923217773\n",
      "attn17.14@11 <= attn15.13@6 <= mlp12@6: 0.13085079193115234\n",
      "attn15.13@6 <= mlp12@6 <= embedding@6: 0.0037565231323242188\n",
      "attn15.13@6 <= embedding@6: 0.002132415771484375\n",
      "attn15.13@6 <= mlp0@6 <= embedding@6: 0.0011744499206542969\n",
      "attn13.11@6 <= attn6.6@6 <= embedding@6: 0.00078582763671875\n",
      "attn15.13@6 <= attn6.6@6 <= embedding@6: 0.0004639625549316406\n",
      "mlp18@-1 <= attn15.13@6 <= embedding@6: 0.0003752708435058594\n",
      "attn17.14@7 <= attn15.13@6 <= embedding@6: 0.00030422210693359375\n",
      "attn17.14@11 <= attn15.13@6 <= embedding@6: 0.0002808570861816406\n",
      "attn18.11@6 <= embedding@6: 0.00024175643920898438\n",
      "embedding@-1: 0.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = patch_get_max_paths(model, cur_obj_embeddings_female, cur_obj_embeddings_male, obj_ln_f_normal, 3, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08ecd769-9aee-4b22-8212-45d1f8bb16f2",
   "metadata": {},
   "source": [
    "### Occupations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "eac33ba0-5acc-4b50-861e-ed8956b48468",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paths of length 1:\n",
      "===================\n",
      "mlp18@-1: 0.8984694480895996\n",
      "mlp22@-1: 0.5668761730194092\n",
      "mlp16@-1: 0.5379655361175537\n",
      "attn23.8@6: 0.3917241096496582\n",
      "mlp21@-1: 0.3572816848754883\n",
      "attn23.1@6: 0.3237144947052002\n",
      "mlp20@-1: 0.30431365966796875\n",
      "attn21.13@5: 0.2827794551849365\n",
      "mlp19@-1: 0.2637805938720703\n",
      "attn15.13@3: 0.21320676803588867\n",
      "embedding@-1: 0.0\n",
      "\n",
      "Paths of length 2:\n",
      "===================\n",
      "mlp18@-1 <= mlp16@-1: 0.22571659088134766\n",
      "mlp22@-1 <= mlp20@-1: 0.16983246803283691\n",
      "mlp21@-1 <= mlp18@-1: 0.15436887741088867\n",
      "mlp19@-1 <= mlp16@-1: 0.14850091934204102\n",
      "mlp16@-1 <= attn15.13@3: 0.13726472854614258\n",
      "mlp20@-1 <= mlp15@-1: 0.13591718673706055\n",
      "mlp21@-1 <= mlp16@-1: 0.1356348991394043\n",
      "mlp16@-1 <= attn13.3@3: 0.13139772415161133\n",
      "mlp18@-1 <= attn15.13@3: 0.11214351654052734\n",
      "mlp16@-1 <= attn9.1@3: 0.10793447494506836\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp22@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "attn23.8@6 <= embedding@6: 4.76837158203125e-07\n",
      "attn23.1@6 <= embedding@6: 4.76837158203125e-07\n",
      "attn21.13@5 <= embedding@5: 4.76837158203125e-07\n",
      "embedding@-1: 0.0\n",
      "mlp16@-1 <= embedding@-1: 0.0\n",
      "mlp20@-1 <= embedding@-1: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "\n",
      "Paths of length 3:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3: 0.10055208206176758\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1: 0.09609651565551758\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1: 0.0830540657043457\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1: 0.08109569549560547\n",
      "mlp18@-1 <= mlp16@-1 <= attn15.13@3: 0.07259750366210938\n",
      "mlp21@-1 <= mlp16@-1 <= attn15.13@3: 0.06392621994018555\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.061102867126464844\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3: 0.05198240280151367\n",
      "mlp18@-1 <= mlp16@-1 <= attn13.3@3: 0.04359769821166992\n",
      "mlp22@-1 <= mlp20@-1 <= attn17.14@4: 0.04315042495727539\n",
      "mlp16@-1 <= attn13.3@3 <= embedding@3: 0.0006103515625\n",
      "mlp16@-1 <= attn9.1@3 <= embedding@3: 0.0002551078796386719\n",
      "mlp18@-1 <= attn15.13@3 <= embedding@3: 9.489059448242188e-05\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp22@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "attn23.8@6 <= embedding@6: 4.76837158203125e-07\n",
      "\n",
      "Paths of length 4:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.03602123260498047\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3: 0.029163837432861328\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3: 0.02577829360961914\n",
      "mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.02532482147216797\n",
      "mlp21@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.022521495819091797\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1: 0.022162914276123047\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3 <= mlp12@3: 0.020623207092285156\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.018641948699951172\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= attn15.13@3: 0.01566600799560547\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3: 0.014591693878173828\n",
      "mlp16@-1 <= attn13.3@3 <= embedding@3: 0.0006103515625\n",
      "mlp16@-1 <= attn9.1@3 <= embedding@3: 0.0002551078796386719\n",
      "mlp18@-1 <= attn15.13@3 <= embedding@3: 9.489059448242188e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= embedding@3: 8.20159912109375e-05\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3 <= embedding@3: 1.0967254638671875e-05\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = patch_get_max_paths(model, cur_embeddings_female, cur_embeddings_male, better_diff_ln_f_normal, 4, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "id": "9c65d8e0-d39a-469b-84e2-64b606155176",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paths of length 1:\n",
      "===================\n",
      "mlp18@-1: 0.8984694480895996\n",
      "mlp22@-1: 0.5668761730194092\n",
      "mlp16@-1: 0.5379655361175537\n",
      "attn23.8@6: 0.3917241096496582\n",
      "mlp21@-1: 0.3572816848754883\n",
      "attn23.1@6: 0.3237144947052002\n",
      "mlp20@-1: 0.30431365966796875\n",
      "attn21.13@5: 0.2827794551849365\n",
      "mlp19@-1: 0.2637805938720703\n",
      "attn15.13@3: 0.21320676803588867\n",
      "attn23.12@6: 0.17145609855651855\n",
      "attn23.9@6: 0.1677227020263672\n",
      "attn23.13@6: 0.14931273460388184\n",
      "attn13.10@4: 0.11520195007324219\n",
      "attn23.0@6: 0.10534524917602539\n",
      "embedding@-1: 0.0\n",
      "\n",
      "Paths of length 2:\n",
      "===================\n",
      "mlp18@-1 <= mlp16@-1: 0.22571659088134766\n",
      "mlp22@-1 <= mlp20@-1: 0.16983246803283691\n",
      "mlp21@-1 <= mlp18@-1: 0.15436887741088867\n",
      "mlp19@-1 <= mlp16@-1: 0.14850091934204102\n",
      "mlp16@-1 <= attn15.13@3: 0.13726472854614258\n",
      "mlp20@-1 <= mlp15@-1: 0.13591718673706055\n",
      "mlp21@-1 <= mlp16@-1: 0.1356348991394043\n",
      "mlp16@-1 <= attn13.3@3: 0.13139772415161133\n",
      "mlp18@-1 <= attn15.13@3: 0.11214351654052734\n",
      "mlp16@-1 <= attn9.1@3: 0.10793447494506836\n",
      "mlp20@-1 <= mlp17@-1: 0.10595941543579102\n",
      "mlp16@-1 <= mlp12@-1: 0.09309911727905273\n",
      "mlp16@-1 <= attn13.3@4: 0.0912923812866211\n",
      "mlp18@-1 <= attn17.14@4: 0.08816957473754883\n",
      "attn15.13@3 <= mlp12@3: 0.08452558517456055\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp22@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "attn23.8@6 <= embedding@6: 4.76837158203125e-07\n",
      "attn23.1@6 <= embedding@6: 4.76837158203125e-07\n",
      "attn21.13@5 <= embedding@5: 4.76837158203125e-07\n",
      "embedding@-1: 0.0\n",
      "mlp16@-1 <= embedding@-1: 0.0\n",
      "mlp20@-1 <= embedding@-1: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "attn23.12@6 <= embedding@6: 0.0\n",
      "attn23.9@6 <= embedding@6: 0.0\n",
      "attn23.13@6 <= embedding@6: 0.0\n",
      "attn13.10@4 <= embedding@4: 0.0\n",
      "attn23.0@6 <= embedding@6: 0.0\n",
      "\n",
      "Paths of length 3:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3: 0.10055208206176758\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1: 0.09609651565551758\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1: 0.0830540657043457\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1: 0.08109569549560547\n",
      "mlp18@-1 <= mlp16@-1 <= attn15.13@3: 0.07259750366210938\n",
      "mlp21@-1 <= mlp16@-1 <= attn15.13@3: 0.06392621994018555\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.061102867126464844\n",
      "mlp16@-1 <= mlp12@-1 <= attn6.6@3: 0.05743122100830078\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3: 0.05198240280151367\n",
      "mlp16@-1 <= mlp12@-1 <= attn10.5@3: 0.044075965881347656\n",
      "mlp18@-1 <= mlp16@-1 <= attn13.3@3: 0.04359769821166992\n",
      "mlp22@-1 <= mlp20@-1 <= attn17.14@4: 0.04315042495727539\n",
      "mlp19@-1 <= mlp16@-1 <= mlp12@-1: 0.03871297836303711\n",
      "mlp18@-1 <= attn15.13@3 <= mlp12@3: 0.03700876235961914\n",
      "mlp19@-1 <= mlp16@-1 <= attn13.3@3: 0.036751747131347656\n",
      "mlp16@-1 <= attn13.3@3 <= embedding@3: 0.0006103515625\n",
      "mlp16@-1 <= attn9.1@3 <= embedding@3: 0.0002551078796386719\n",
      "mlp18@-1 <= attn15.13@3 <= embedding@3: 9.489059448242188e-05\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= attn17.14@4 <= embedding@4: 9.5367431640625e-07\n",
      "mlp22@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "attn23.8@6 <= embedding@6: 4.76837158203125e-07\n",
      "attn23.1@6 <= embedding@6: 4.76837158203125e-07\n",
      "attn21.13@5 <= embedding@5: 4.76837158203125e-07\n",
      "mlp22@-1 <= mlp20@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "embedding@-1: 0.0\n",
      "\n",
      "Paths of length 4:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.03602123260498047\n",
      "mlp16@-1 <= mlp12@-1 <= attn6.6@3 <= mlp0@3: 0.030047893524169922\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3: 0.029163837432861328\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3: 0.02577829360961914\n",
      "mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.02532482147216797\n",
      "mlp16@-1 <= mlp12@-1 <= attn6.6@3 <= mlp1@3: 0.023015499114990234\n",
      "mlp21@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.022521495819091797\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1: 0.022162914276123047\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3 <= mlp12@3: 0.020623207092285156\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.018641948699951172\n",
      "mlp19@-1 <= mlp16@-1 <= mlp12@-1 <= attn6.6@3: 0.015823841094970703\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= attn15.13@3: 0.01566600799560547\n",
      "mlp16@-1 <= mlp12@-1 <= attn10.5@3 <= attn6.6@3: 0.01559305191040039\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3: 0.014591693878173828\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= attn17.14@4: 0.01455545425415039\n",
      "mlp16@-1 <= attn13.3@3 <= embedding@3: 0.0006103515625\n",
      "mlp16@-1 <= attn9.1@3 <= embedding@3: 0.0002551078796386719\n",
      "mlp18@-1 <= attn15.13@3 <= embedding@3: 9.489059448242188e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= embedding@3: 8.20159912109375e-05\n",
      "mlp18@-1 <= attn15.13@3 <= mlp12@3 <= embedding@3: 3.6716461181640625e-05\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3 <= embedding@3: 1.0967254638671875e-05\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= attn17.14@4 <= embedding@4: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp22@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "attn23.8@6 <= embedding@6: 4.76837158203125e-07\n",
      "\n",
      "Paths of length 5:\n",
      "===================\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.011118412017822266\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.011085033416748047\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.010155200958251953\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3: 0.008693218231201172\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp1@3: 0.00819540023803711\n",
      "mlp16@-1 <= mlp12@-1 <= attn10.5@3 <= attn6.6@3 <= mlp0@3: 0.008183956146240234\n",
      "mlp16@-1 <= mlp12@-1 <= attn10.5@3 <= attn6.6@3 <= mlp1@3: 0.007765293121337891\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3: 0.0075626373291015625\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp0@3: 0.007389545440673828\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3: 0.007136344909667969\n",
      "mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.006909847259521484\n",
      "mlp19@-1 <= mlp16@-1 <= mlp12@-1 <= attn6.6@3 <= mlp0@3: 0.006831645965576172\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= mlp14@-1: 0.006800651550292969\n",
      "mlp19@-1 <= mlp16@-1 <= mlp12@-1 <= attn6.6@3 <= mlp1@3: 0.006596088409423828\n",
      "mlp21@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.006405830383300781\n",
      "mlp16@-1 <= attn13.3@3 <= embedding@3: 0.0006103515625\n",
      "mlp16@-1 <= attn9.1@3 <= embedding@3: 0.0002551078796386719\n",
      "mlp18@-1 <= attn15.13@3 <= embedding@3: 9.489059448242188e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= embedding@3: 8.20159912109375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= mlp12@-1 <= attn6.6@3 <= embedding@3: 5.3882598876953125e-05\n",
      "mlp18@-1 <= attn15.13@3 <= mlp12@3 <= embedding@3: 3.6716461181640625e-05\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3 <= embedding@3: 1.0967254638671875e-05\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= embedding@3: 7.152557373046875e-06\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= attn17.14@4 <= embedding@4: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "\n",
      "Paths of length 6:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3: 0.004630088806152344\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp0@3: 0.004534244537353516\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.0034027099609375\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.0031981468200683594\n",
      "mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3: 0.002883434295654297\n",
      "mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp0@3: 0.0028557777404785156\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3: 0.0027265548706054688\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= mlp14@-1 <= mlp9@-1: 0.002647876739501953\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3: 0.0026330947875976562\n",
      "mlp21@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp0@3: 0.0026063919067382812\n",
      "mlp21@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3: 0.0025963783264160156\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3: 0.002471446990966797\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp1@3: 0.0022878646850585938\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3: 0.0021376609802246094\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp1@3: 0.0020694732666015625\n",
      "mlp16@-1 <= attn13.3@3 <= embedding@3: 0.0006103515625\n",
      "mlp16@-1 <= attn9.1@3 <= embedding@3: 0.0002551078796386719\n",
      "mlp18@-1 <= attn15.13@3 <= embedding@3: 9.489059448242188e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= embedding@3: 8.20159912109375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= mlp12@-1 <= attn6.6@3 <= embedding@3: 5.3882598876953125e-05\n",
      "mlp18@-1 <= attn15.13@3 <= mlp12@3 <= embedding@3: 3.6716461181640625e-05\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3 <= embedding@3: 1.0967254638671875e-05\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= embedding@3: 7.152557373046875e-06\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= attn17.14@4 <= embedding@4: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "\n",
      "Paths of length 7:\n",
      "===================\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3: 0.0014195442199707031\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp0@3: 0.0013828277587890625\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp0@3: 0.0013451576232910156\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3: 0.001312255859375\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= mlp14@-1 <= mlp9@-1 <= mlp7@-1: 0.0010981559753417969\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3: 0.0009961128234863281\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp0@3: 0.0009665489196777344\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.0008406639099121094\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= mlp14@-1 <= mlp9@-1 <= mlp6@-1: 0.0007433891296386719\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= mlp14@-1 <= mlp9@-1 <= mlp4@-1: 0.0006918907165527344\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= mlp14@-1 <= mlp9@-1 <= attn1.3@3: 0.0006895065307617188\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3: 0.0006761550903320312\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3: 0.0006518363952636719\n",
      "mlp22@-1 <= mlp20@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3: 0.0006098747253417969\n",
      "mlp22@-1 <= mlp20@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp1@3: 0.0005812644958496094\n",
      "mlp16@-1 <= attn13.3@3 <= embedding@3: 0.0006103515625\n",
      "mlp16@-1 <= attn9.1@3 <= embedding@3: 0.0002551078796386719\n",
      "mlp18@-1 <= attn15.13@3 <= embedding@3: 9.489059448242188e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= embedding@3: 8.20159912109375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= mlp12@-1 <= attn6.6@3 <= embedding@3: 5.3882598876953125e-05\n",
      "mlp18@-1 <= attn15.13@3 <= mlp12@3 <= embedding@3: 3.6716461181640625e-05\n",
      "mlp22@-1 <= mlp20@-1 <= attn15.13@3 <= embedding@3: 1.0967254638671875e-05\n",
      "mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= embedding@3: 7.152557373046875e-06\n",
      "mlp21@-1 <= mlp18@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= embedding@3: 2.384185791015625e-06\n",
      "mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp18@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp21@-1 <= mlp16@-1 <= embedding@-1: 9.5367431640625e-07\n",
      "mlp18@-1 <= attn17.14@4 <= embedding@4: 9.5367431640625e-07\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = patch_get_max_paths(model, cur_embeddings_female, cur_embeddings_male, better_diff_ln_f_normal, 7, 15)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9e985bc-f381-4ee1-a35a-beee59145435",
   "metadata": {},
   "source": [
    "Let's see if different paths converge to the same feature vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "219d368f-1dfa-4ef7-9d7f-7629b2e5d1c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(0.9602, device='cuda:0'),\n",
       " tensor(0.9781, device='cuda:0'),\n",
       " tensor(0.9756, device='cuda:0'))"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "occu_normal_path_1 = get_normal_for_path(model, cur_occu_embeddings_female, cur_occu_embeddings_male, occu_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 19, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 16, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "        {'layer': 12, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "    ]\n",
    ")\n",
    "\n",
    "occu_normal_path_2 = get_normal_for_path(model, cur_occu_embeddings_female, cur_occu_embeddings_male, occu_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 22, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 20, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 16, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "        {'layer': 12, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "    ]\n",
    ")\n",
    "\n",
    "occu_normal_path_3 = get_normal_for_path(model, cur_occu_embeddings_female, cur_occu_embeddings_male, occu_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 21, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 18, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 16, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "        {'layer': 12, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "    ]\n",
    ")\n",
    "\n",
    "cossim(occu_normal_path_1, occu_normal_path_2),\\\n",
    "    cossim(occu_normal_path_2, occu_normal_path_3),\\\n",
    "    cossim(occu_normal_path_1, occu_normal_path_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "876ee6bd-4ee1-4e7f-8de3-de00aec38035",
   "metadata": {},
   "source": [
    "This motivates a good choice of starting path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "5217a298-e841-445f-9a92-7d25a9bb5140",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paths of length 1:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3: 0.0009961128234863281\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp0@3: 0.0009665489196777344\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp2@3: 0.00011682510375976562\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.14@3: 0.00010156631469726562\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.11@3: 4.9114227294921875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.6@3: 4.57763671875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.3@3: 3.814697265625e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.8@3: 3.7670135498046875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.9@3: 3.7670135498046875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.15@3: 3.4809112548828125e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= embedding@3: 0.0\n",
      "\n",
      "Paths of length 2:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp2@3 <= mlp0@3: 0.00012350082397460938\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.14@3: 9.5367431640625e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.15@3: 7.724761962890625e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.13@3: 7.009506225585938e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.0@3: 6.771087646484375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.2@3: 5.4836273193359375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.6@3: 4.1484832763671875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.3@3: 3.910064697265625e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.8@3: 3.0994415283203125e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp2@3 <= attn0.0@3: 2.956390380859375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.14@3 <= embedding@3: 0.00010156631469726562\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.11@3 <= embedding@3: 4.9114227294921875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.6@3 <= embedding@3: 4.57763671875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.3@3 <= embedding@3: 3.814697265625e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.8@3 <= embedding@3: 3.7670135498046875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.9@3 <= embedding@3: 3.7670135498046875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.15@3 <= embedding@3: 3.4809112548828125e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp2@3 <= embedding@3: 4.291534423828125e-06\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= embedding@3: 0.0\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp0@3 <= embedding@3: -3.337860107421875e-06\n",
      "\n",
      "Paths of length 3:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.14@3 <= embedding@3: 0.00010156631469726562\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.14@3 <= embedding@3: 9.5367431640625e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.15@3 <= embedding@3: 7.724761962890625e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.13@3 <= embedding@3: 7.009506225585938e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.0@3 <= embedding@3: 6.771087646484375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.2@3 <= embedding@3: 5.4836273193359375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.11@3 <= embedding@3: 4.9114227294921875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= attn0.6@3 <= embedding@3: 4.57763671875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.6@3 <= embedding@3: 4.1484832763671875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.3@3 <= embedding@3: 3.910064697265625e-05\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = patch_get_max_paths(model, cur_embeddings_female, cur_embeddings_male, better_diff_ln_f_normal, 3, 10,\n",
    "    starting_path=list(reversed([\n",
    "        {'layer': 19, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 16, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "        {'layer': 12, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "    ]))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "c7a742e1-a089-4ebc-9225-c244dbb32e53",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paths of length 1:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3: 0.011085033416748047\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3: 0.008693218231201172\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp1@3: 0.00819540023803711\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3: 0.005135536193847656\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp0@3: 0.004185676574707031\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn0.9@3: 0.0016169548034667969\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp10@3: 0.0014848709106445312\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn8.14@3: 0.0014500617980957031\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn0.14@3: 0.0014009475708007812\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp6@3: 0.0013060569763183594\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= embedding@3: -0.00014925003051757812\n",
      "\n",
      "Paths of length 2:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3: 0.004630088806152344\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp0@3: 0.004534244537353516\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= mlp1@3: 0.002342700958251953\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3: 0.0021376609802246094\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= mlp1@3: 0.0018582344055175781\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= mlp0@3: 0.0018200874328613281\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= mlp0@3: 0.0017361640930175781\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp10@3 <= mlp1@3: 0.0011358261108398438\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp6@3 <= mlp4@3: 0.0010104179382324219\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= mlp5@3: 0.0009679794311523438\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn0.9@3 <= embedding@3: 0.0016169548034667969\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn0.14@3 <= embedding@3: 0.0014009475708007812\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp6@3 <= embedding@3: 0.00014781951904296875\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp10@3 <= embedding@3: 5.626678466796875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp0@3 <= embedding@3: 2.4318695068359375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= embedding@3: 2.193450927734375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= embedding@3: -4.76837158203125e-07\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn8.14@3 <= embedding@3: -6.198883056640625e-06\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= embedding@3: -6.67572021484375e-06\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp1@3 <= embedding@3: -5.1021575927734375e-05\n",
      "\n",
      "Paths of length 3:\n",
      "===================\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp1@3: 0.0009961128234863281\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= mlp0@3: 0.0009665489196777344\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= mlp5@3 <= mlp0@3: 0.0006761550903320312\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= mlp1@3 <= attn0.8@3: 0.0005140304565429688\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3 <= attn0.14@3: 0.0004229545593261719\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3 <= attn0.15@3: 0.0003714561462402344\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= mlp5@3 <= attn0.8@3: 0.0003285408020019531\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn6.6@3 <= mlp1@3 <= attn0.13@3: 0.0003247261047363281\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp6@3 <= mlp4@3 <= mlp0@3: 0.0003209114074707031\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= mlp5@3 <= attn0.4@3: 0.00031185150146484375\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn0.9@3 <= embedding@3: 0.0016169548034667969\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn0.14@3 <= embedding@3: 0.0014009475708007812\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp6@3 <= embedding@3: 0.00014781951904296875\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp10@3 <= embedding@3: 5.626678466796875e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp0@3 <= embedding@3: 2.4318695068359375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp8@3 <= embedding@3: 2.193450927734375e-05\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= mlp10@3 <= mlp1@3 <= embedding@3: 8.106231689453125e-06\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= attn6.6@3 <= embedding@3: 0.0\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= embedding@3: -4.76837158203125e-07\n",
      "mlp19@-1 <= mlp16@-1 <= attn15.13@3 <= mlp12@3 <= attn9.1@3 <= mlp0@3 <= embedding@3: -5.245208740234375e-06\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = patch_get_max_paths(model, cur_embeddings_female, cur_embeddings_male, better_diff_ln_f_normal, 3, 10,\n",
    "    starting_path=list(reversed([\n",
    "        {'layer': 19, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 16, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "        {'layer': 12, 'sublayer': 'mlp', 'token': 3, 'head': -1}\n",
    "    ]))\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "12869e33-d228-48cf-a8c6-dbfebae1252c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Paths of length 1:\n",
      "===================\n",
      "attn13.11@5: 3.427302122116089\n",
      "mlp18@-1: 2.334465980529785\n",
      "attn17.14@4: 1.6759061813354492\n",
      "mlp16@-1: 1.548098087310791\n",
      "mlp19@-1: 1.0288801193237305\n",
      "attn17.14@9: 0.8834958076477051\n",
      "attn17.14@10: 0.8299517631530762\n",
      "mlp17@-1: 0.6939740180969238\n",
      "attn13.11@4: 0.6556978225708008\n",
      "attn17.14@5: 0.6509799957275391\n",
      "attn15.13@5: 0.5109343528747559\n",
      "mlp15@-1: 0.3280806541442871\n",
      "attn15.13@3: 0.28732824325561523\n",
      "attn18.11@8: 0.27251768112182617\n",
      "attn17.14@8: 0.26997947692871094\n",
      "attn13.3@3: 0.26619482040405273\n",
      "attn17.14@3: 0.2450103759765625\n",
      "attn23.0@11: 0.22838592529296875\n",
      "attn15.13@4: 0.20160531997680664\n",
      "attn13.11@6: 0.19784832000732422\n",
      "embedding@-1: 0.0\n",
      "\n",
      "Paths of length 2:\n",
      "===================\n",
      "attn13.11@5 <= attn9.1@3: 1.33689546585083\n",
      "attn13.11@5 <= attn6.6@3: 0.8091940879821777\n",
      "attn17.14@4 <= attn13.3@3: 0.4383659362792969\n",
      "mlp16@-1 <= attn13.3@3: 0.3755531311035156\n",
      "attn17.14@4 <= attn9.1@3: 0.34485578536987305\n",
      "mlp17@-1 <= attn13.11@5: 0.3383779525756836\n",
      "attn13.11@4 <= attn9.1@3: 0.3243894577026367\n",
      "attn17.14@10 <= attn9.1@3: 0.31556034088134766\n",
      "attn13.11@5 <= attn10.5@5: 0.3076443672180176\n",
      "attn15.13@5 <= mlp12@5: 0.2980780601501465\n",
      "attn17.14@4 <= attn15.13@3: 0.257474422454834\n",
      "attn17.14@4 <= mlp12@4: 0.24575042724609375\n",
      "attn18.11@8 <= mlp12@8: 0.22520208358764648\n",
      "attn13.11@5 <= attn7.12@4: 0.22105884552001953\n",
      "mlp16@-1 <= attn13.11@5: 0.2202315330505371\n",
      "mlp16@-1 <= attn13.3@8: 0.21593809127807617\n",
      "mlp16@-1 <= attn9.1@3: 0.2105250358581543\n",
      "attn13.11@5 <= attn10.5@4: 0.17593812942504883\n",
      "attn17.14@5 <= attn13.3@3: 0.17308568954467773\n",
      "attn13.11@5 <= attn10.5@3: 0.15626096725463867\n",
      "mlp18@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "mlp17@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "embedding@-1: 0.0\n",
      "attn13.11@5 <= embedding@5: 0.0\n",
      "attn17.14@4 <= embedding@4: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "attn17.14@9 <= embedding@9: 0.0\n",
      "attn17.14@10 <= embedding@10: 0.0\n",
      "attn13.11@4 <= embedding@4: 0.0\n",
      "attn17.14@5 <= embedding@5: 0.0\n",
      "attn15.13@5 <= embedding@5: 0.0\n",
      "attn18.11@8 <= embedding@8: 0.0\n",
      "attn17.14@8 <= embedding@8: 0.0\n",
      "attn23.0@11 <= embedding@11: 0.0\n",
      "attn15.13@4 <= embedding@4: 0.0\n",
      "attn13.11@6 <= embedding@6: 0.0\n",
      "mlp16@-1 <= embedding@-1: -4.76837158203125e-07\n",
      "mlp15@-1 <= embedding@-1: -4.76837158203125e-07\n",
      "attn15.13@3 <= embedding@3: -4.291534423828125e-06\n",
      "attn13.3@3 <= embedding@3: -5.1021575927734375e-05\n",
      "\n",
      "Paths of length 3:\n",
      "===================\n",
      "attn13.11@5 <= attn6.6@3 <= mlp1@3: 0.44770383834838867\n",
      "attn13.11@5 <= attn6.6@3 <= mlp0@3: 0.42350244522094727\n",
      "attn13.11@5 <= attn9.1@3 <= mlp1@3: 0.3361649513244629\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3: 0.3288254737854004\n",
      "attn13.11@5 <= attn9.1@3 <= mlp0@3: 0.30481624603271484\n",
      "attn15.13@5 <= mlp12@5 <= attn9.1@3: 0.24492216110229492\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3: 0.20327425003051758\n",
      "mlp17@-1 <= attn13.11@5 <= attn9.1@3: 0.18024110794067383\n",
      "attn18.11@8 <= mlp12@8 <= attn9.1@3: 0.16224336624145508\n",
      "attn17.14@4 <= mlp12@4 <= attn6.6@3: 0.1566624641418457\n",
      "attn15.13@5 <= mlp12@5 <= attn6.6@3: 0.1527853012084961\n",
      "attn13.11@5 <= attn10.5@5 <= attn6.6@3: 0.15015602111816406\n",
      "mlp16@-1 <= attn13.11@5 <= attn9.1@3: 0.1443042755126953\n",
      "attn18.11@8 <= mlp12@8 <= attn6.6@3: 0.12981700897216797\n",
      "mlp17@-1 <= attn13.11@5 <= attn6.6@3: 0.12578821182250977\n",
      "attn17.14@4 <= attn15.13@3 <= mlp12@3: 0.09822702407836914\n",
      "attn13.11@5 <= attn9.1@3 <= mlp6@3: 0.09787988662719727\n",
      "attn17.14@4 <= attn9.1@3 <= mlp0@3: 0.08853960037231445\n",
      "attn13.11@5 <= attn6.6@3 <= mlp2@3: 0.08747339248657227\n",
      "attn13.11@5 <= attn9.1@3 <= mlp5@3: 0.08484411239624023\n",
      "attn13.11@5 <= attn10.5@3 <= embedding@3: 8.249282836914062e-05\n",
      "attn17.14@4 <= attn15.13@3 <= embedding@3: 2.09808349609375e-05\n",
      "mlp18@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "mlp17@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "mlp17@-1 <= attn13.11@5 <= embedding@5: 4.76837158203125e-07\n",
      "embedding@-1: 0.0\n",
      "attn13.11@5 <= embedding@5: 0.0\n",
      "attn17.14@4 <= embedding@4: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "attn17.14@9 <= embedding@9: 0.0\n",
      "attn17.14@10 <= embedding@10: 0.0\n",
      "attn13.11@4 <= embedding@4: 0.0\n",
      "attn17.14@5 <= embedding@5: 0.0\n",
      "attn15.13@5 <= embedding@5: 0.0\n",
      "attn18.11@8 <= embedding@8: 0.0\n",
      "attn17.14@8 <= embedding@8: 0.0\n",
      "attn23.0@11 <= embedding@11: 0.0\n",
      "attn15.13@4 <= embedding@4: 0.0\n",
      "attn13.11@6 <= embedding@6: 0.0\n",
      "attn13.11@5 <= attn10.5@5 <= embedding@5: 0.0\n",
      "\n",
      "Paths of length 4:\n",
      "===================\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3: 0.18532848358154297\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp0@3: 0.17064619064331055\n",
      "attn17.14@4 <= mlp12@4 <= attn6.6@3 <= mlp1@3: 0.0882258415222168\n",
      "attn17.14@4 <= mlp12@4 <= attn6.6@3 <= mlp0@3: 0.08332204818725586\n",
      "attn13.11@5 <= attn10.5@5 <= attn6.6@3 <= mlp1@3: 0.08254146575927734\n",
      "attn13.11@5 <= attn10.5@5 <= attn6.6@3 <= mlp0@3: 0.08019685745239258\n",
      "mlp17@-1 <= attn13.11@5 <= attn6.6@3 <= mlp1@3: 0.07691574096679688\n",
      "attn15.13@5 <= mlp12@5 <= attn6.6@3 <= mlp1@3: 0.0755009651184082\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= mlp1@3: 0.07542610168457031\n",
      "attn18.11@8 <= mlp12@8 <= attn6.6@3 <= mlp1@3: 0.07135772705078125\n",
      "attn15.13@5 <= mlp12@5 <= attn6.6@3 <= mlp0@3: 0.07019472122192383\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= attn6.6@3: 0.0701436996459961\n",
      "attn13.11@5 <= attn6.6@3 <= mlp2@3 <= mlp0@3: 0.06853008270263672\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= mlp0@3: 0.06675386428833008\n",
      "attn18.11@8 <= mlp12@8 <= attn6.6@3 <= mlp0@3: 0.06638813018798828\n",
      "mlp17@-1 <= attn13.11@5 <= attn6.6@3 <= mlp0@3: 0.06206703186035156\n",
      "mlp17@-1 <= attn13.11@5 <= attn9.1@3 <= mlp0@3: 0.05882453918457031\n",
      "attn15.13@5 <= mlp12@5 <= attn9.1@3 <= mlp1@3: 0.056611061096191406\n",
      "mlp17@-1 <= attn13.11@5 <= attn9.1@3 <= mlp1@3: 0.055787086486816406\n",
      "attn15.13@5 <= mlp12@5 <= attn9.1@3 <= attn6.6@3: 0.05176258087158203\n",
      "attn13.11@5 <= attn9.1@3 <= mlp6@3 <= embedding@3: 0.0047321319580078125\n",
      "attn13.11@5 <= attn6.6@3 <= mlp2@3 <= embedding@3: 0.0013599395751953125\n",
      "mlp16@-1 <= attn13.11@5 <= attn9.1@3 <= embedding@3: 0.0007224082946777344\n",
      "attn13.11@5 <= attn10.5@3 <= embedding@3: 8.249282836914062e-05\n",
      "attn18.11@8 <= mlp12@8 <= attn9.1@3 <= embedding@3: 6.818771362304688e-05\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= embedding@3: 3.6716461181640625e-05\n",
      "attn17.14@4 <= attn15.13@3 <= embedding@3: 2.09808349609375e-05\n",
      "attn15.13@5 <= mlp12@5 <= attn9.1@3 <= embedding@3: 1.6689300537109375e-05\n",
      "mlp18@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "mlp17@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "mlp17@-1 <= attn13.11@5 <= embedding@5: 4.76837158203125e-07\n",
      "embedding@-1: 0.0\n",
      "attn13.11@5 <= embedding@5: 0.0\n",
      "attn17.14@4 <= embedding@4: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "attn17.14@9 <= embedding@9: 0.0\n",
      "attn17.14@10 <= embedding@10: 0.0\n",
      "attn13.11@4 <= embedding@4: 0.0\n",
      "attn17.14@5 <= embedding@5: 0.0\n",
      "attn15.13@5 <= embedding@5: 0.0\n",
      "\n",
      "Paths of length 5:\n",
      "===================\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= attn6.6@3 <= mlp1@3: 0.038521766662597656\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= attn6.6@3 <= mlp0@3: 0.035794734954833984\n",
      "attn15.13@5 <= mlp12@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3: 0.027740955352783203\n",
      "attn15.13@5 <= mlp12@5 <= attn9.1@3 <= attn6.6@3 <= mlp0@3: 0.025702476501464844\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.14@3: 0.01629781723022461\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.15@3: 0.013331890106201172\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.13@3: 0.01225900650024414\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.0@3: 0.011886119842529297\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.2@3: 0.009170055389404297\n",
      "attn17.14@4 <= mlp12@4 <= attn6.6@3 <= mlp1@3 <= attn0.14@3: 0.007791996002197266\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.3@3: 0.006853580474853516\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= mlp1@3 <= attn0.14@3: 0.006653308868408203\n",
      "attn18.11@8 <= mlp12@8 <= attn6.6@3 <= mlp1@3 <= attn0.14@3: 0.006648540496826172\n",
      "attn13.11@5 <= attn10.5@5 <= attn6.6@3 <= mlp1@3 <= attn0.14@3: 0.006526470184326172\n",
      "attn17.14@4 <= mlp12@4 <= attn6.6@3 <= mlp1@3 <= attn0.15@3: 0.006291866302490234\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.6@3: 0.006194591522216797\n",
      "attn15.13@5 <= mlp12@5 <= attn6.6@3 <= mlp1@3 <= attn0.14@3: 0.006148815155029297\n",
      "attn17.14@4 <= mlp12@4 <= attn6.6@3 <= mlp1@3 <= attn0.13@3: 0.006104946136474609\n",
      "attn13.11@5 <= attn9.1@3 <= attn6.6@3 <= mlp1@3 <= attn0.11@3: 0.005971431732177734\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= attn6.6@3 <= mlp2@3: 0.0058746337890625\n",
      "attn13.11@5 <= attn9.1@3 <= mlp6@3 <= embedding@3: 0.0047321319580078125\n",
      "attn13.11@5 <= attn6.6@3 <= mlp2@3 <= embedding@3: 0.0013599395751953125\n",
      "mlp16@-1 <= attn13.11@5 <= attn9.1@3 <= embedding@3: 0.0007224082946777344\n",
      "attn13.11@5 <= attn10.5@3 <= embedding@3: 8.249282836914062e-05\n",
      "attn18.11@8 <= mlp12@8 <= attn9.1@3 <= embedding@3: 6.818771362304688e-05\n",
      "attn17.14@4 <= mlp12@4 <= attn9.1@3 <= embedding@3: 3.6716461181640625e-05\n",
      "attn17.14@4 <= attn15.13@3 <= embedding@3: 2.09808349609375e-05\n",
      "attn15.13@5 <= mlp12@5 <= attn9.1@3 <= embedding@3: 1.6689300537109375e-05\n",
      "attn13.11@5 <= attn6.6@3 <= mlp2@3 <= mlp0@3 <= embedding@3: 1.1920928955078125e-05\n",
      "mlp18@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "mlp17@-1 <= embedding@-1: 4.76837158203125e-07\n",
      "mlp17@-1 <= attn13.11@5 <= embedding@5: 4.76837158203125e-07\n",
      "embedding@-1: 0.0\n",
      "attn13.11@5 <= embedding@5: 0.0\n",
      "attn17.14@4 <= embedding@4: 0.0\n",
      "mlp19@-1 <= embedding@-1: 0.0\n",
      "attn17.14@9 <= embedding@9: 0.0\n",
      "attn17.14@10 <= embedding@10: 0.0\n",
      "attn13.11@4 <= embedding@4: 0.0\n",
      "attn17.14@5 <= embedding@5: 0.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "_ = patch_get_max_paths(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal, 5, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fa91749-09b0-42ee-931b-f4031a11b1fb",
   "metadata": {},
   "source": [
    "## Finding feature vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "2042893d-2447-450b-97af-4f707f0ab901",
   "metadata": {},
   "outputs": [],
   "source": [
    "occu_mlp1_normal = get_normal_for_path(model, cur_occu_embeddings_female, cur_occu_embeddings_male, occu_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 19, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 16, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "        {'layer': 12, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "        {'layer': 1, 'sublayer': 'mlp', 'token': 3, 'head': -1}\n",
    "    ], use_ln=False, normalize=True\n",
    ")\n",
    "\n",
    "occu_mlp1_attn0_normal = get_normal_for_path(model, cur_occu_embeddings_female, cur_occu_embeddings_male, occu_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 19, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 16, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "        {'layer': 12, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "        {'layer': 1, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 0, 'sublayer': 'attn', 'token': 3, 'head': -1},\n",
    "    ], use_ln=False, normalize=True\n",
    ")\n",
    "\n",
    "occu_attn6_normal = get_normal_for_path(model, cur_occu_embeddings_female, cur_occu_embeddings_male, occu_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 19, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 16, 'sublayer': 'mlp', 'token': -1, 'head': -1},\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "        {'layer': 12, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "    ], use_ln=False, normalize=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "dabb78cd-f83f-4053-9078-194e73791e6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_mlp1_normal = get_normal_for_path(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 13, 'sublayer': 'attn', 'token': 3, 'head': 11},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "        {'layer': 1, 'sublayer': 'mlp', 'token': 3, 'head': -1}\n",
    "    ], use_ln=False, normalize=True\n",
    ")\n",
    "\n",
    "subj_mlp1_attn0_normal = get_normal_for_path(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 13, 'sublayer': 'attn', 'token': 3, 'head': 11},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "        {'layer': 1, 'sublayer': 'mlp', 'token': 3, 'head': -1},\n",
    "        {'layer': 0, 'sublayer': 'attn', 'token': 3, 'head': -1}\n",
    "    ], use_ln=False, normalize=True\n",
    ")\n",
    "\n",
    "subj_attn6_normal = get_normal_for_path(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 13, 'sublayer': 'attn', 'token': 3, 'head': 11},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "    ], use_ln=False, normalize=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "f05c7cd6-99fe-4aed-aebd-5f16825e133b",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_attn6_normal_with_mag = get_normal_for_path(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 13, 'sublayer': 'attn', 'token': 3, 'head': 11},\n",
    "        {'layer': 9, 'sublayer': 'attn', 'token': 3, 'head': 1},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 3, 'head': 6},\n",
    "    ], use_ln=True\n",
    ")\n",
    "\n",
    "obj_attn6_normal_with_mag = get_normal_for_path(model, cur_obj_embeddings_female, cur_obj_embeddings_male, obj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 13, 'sublayer': 'attn', 'token': 6, 'head': 11},\n",
    "        {'layer': 6, 'sublayer': 'attn', 'token': 6, 'head': 6},\n",
    "    ], use_ln=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "7ea54719-a232-4efe-8392-2aa06b5ee6fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9520992040634155"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cossim(subj_attn6_normal_with_mag, obj_attn6_normal_with_mag).item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "768bded7-0963-4b8c-8a4a-b5b3c58be1a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(0.9771, device='cuda:0'),\n",
       " tensor(0.9750, device='cuda:0'),\n",
       " tensor(0.9663, device='cuda:0'))"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cossim(subj_mlp1_normal, occu_mlp1_normal),\\\n",
    "cossim(subj_mlp1_attn0_normal, occu_mlp1_attn0_normal),\\\n",
    "cossim(subj_attn6_normal, occu_attn6_normal)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca23531d-7567-43e2-9aba-e812417d86a0",
   "metadata": {},
   "source": [
    "# Get observable scores and feature scores"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8a02e69-2b70-4236-81cd-5be532978301",
   "metadata": {},
   "source": [
    "## Occupations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "8e1509e5-aa28-48df-bf01-c63cc5c2b484",
   "metadata": {},
   "outputs": [],
   "source": [
    "occu_observable = make_lm_head_normal([' nurse', ' teacher', ' secretary'], [' programmer', ' doctor', ' engineer'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "a382a620-9b82-4990-a634-9fd45f68d049",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "300it [03:54,  1.28it/s]\n",
      "300it [03:54,  1.28it/s]\n"
     ]
    }
   ],
   "source": [
    "occu_scores_male = get_normal_list_scores_for_prompt_list(model,[\n",
    "    {'normal': occu_mlp1_normal.detach().cpu().numpy(), 'layer': 1, 'sublayer': 'ln_2_in', 'token': 3, 'name': 'occu_mlp1_normal'},\n",
    "    {'normal': occu_attn6_normal.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': 3, 'name': 'occu_attn6_normal'},\n",
    "    {'normal': occu_observable.detach().cpu().numpy(), 'layer': None, 'sublayer': 'lm_out', 'token': -1, 'name': 'occu_observable'},\n",
    "], occu_prompts_male)\n",
    "\n",
    "occu_scores_female = get_normal_list_scores_for_prompt_list(model,[\n",
    "    {'normal': occu_mlp1_normal.detach().cpu().numpy(), 'layer': 1, 'sublayer': 'ln_2_in', 'token': 3, 'name': 'occu_mlp1_normal'},\n",
    "    {'normal': occu_attn6_normal.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': 3, 'name': 'occu_attn6_normal'},\n",
    "    {'normal': occu_observable.detach().cpu().numpy(), 'layer': None, 'sublayer': 'lm_out', 'token': -1, 'name': 'occu_observable'},\n",
    "], occu_prompts_female)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90ce07ba-5c5c-44ed-b600-329e4b534131",
   "metadata": {},
   "source": [
    "## Pronouns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "d60b17ae-8650-4398-949e-808a80f7d9ca",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_observable = make_lm_head_normal([' she'], [' he'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "7f17125f-a7e6-4a4f-8091-1bf8d7223352",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "300it [03:55,  1.28it/s]\n",
      "300it [03:55,  1.28it/s]\n"
     ]
    }
   ],
   "source": [
    "subj_scores_male = get_normal_list_scores_for_prompt_list(model,[\n",
    "    {'normal': subj_mlp1_normal.detach().cpu().numpy(), 'layer': 1, 'sublayer': 'ln_2_in', 'token': 3, 'name': 'subj_mlp1_normal'},\n",
    "    {'normal': subj_attn6_normal.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': 3, 'name': 'subj_attn6_normal'},\n",
    "    {'normal': subj_observable.detach().cpu().numpy(), 'layer': None, 'sublayer': 'lm_out', 'token': -1, 'name': 'subj_observable'},\n",
    "], subj_prompts_male)\n",
    "\n",
    "subj_scores_female = get_normal_list_scores_for_prompt_list(model,[\n",
    "    {'normal': subj_mlp1_normal.detach().cpu().numpy(), 'layer': 1, 'sublayer': 'ln_2_in', 'token': 3, 'name': 'subj_mlp1_normal'},\n",
    "    {'normal': subj_attn6_normal.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': 3, 'name': 'subj_attn6_normal'},\n",
    "    {'normal': subj_observable.detach().cpu().numpy(), 'layer': None, 'sublayer': 'lm_out', 'token': -1, 'name': 'subj_observable'},\n",
    "], subj_prompts_female)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a1cb9bc-1f90-4616-bcc4-20d58ce793b5",
   "metadata": {},
   "source": [
    "## Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "d7750436-3c4e-43c7-ad5a-549b90f7a7a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "pickle.dump({\n",
    "    'occu_scores_male': occu_scores_male,\n",
    "    'occu_scores_female': occu_scores_female,\n",
    "    'subj_scores_male': subj_scores_male,\n",
    "    'subj_scores_female': subj_scores_female,\n",
    "}, open(\"normal_scores_new.pkl\", \"wb\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "f087b22a-6adb-4583-a862-94b5ab51978e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "my_scores = pickle.load(open(\"normal_scores_new.pkl\", \"rb\"))\n",
    "occu_scores_male = my_scores['occu_scores_male']\n",
    "occu_scores_female = my_scores['occu_scores_female']\n",
    "subj_scores_male = my_scores['subj_scores_male']\n",
    "subj_scores_female = my_scores['subj_scores_female']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "c8eaba2a-78b4-4799-aa2d-58655984bc7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "84f803a5-fce9-4e8c-840d-4aa82b6f7d3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Polynomial([0.01955477, 0.50863145], domain=[-1.,  1.], window=[-1.,  1.], symbol='x'),\n",
       " array([0.8816692], dtype=float32))"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = occu_scores_male[1]['scores'] + occu_scores_female[1]['scores']\n",
    "ys = occu_scores_male[2]['scores'] + occu_scores_female[2]['scores']\n",
    "\n",
    "fit, fit_info = np.polynomial.Polynomial.fit(xs, ys, 1, full=True)\n",
    "fit = fit.convert()\n",
    "r2 = 1 - fit_info[0] / (len(ys) * np.array(ys).var())\n",
    "fit, r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "464a60e9-ce76-45af-9441-b0f464d5d1d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x152d2d004dc0>"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = occu_scores_male[1]['scores'] + occu_scores_female[1]['scores']\n",
    "ys = occu_scores_male[2]['scores'] + occu_scores_female[2]['scores']\n",
    "\n",
    "fit, fit_info = np.polynomial.Polynomial.fit(xs, ys, 1, full=True)\n",
    "fit = fit.convert()\n",
    "r2 = 1 - fit_info[0] / (len(ys) * np.array(ys).var())\n",
    "fit, r2\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.scatter(occu_scores_male[1]['scores'][:100], occu_scores_male[-1]['scores'][:100])\n",
    "ax.scatter(occu_scores_female[1]['scores'][:100], occu_scores_female[-1]['scores'][:100])\n",
    "\n",
    "ax.scatter(occu_scores_male[1]['scores'][100:200], occu_scores_male[-1]['scores'][100:200])\n",
    "ax.scatter(occu_scores_female[1]['scores'][100:200], occu_scores_female[-1]['scores'][100:200])\n",
    "\n",
    "ax.scatter(occu_scores_male[1]['scores'][200:300], occu_scores_male[-1]['scores'][200:300])\n",
    "ax.scatter(occu_scores_female[1]['scores'][200:300], occu_scores_female[-1]['scores'][200:300])\n",
    "\n",
    "\n",
    "xmin, xmax = ax.get_xlim()\n",
    "ax.plot([xmin, xmax], fit.coef[0] + np.array([xmin, xmax])*fit.coef[1], label=f'Best fit $r^2 = {r2[0]:.3f}$')\n",
    "plt.xlabel(\"Normalized 6::6 feature vector score\", fontsize=12)\n",
    "plt.ylabel(\"Language model output score for $n_{bias}$\", fontsize=12)\n",
    "plt.title(\"$n_{bias}$ score versus 6::6 feature vector score\", fontsize=15)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "a55dce82-6ab1-4ef0-ad09-79d52fcef130",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x152d2cf4cf10>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = subj_scores_male[1]['scores'] + subj_scores_female[1]['scores']\n",
    "ys = subj_scores_male[-1]['scores'] + subj_scores_female[-1]['scores']\n",
    "\n",
    "fit, fit_info = np.polynomial.Polynomial.fit(xs, ys, 1, full=True)\n",
    "fit = fit.convert()\n",
    "r2 = 1 - fit_info[0] / (len(ys) * np.array(ys).var())\n",
    "fit, r2\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.scatter(subj_scores_male[1]['scores'][:100], subj_scores_male[-1]['scores'][:100])\n",
    "ax.scatter(subj_scores_female[1]['scores'][:100], subj_scores_female[-1]['scores'][:100])\n",
    "\n",
    "ax.scatter(subj_scores_male[1]['scores'][100:200], subj_scores_male[-1]['scores'][100:200])\n",
    "ax.scatter(subj_scores_female[1]['scores'][100:200], subj_scores_female[-1]['scores'][100:200])\n",
    "\n",
    "ax.scatter(subj_scores_male[1]['scores'][200:300], subj_scores_male[-1]['scores'][200:300])\n",
    "ax.scatter(subj_scores_female[1]['scores'][200:300], subj_scores_female[-1]['scores'][200:300])\n",
    "\n",
    "\n",
    "xmin, xmax = ax.get_xlim()\n",
    "ax.plot([xmin, xmax], fit.coef[0] + np.array([xmin, xmax])*fit.coef[1], label=f'Best fit $r^2 = {r2[0]:.3f}$')\n",
    "plt.xlabel(\"Normalized 6::6 feature vector score\", fontsize=12)\n",
    "plt.ylabel(\"Language model output score for $n_{subj}$\", fontsize=12)\n",
    "plt.title(\"$n_{subj}$ score versus 6::6 feature vector score\", fontsize=15)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a222641-4d15-4f4b-b404-95a89df8760a",
   "metadata": {},
   "source": [
    "# Top activating examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "6831a05a-9b49-401d-a494-351a4a6f4500",
   "metadata": {},
   "outputs": [],
   "source": [
    "def decode_prompt_and_tokens(prompts, prompt, mid_token, window_size=5):\n",
    "    print(tokenizer.batch_decode(prompts[prompt]['input_ids'][:,max(0,mid_token-window_size):mid_token+window_size]))\n",
    "    print(tokenizer.batch_decode(prompts[prompt]['input_ids'][:,mid_token]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "456c2506-10f4-49ad-810f-9193de420916",
   "metadata": {},
   "source": [
    "## Get scores on pile-10k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "375173a6-0ce2-4941-b1fb-8ed99cf7aebf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Found cached dataset parquet (/home/jhd43/.cache/huggingface/datasets/NeelNanda___parquet/NeelNanda--pile-10k-72f566e9f7c464ab/0.0.0/2a3b91fbd88a2c90d1dbbb32b460cf621d31bd5b05b934492fdef7d8d6f236ec)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2d34e8fc3ad447409f102765ace25860",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/1 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from datasets import load_dataset\n",
    "pile10k = load_dataset(\"NeelNanda/pile-10k\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "35a230a7-191e-4679-ac93-001a644f0a2b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Token indices sequence length is longer than the specified maximum sequence length for this model (3180 > 2048). Running this sequence through the model will result in indexing errors\n"
     ]
    }
   ],
   "source": [
    "tokenized_prompts = []\n",
    "for prompt in pile10k['train']['text']:\n",
    "    tokenized_prompts.append(tokenizer(prompt, return_tensors=\"pt\"))\n",
    "tokenized_prompts = slice_tokenized_prompts_into_context_windows(tokenized_prompts, 128, max_tokens=1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "56d12e88-b0bb-4627-a650-94a09e31eaa7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7860"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(tokenized_prompts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "76066b16-ef89-4ac8-9c5a-e5e2d3527800",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/gpfs/gibbs/project/cohan/jhd43/conda_envs/nlp_env/lib/python3.9/site-packages/torch/distributed/distributed_c10d.py:293: UserWarning: torch.distributed.reduce_op is deprecated, please use torch.distributed.ReduceOp instead\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_num_tensors()\n",
    "do_free()\n",
    "get_num_tensors()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "3e74b41b-5191-43bb-8f6a-fe8ac87d562b",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_attn17_normal_with_mag = get_normal_for_path(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 17, 'sublayer': 'attn', 'token': 3, 'head': 14},\n",
    "    ], use_ln=True\n",
    ")\n",
    "obj_attn17_normal_with_mag = get_normal_for_path(model, cur_obj_embeddings_female, cur_obj_embeddings_male, obj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 17, 'sublayer': 'attn', 'token': 6, 'head': 14},\n",
    "    ], use_ln=True\n",
    ")\n",
    "\n",
    "subj_attn15_normal_with_mag = get_normal_for_path(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 3, 'head': 13},\n",
    "    ], use_ln=True\n",
    ")\n",
    "obj_attn15_normal_with_mag = get_normal_for_path(model, cur_obj_embeddings_female, cur_obj_embeddings_male, obj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 15, 'sublayer': 'attn', 'token': 6, 'head': 13},\n",
    "    ], use_ln=True\n",
    ")\n",
    "\n",
    "subj_attn13_normal_with_mag = get_normal_for_path(model, cur_subj_embeddings_female, cur_subj_embeddings_male, subj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 13, 'sublayer': 'attn', 'token': 3, 'head': 11},\n",
    "    ], use_ln=True\n",
    ")\n",
    "obj_attn13_normal_with_mag = get_normal_for_path(model, cur_obj_embeddings_female, cur_obj_embeddings_male, obj_ln_f_normal,\n",
    "    [\n",
    "        {'layer': 13, 'sublayer': 'attn', 'token': 6, 'head': 11},\n",
    "    ], use_ln=True\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "0e0ef724-9dd1-47ef-aa18-f8ab889d19c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.7122678160667419, 0.8010773062705994, 0.7477921843528748)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coupling_coeff(subj_attn17_normal_with_mag, obj_attn17_normal_with_mag).item(),\\\n",
    "coupling_coeff(subj_attn15_normal_with_mag, obj_attn15_normal_with_mag).item(),\\\n",
    "coupling_coeff(subj_attn13_normal_with_mag, obj_attn13_normal_with_mag).item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "d9c147a6-dcd8-44fe-9564-817428846afb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.988246738910675, 0.981793224811554, 0.9359292387962341)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cossim(subj_attn17_normal_with_mag, obj_attn17_normal_with_mag).item(),\\\n",
    "cossim(subj_attn15_normal_with_mag, obj_attn15_normal_with_mag).item(),\\\n",
    "cossim(subj_attn13_normal_with_mag, obj_attn13_normal_with_mag).item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "fa4a8042-18a2-402d-9935-130439cb9480",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "7860it [3:07:12,  1.43s/it]\n"
     ]
    }
   ],
   "source": [
    "pile_scores = get_normal_list_scores_for_prompt_list(model,[\n",
    "    {'normal': occu_mlp1_normal.detach().cpu().numpy(), 'layer': 1, 'sublayer': 'ln_2_in', 'token': None, 'name': 'occu_mlp1_normal'},\n",
    "    {'normal': occu_attn6_normal.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'occu_attn6_normal'},\n",
    "    {'normal': subj_mlp1_normal.detach().cpu().numpy(), 'layer': 1, 'sublayer': 'ln_2_in', 'token': None, 'name': 'subj_mlp1_normal'},\n",
    "    {'normal': subj_attn6_normal.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'subj_attn6_normal'},\n",
    "    {'normal': obj_attn6_normal_with_mag.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'obj_attn6_normal_with_mag'},\n",
    "    {'normal': subj_attn17_normal_with_mag.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'subj_attn17_normal_with_mag'},\n",
    "    {'normal': obj_attn17_normal_with_mag.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'obj_attn17_normal_with_mag'},\n",
    "    {'normal': subj_attn15_normal_with_mag.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'subj_attn15_normal_with_mag'},\n",
    "    {'normal': obj_attn15_normal_with_mag.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'obj_attn15_normal_with_mag'},\n",
    "    {'normal': subj_attn13_normal_with_mag.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'subj_attn13_normal_with_mag'},\n",
    "    {'normal': obj_attn13_normal_with_mag.detach().cpu().numpy(), 'layer': 6, 'sublayer': 'ln_1_in', 'token': None, 'name': 'obj_attn13_normal_with_mag'},\n",
    "], tokenized_prompts, pre_tokenized=True, save_every=10, save_out=\"scores_on_pile.pkl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "b01ea97d-f2d5-4263-a6a0-5e0de96d18bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "pickle.dump(pile_scores, open(\"pile_scores_full.pkl\", \"wb\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4ee402d-e68e-4889-be48-f9ff7106f632",
   "metadata": {},
   "source": [
    "## `occu_mlp1_normal`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "346bd0ba-6c08-41c4-9838-67ef725053bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 298/298 [03:25<00:00,  1.45it/s]\n"
     ]
    }
   ],
   "source": [
    "occu_mlp1_top_scores = get_top_normal_scores_for_prompt_list(model, 1, 'ln_2_in', tokenized_prompts, occu_mlp1_normal, k=20, pre_tokenized=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "b7b8e338-54de-42b7-9be4-639f9a5c5ad9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[' across the globe with WebEx Meetings. In this course, author and webinar specialist Sally Norred shows you how to use WebEx Meetings to host, run, and']\n",
      "[' Sally']\n",
      "Score: 12.807328224182129\n",
      "\n",
      "[\"\\nHello! It's nice to meet you! I'm Mary. Thank you for stopping by Stirring Up Delight. I hope you'll find\"]\n",
      "[' Mary']\n",
      "Score: 12.135202407836914\n",
      "\n",
      "[' phosphate (Pi) uptake across the vacuolar membrane of intact vacuoles isolated from Catharanthus roseus suspension-cultured cells was measured. Under low Pi status,']\n",
      "[' Cath']\n",
      "Score: 12.103666305541992\n",
      "\n",
      "['Inorganic phosphate uptake in intact vacuoles isolated from suspension-cultured cells of Catharanthus roseus (L.) G. Don under varying Pi status.\\nIn']\n",
      "[' Cath']\n",
      "Score: 11.904487609863281\n",
      "\n",
      "[' theme. But how to make it work? Are you the borg, or fighting the Borg?\\n\\nThe third and final idea came to me through my girlfriend']\n",
      "[' Borg']\n",
      "Score: 11.679457664489746\n",
      "\n",
      "[' especially when the food is good. Good food tastes even better when enjoyed with people. Tonight Amy came over to try my second attempt at the Brussels Sprouts Veggie Soup to which']\n",
      "[' Amy']\n",
      "Score: 11.103818893432617\n",
      "\n",
      "[' Hódmezővásárhely – Doubles\\n\\nLaura Pigossi and Nadia Podoroska were the defending champions, but both players']\n",
      "['Laura']\n",
      "Score: 10.972723007202148\n",
      "\n",
      "[' and unfortunately now something really bad happened, and that’s scary,” said Francesco Fabba, who has lived on the block since 2009.\\n\\nHe pointed']\n",
      "[' Frances']\n",
      "Score: 10.936155319213867\n",
      "\n",
      "[' paid time off work during menstruation\\n• (often from male workers, who viewed the employment of women as competition']\n",
      "[' menstru']\n",
      "Score: 10.315485000610352\n",
      "\n",
      "[' will add 4,000 square feet to its current space. View Full Caption DNAinfo/Katie Honan\\n\\nJACKSON HEIGHTS — Indian grocery store Patel Brothers is']\n",
      "['Kat']\n",
      "Score: 10.14991569519043\n",
      "\n",
      "[', scientific researchers and labour hygiene specialists in the Soviet Union conducted extensive investigations into the impact of menstruation on women’s capacity to work in manual and industrial jobs requiring a significant']\n",
      "[' menstru']\n",
      "Score: 9.983203887939453\n",
      "\n",
      "[' simultaneous measurement of conjugate pairs of properties.\\n\\nFor example, the Heisenberg uncertainty principle states that one cannot simultaneously know, with arbitrarily high precision, both the position']\n",
      "['berg']\n",
      "Score: 9.952775001525879\n",
      "\n",
      "[' it is characterized by a\\nlifetime of a few nanoseconds of the lowest vibrational level of the first excited state.\\nDe-excitation from the excited sing']\n",
      "[' vibr']\n",
      "Score: 9.89829158782959\n",
      "\n",
      "['i Hark’s “Flying Swords of Dragon Gate;” and the Jackie Chan production-starring vehicle “CZ12,” which Huay']\n",
      "[' Jackie']\n",
      "Score: 9.744733810424805\n",
      "\n",
      "[' specific categories of women workers:\\n\\nDecree ‘On the release from work during menstruation of machinists and iron press workers working on cutting machines without mechanised gears']\n",
      "[' menstru']\n",
      "Score: 9.624755859375\n",
      "\n",
      "[' a few days later.  On January 8, 2004, more than four years later, Rose admitted publicly to betting on baseball games in his autobiography My Prison Without Bars.\\n\\n']\n",
      "[' Rose']\n",
      "Score: 9.476816177368164\n",
      "\n",
      "['a de recursividad y este simple código... mi pregunta ya que la variable counter comienza desde 10 y dentro del loop While el']\n",
      "[' ya']\n",
      "Score: 9.473194122314453\n",
      "\n",
      "[' at machines and on tractors resulted in congestion and tension in the abdomen that was exacerbated during menstruation. In practice, the decre']\n",
      "[' menstru']\n",
      "Score: 9.463767051696777\n",
      "\n",
      "[\" in Norway in February and March 1927, during which he received a letter from Werner Heisenberg regarding the latter's newly discovered (and not yet published) uncertainty principle. Upon returning\"]\n",
      "['berg']\n",
      "Score: 9.408309936523438\n",
      "\n",
      "['ővásárhely – Doubles\\n\\nLaura Pigossi and Nadia Podoroska were the defending champions, but both players chose not to participate.']\n",
      "[' Nad']\n",
      "Score: 9.402674674987793\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for entry in occu_mlp1_top_scores:\n",
    "    decode_prompt_and_tokens(tokenized_prompts, entry['prompt_idx'], entry['token_idx'], window_size=18)\n",
    "    print(f\"Score: {entry['score']}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae0fff58-a680-41c2-a8a0-a14dcd464f98",
   "metadata": {},
   "source": [
    "## `occu_attn6_normal`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "c92df76e-164a-462e-875b-981ee25a330b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 298/298 [03:26<00:00,  1.45it/s]\n"
     ]
    }
   ],
   "source": [
    "occu_attn6_top_scores = get_top_normal_scores_for_prompt_list(model, 6, 'ln_1_in', tokenized_prompts, occu_attn6_normal, k=20, pre_tokenized=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "3b62291a-513f-46eb-9f74-8e865966dcf3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[' add 4,000 square feet to its current space. View Full Caption DNAinfo/Katie Honan\\n\\nJACKSON HEIGHTS — Indian grocery store Patel Brothers is planning']\n",
      "['ie']\n",
      "Score: 11.403040885925293\n",
      "\n",
      "['.\\n\\nAn individual may bring a private right of action in federal court against his/her employer for such retaliation. In addition, the SEC may bring an enforcement action against a']\n",
      "['her']\n",
      "Score: 11.098417282104492\n",
      "\n",
      "['Jeanette Sawyer Cohen, PhD, clinical assistant professor of psychology in pediatrics at Weill Cornell']\n",
      "['ette']\n",
      "Score: 10.28715705871582\n",
      "\n",
      "['changing” economics, no matter how combatively BJP chief Amit Shah defended it in his maiden speech in the Rajya Sabha.\\n\\nYoung Indians of any class, on whose']\n",
      "[' maiden']\n",
      "Score: 10.135647773742676\n",
      "\n",
      "['�vásárhely – Doubles\\n\\nLaura Pigossi and Nadia Podoroska were the defending champions, but both players chose not to participate.\\n']\n",
      "['ia']\n",
      "Score: 10.087481498718262\n",
      "\n",
      "[' Hódmezővásárhely – Doubles\\n\\nLaura Pigossi and Nadia Podoroska were the defending champions, but both players']\n",
      "['Laura']\n",
      "Score: 9.996930122375488\n",
      "\n",
      "[', or fighting the Borg?\\n\\nThe third and final idea came to me through my girlfriend']\n",
      "[' girlfriend']\n",
      "Score: 9.702834129333496\n",
      "\n",
      "[' extensive research conducted for my PhD, is devoted to ‘Provision for “Menstrual Leave”’.\\n\\nIn the 1920s, scientific researchers and']\n",
      "['stru']\n",
      "Score: 9.455649375915527\n",
      "\n",
      "['isation, no analyst or political planner can afford to overlook jobless growth.\\n\\nPakora growth, a close enough synonym, staring the country in the face is hardly a']\n",
      "['ora']\n",
      "Score: 9.4014310836792\n",
      "\n",
      "[' and unfortunately now something really bad happened, and that’s scary,” said Francesco Fabba, who has lived on the block since 2009.\\n\\nHe pointed']\n",
      "[' Frances']\n",
      "Score: 9.190688133239746\n",
      "\n",
      "[' waters and my son was able to land a nice barracuda. The next day my wife, daughter, son […]\\n\\nWhen we arrived the crew made us feel right at']\n",
      "[' wife']\n",
      "Score: 9.141470909118652\n",
      "\n",
      "[\"'s Head. The topic was selling stuff he stole from Sirius' place:\\n\\nNikki: How did sirius twoway mirror end up with aberforth or is it another\"]\n",
      "['ki']\n",
      "Score: 8.33499526977539\n",
      "\n",
      "[' chains in other territories have ordered IMAX screens in ones and twos, Dalian Wanda in March 2011 put in an order for 75 screens. In Nov 2012 South Korea�']\n",
      "['anda']\n",
      "Score: 8.258329391479492\n",
      "\n",
      "[\"\\nHello! It's nice to meet you! I'm Mary. Thank you for stopping by Stirring Up Delight. I hope you'll find\"]\n",
      "[' Mary']\n",
      "Score: 8.189534187316895\n",
      "\n",
      "[' and is a genuine made-in-China co-venture involving China Film Group, Wanda Media, Village Roadshow Pictures Asia, and Universal Pictures.\\n\\nThe contemporary action']\n",
      "['anda']\n",
      "Score: 8.111015319824219\n",
      "\n",
      "[' of sickness than their female colleagues. Many of the problems experienced by women in the workplace could be mitigated by']\n",
      "[' female']\n",
      "Score: 8.006994247436523\n",
      "\n",
      "[' especially when the food is good. Good food tastes even better when enjoyed with people. Tonight Amy came over to try my second attempt at the Brussels Sprouts Veggie Soup to which']\n",
      "[' Amy']\n",
      "Score: 7.959303855895996\n",
      "\n",
      "[' across the globe with WebEx Meetings. In this course, author and webinar specialist Sally Norred shows you how to use WebEx Meetings to host, run, and']\n",
      "[' Sally']\n",
      "Score: 7.891899108886719\n",
      "\n",
      "['’re going to have to tell her you’ll help a little. Go ahead and help, but let her do']\n",
      "[' her']\n",
      "Score: 7.804708003997803\n",
      "\n",
      "[' protect the professionalism of certain categories of workers: the debates here centred on performance artists and female theatrical employees engaged in highly physical and intensely emotional work\\n• heavy physical labour and stren']\n",
      "[' female']\n",
      "Score: 7.6647210121154785\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for entry in occu_attn6_top_scores:\n",
    "    decode_prompt_and_tokens(tokenized_prompts, entry['prompt_idx'], entry['token_idx'], window_size=18)\n",
    "    print(f\"Score: {entry['score']}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2581f353-473b-4aea-b985-d578e3348aaf",
   "metadata": {},
   "source": [
    "## `subj_mlp1_normal`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "af89c71a-0af9-4122-bec2-6fed08e9dba3",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 298/298 [03:07<00:00,  1.59it/s]\n"
     ]
    }
   ],
   "source": [
    "subj_mlp1_top_scores = get_top_normal_scores_for_prompt_list(model, 1, 'ln_2_in', tokenized_prompts[:298], subj_mlp1_normal, k=20, pre_tokenized=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "1240f947-262b-4064-a070-6b968ba7abde",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[' across the globe with WebEx Meetings. In this course, author and webinar specialist Sally Norred shows you how to use WebEx Meetings to host, run, and']\n",
      "[' Sally']\n",
      "Score: 11.065218925476074\n",
      "\n",
      "[\"\\nHello! It's nice to meet you! I'm Mary. Thank you for stopping by Stirring Up Delight. I hope you'll find\"]\n",
      "[' Mary']\n",
      "Score: 10.82946491241455\n",
      "\n",
      "[' phosphate (Pi) uptake across the vacuolar membrane of intact vacuoles isolated from Catharanthus roseus suspension-cultured cells was measured. Under low Pi status,']\n",
      "[' Cath']\n",
      "Score: 10.75033950805664\n",
      "\n",
      "[' theme. But how to make it work? Are you the borg, or fighting the Borg?\\n\\nThe third and final idea came to me through my girlfriend']\n",
      "[' Borg']\n",
      "Score: 10.398216247558594\n",
      "\n",
      "[' especially when the food is good. Good food tastes even better when enjoyed with people. Tonight Amy came over to try my second attempt at the Brussels Sprouts Veggie Soup to which']\n",
      "[' Amy']\n",
      "Score: 10.381427764892578\n",
      "\n",
      "['Inorganic phosphate uptake in intact vacuoles isolated from suspension-cultured cells of Catharanthus roseus (L.) G. Don under varying Pi status.\\nIn']\n",
      "[' Cath']\n",
      "Score: 10.288225173950195\n",
      "\n",
      "[' Hódmezővásárhely – Doubles\\n\\nLaura Pigossi and Nadia Podoroska were the defending champions, but both players']\n",
      "['Laura']\n",
      "Score: 9.701141357421875\n",
      "\n",
      "[' and unfortunately now something really bad happened, and that’s scary,” said Francesco Fabba, who has lived on the block since 2009.\\n\\nHe pointed']\n",
      "[' Frances']\n",
      "Score: 9.693242073059082\n",
      "\n",
      "[' paid time off work during menstruation\\n• (often from male workers, who viewed the employment of women as competition']\n",
      "[' menstru']\n",
      "Score: 9.413023948669434\n",
      "\n",
      "[' will add 4,000 square feet to its current space. View Full Caption DNAinfo/Katie Honan\\n\\nJACKSON HEIGHTS — Indian grocery store Patel Brothers is']\n",
      "['Kat']\n",
      "Score: 9.285762786865234\n",
      "\n",
      "[', scientific researchers and labour hygiene specialists in the Soviet Union conducted extensive investigations into the impact of menstruation on women’s capacity to work in manual and industrial jobs requiring a significant']\n",
      "[' menstru']\n",
      "Score: 9.093881607055664\n",
      "\n",
      "[' robot\\'s name is \"Patrick\" and he\\'s an interactive butt.\\n\\nProfessor Benjamin Lok\\n\\n\"Patrick is part of a simulation where students get to practice prostate exams,\"']\n",
      "[' Lok']\n",
      "Score: 9.038108825683594\n",
      "\n",
      "[' a few days later.  On January 8, 2004, more than four years later, Rose admitted publicly to betting on baseball games in his autobiography My Prison Without Bars.\\n\\n']\n",
      "[' Rose']\n",
      "Score: 9.01738166809082\n",
      "\n",
      "[' at machines and on tractors resulted in congestion and tension in the abdomen that was exacerbated during menstruation. In practice, the decre']\n",
      "[' menstru']\n",
      "Score: 8.83597183227539\n",
      "\n",
      "[' specific categories of women workers:\\n\\nDecree ‘On the release from work during menstruation of machinists and iron press workers working on cutting machines without mechanised gears']\n",
      "[' menstru']\n",
      "Score: 8.806462287902832\n",
      "\n",
      "[' the regions and if you\\'re pressing with enough pressure,\" Lok continues.\\n\\nThe sensor displays traffic light-style signals of green, yellow or']\n",
      "[' Lok']\n",
      "Score: 8.74221134185791\n",
      "\n",
      "[' it is characterized by a\\nlifetime of a few nanoseconds of the lowest vibrational level of the first excited state.\\nDe-excitation from the excited sing']\n",
      "[' vibr']\n",
      "Score: 8.736566543579102\n",
      "\n",
      "[' see The MLB All-Century Team.\\n\\nSelected players\\n\\nPete Rose controversy\\nThere']\n",
      "[' Rose']\n",
      "Score: 8.665071487426758\n",
      "\n",
      "['ővásárhely – Doubles\\n\\nLaura Pigossi and Nadia Podoroska were the defending champions, but both players chose not to participate.']\n",
      "[' Nad']\n",
      "Score: 8.590447425842285\n",
      "\n",
      "[' Florida professor Benjamin Lok explains to As It Happens guest host Tom Harrington. \"The simulator itself is a']\n",
      "[' Lok']\n",
      "Score: 8.578767776489258\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for entry in subj_mlp1_top_scores:\n",
    "    decode_prompt_and_tokens(tokenized_prompts[:298], entry['prompt_idx'], entry['token_idx'], window_size=18)\n",
    "    print(f\"Score: {entry['score']}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9ec1ec4-ae9e-4bfa-9ed8-0aa0a54787a8",
   "metadata": {},
   "source": [
    "## `subj_attn6_normal`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "597d0b21-d117-49e4-aa8e-7929383ee6a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 298/298 [03:08<00:00,  1.58it/s]\n"
     ]
    }
   ],
   "source": [
    "subj_attn6_top_scores = get_top_normal_scores_for_prompt_list(model, 6, 'ln_1_in', tokenized_prompts[:298], subj_attn6_normal, k=20, pre_tokenized=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "debbb9c8-d635-4cfd-8744-64581cc4ae45",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['.\\n\\nAn individual may bring a private right of action in federal court against his/her employer for such retaliation. In addition, the SEC may bring an enforcement action against a']\n",
      "['her']\n",
      "Score: 11.647647857666016\n",
      "\n",
      "['Jeanette Sawyer Cohen, PhD, clinical assistant professor of psychology in pediatrics at Weill Cornell']\n",
      "['ette']\n",
      "Score: 11.624452590942383\n",
      "\n",
      "[' add 4,000 square feet to its current space. View Full Caption DNAinfo/Katie Honan\\n\\nJACKSON HEIGHTS — Indian grocery store Patel Brothers is planning']\n",
      "['ie']\n",
      "Score: 11.164230346679688\n",
      "\n",
      "['�vásárhely – Doubles\\n\\nLaura Pigossi and Nadia Podoroska were the defending champions, but both players chose not to participate.\\n']\n",
      "['ia']\n",
      "Score: 10.408307075500488\n",
      "\n",
      "[' Hódmezővásárhely – Doubles\\n\\nLaura Pigossi and Nadia Podoroska were the defending champions, but both players']\n",
      "['Laura']\n",
      "Score: 10.252385139465332\n",
      "\n",
      "[', or fighting the Borg?\\n\\nThe third and final idea came to me through my girlfriend']\n",
      "[' girlfriend']\n",
      "Score: 10.105398178100586\n",
      "\n",
      "['changing” economics, no matter how combatively BJP chief Amit Shah defended it in his maiden speech in the Rajya Sabha.\\n\\nYoung Indians of any class, on whose']\n",
      "[' maiden']\n",
      "Score: 9.551288604736328\n",
      "\n",
      "[' and unfortunately now something really bad happened, and that’s scary,” said Francesco Fabba, who has lived on the block since 2009.\\n\\nHe pointed']\n",
      "[' Frances']\n",
      "Score: 9.482931137084961\n",
      "\n",
      "[' waters and my son was able to land a nice barracuda. The next day my wife, daughter, son […]\\n\\nWhen we arrived the crew made us feel right at']\n",
      "[' wife']\n",
      "Score: 9.472848892211914\n",
      "\n",
      "['isation, no analyst or political planner can afford to overlook jobless growth.\\n\\nPakora growth, a close enough synonym, staring the country in the face is hardly a']\n",
      "['ora']\n",
      "Score: 9.19100284576416\n",
      "\n",
      "[\"\\nHello! It's nice to meet you! I'm Mary. Thank you for stopping by Stirring Up Delight. I hope you'll find\"]\n",
      "[' Mary']\n",
      "Score: 8.993080139160156\n",
      "\n",
      "[\"'s Head. The topic was selling stuff he stole from Sirius' place:\\n\\nNikki: How did sirius twoway mirror end up with aberforth or is it another\"]\n",
      "['ki']\n",
      "Score: 8.646184921264648\n",
      "\n",
      "[' especially when the food is good. Good food tastes even better when enjoyed with people. Tonight Amy came over to try my second attempt at the Brussels Sprouts Veggie Soup to which']\n",
      "[' Amy']\n",
      "Score: 8.521955490112305\n",
      "\n",
      "[' across the globe with WebEx Meetings. In this course, author and webinar specialist Sally Norred shows you how to use WebEx Meetings to host, run, and']\n",
      "[' Sally']\n",
      "Score: 8.417619705200195\n",
      "\n",
      "[' chains in other territories have ordered IMAX screens in ones and twos, Dalian Wanda in March 2011 put in an order for 75 screens. In Nov 2012 South Korea�']\n",
      "['anda']\n",
      "Score: 8.249078750610352\n",
      "\n",
      "[' the standard quantum limit, because of the known/ prepared states in the ancillas/NITROGEN VACANCIES\\n\\n']\n",
      "[' states']\n",
      "Score: 8.070146560668945\n",
      "\n",
      "[' of sickness than their female colleagues. Many of the problems experienced by women in the workplace could be mitigated by']\n",
      "[' female']\n",
      "Score: 8.066986083984375\n",
      "\n",
      "[' extensive research conducted for my PhD, is devoted to ‘Provision for “Menstrual Leave”’.\\n\\nIn the 1920s, scientific researchers and']\n",
      "['stru']\n",
      "Score: 8.047263145446777\n",
      "\n",
      "['’re going to have to tell her you’ll help a little. Go ahead and help, but let her do']\n",
      "[' her']\n",
      "Score: 7.9689040184021\n",
      "\n",
      "[' and is a genuine made-in-China co-venture involving China Film Group, Wanda Media, Village Roadshow Pictures Asia, and Universal Pictures.\\n\\nThe contemporary action']\n",
      "['anda']\n",
      "Score: 7.741673946380615\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for entry in subj_attn6_top_scores:\n",
    "    decode_prompt_and_tokens(tokenized_prompts[:298], entry['prompt_idx'], entry['token_idx'], window_size=18)\n",
    "    print(f\"Score: {entry['score']}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41d914ff-5a07-42dd-999f-20653a86626a",
   "metadata": {},
   "source": [
    "# Pairwise activation patching evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "c9eb4fb4-b24f-4b64-812d-be01e1682488",
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_pairwise_activation_patching(prompts_pos, prompts_neg, logits_normal, layer, sublayer, token, feature_vec):\n",
    "    ret_dict = {\n",
    "        'pos_scores': [],\n",
    "        'neg_scores': [],\n",
    "        'patched_pos_scores': [],\n",
    "        'pos_to_neg_KLs': [],\n",
    "        'patched_pos_to_neg_KLs': [],\n",
    "    }\n",
    "    with torch.no_grad():\n",
    "        for i in tqdm.tqdm(range(len(prompts_pos))):\n",
    "            prompt_pos = prompts_pos[i]\n",
    "            prompt_neg = prompts_neg[i]\n",
    "            \n",
    "            pos_out = run_with_patched_activations(model, prompt_pos, [], return_np=False)\n",
    "            pos_score = (pos_out['lm_out'][0,-1] @ logits_normal).item()\n",
    "    \n",
    "            neg_out = run_with_patched_activations(model, prompt_neg, [], return_np=False)\n",
    "            neg_score = (neg_out['lm_out'][0,-1] @ logits_normal).item()\n",
    "    \n",
    "            original_sublayer = sublayer\n",
    "            if sublayer == 'block_in': original_sublayer = 'ln_1_in'\n",
    "            pos_original_embedding = pos_out['layers'][layer][original_sublayer]\n",
    "            neg_original_embedding = neg_out['layers'][layer][original_sublayer]\n",
    "            \n",
    "            # project difference between positive and negative embeddings onto feature vector\n",
    "            diff_embedding = (pos_original_embedding - neg_original_embedding)[0, token]\n",
    "            proj_diff = torch.dot(diff_embedding, feature_vec) * feature_vec\n",
    "            # patch negative embedding with our projected difference\n",
    "            patched_embedding = neg_original_embedding[0,token] + proj_diff\n",
    "            patched_pos_out = run_with_patched_activations(model, prompt_neg,\n",
    "                [\n",
    "                    {'layer': layer, 'sublayer': sublayer, 'token': token, 'patch': patched_embedding}\n",
    "                ], return_np=False\n",
    "            )\n",
    "            # measure patched score\n",
    "            patched_pos_score = patched_pos_out['lm_out'][0,-1] @ logits_normal\n",
    "            # measure KL divergence from pos to neg, and from patched pos to neg\n",
    "            pos_distrib = torch.nn.functional.log_softmax(pos_out['lm_out'][0,-1], dim=0)\n",
    "            neg_distrib = torch.nn.functional.log_softmax(neg_out['lm_out'][0,-1], dim=0)\n",
    "            patched_pos_distrib = torch.nn.functional.log_softmax(patched_pos_out['lm_out'][0,-1], dim=0)\n",
    "\n",
    "            pos_to_neg_KL = torch.nn.functional.kl_div(pos_distrib, neg_distrib, log_target=True).item()\n",
    "            patched_pos_to_neg_KL = torch.nn.functional.kl_div(patched_pos_distrib, neg_distrib, log_target=True).item()\n",
    "            \n",
    "            free_embeddings(pos_out)\n",
    "            free_embeddings(neg_out)\n",
    "            free_embeddings(patched_pos_out)\n",
    "\n",
    "            ret_dict['pos_scores'].append(pos_score)\n",
    "            ret_dict['neg_scores'].append(neg_score)\n",
    "            ret_dict['patched_pos_scores'].append(patched_pos_score.item())\n",
    "            ret_dict['pos_to_neg_KLs'].append(pos_to_neg_KL)\n",
    "            ret_dict['patched_pos_to_neg_KLs'].append(patched_pos_to_neg_KL)\n",
    "    return ret_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "28293e9c-c08a-4add-b360-e433ded212cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 300/300 [03:27<00:00,  1.44it/s]\n"
     ]
    }
   ],
   "source": [
    "occu_pairwise_test_multiply_by_two = test_pairwise_activation_patching(occu_prompts_female, occu_prompts_male, occu_observable.cuda(),\n",
    " 6, 'ln_1_in', 3, 2*occu_attn6_normal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "8606da3b-a3e1-4893-9f52-1d0c65d32301",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 300/300 [03:28<00:00,  1.44it/s]\n"
     ]
    }
   ],
   "source": [
    "occu_pairwise_test_no_multiply = test_pairwise_activation_patching(occu_prompts_female, occu_prompts_male, occu_observable.cuda(),\n",
    " 6, 'ln_1_in', 3, occu_attn6_normal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31ad0927-0a07-4845-aaee-01ef1d0515d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_with_occu_pairwise_test_multiply_by_two = test_pairwise_activation_patching(subj_prompts_female, subj_prompts_male, subj_observable.cuda(),\n",
    " 6, 'block_in', 3, 2*occu_attn6_normal)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "759df18c-1627-4e26-b923-79acf91eb338",
   "metadata": {},
   "source": [
    "# LayerNorm approximations at different points"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fe8bf8e7-4f91-4b2a-9e4d-0039bce5b8ef",
   "metadata": {},
   "source": [
    "## Set up prompts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "2d51202d-1eed-4039-8d07-25d8ba6a005e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_prompts(templates, generic, replacements):\n",
    "    prompts = []\n",
    "    for template in templates:\n",
    "        cur_prompts = []\n",
    "        for replacement in replacements:\n",
    "            cur_prompts.append(template.replace(generic, replacement))\n",
    "        prompts.append(cur_prompts)\n",
    "    return prompts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1214b002-6a78-4d15-93e4-f1c2eb8ba1dc",
   "metadata": {},
   "source": [
    "### Subject pronouns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "e1c9ade9-0646-4638-9481-322ce8d03e9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_prompt_templates = [\n",
    "    \"<|endoftext|>So, [NAME] really is a great friend, isn't\",\n",
    "    \"<|endoftext|>Man, [NAME] is so funny, isn't\",\n",
    "    \"<|endoftext|>Really, [NAME] always works so hard, doesn't\"\n",
    "]\n",
    "\n",
    "subj_prompts_male = make_prompts(subj_prompt_templates, \"[NAME]\", male_names)\n",
    "subj_prompts_female = make_prompts(subj_prompt_templates, \"[NAME]\", female_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a8aadbd-e9d8-4815-8b5a-b3e63e18783c",
   "metadata": {},
   "source": [
    "## Get embeddings"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "405130b2-29c3-459d-ad23-0c08d85966a3",
   "metadata": {},
   "source": [
    "### Subject pronouns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "88b7566d-f4f5-4dea-8385-dbc12d9f11b8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After loading prompt 0, number of tensors: 366\n",
      "After loading prompt 1, number of tensors: 366\n",
      "After loading prompt 2, number of tensors: 366\n",
      "After loading prompt 3, number of tensors: 366\n",
      "After loading prompt 4, number of tensors: 366\n",
      "After loading prompt 5, number of tensors: 366\n",
      "After loading prompt 6, number of tensors: 366\n",
      "After loading prompt 7, number of tensors: 366\n",
      "After loading prompt 8, number of tensors: 366\n",
      "After loading prompt 9, number of tensors: 366\n",
      "After loading prompt 10, number of tensors: 366\n",
      "After loading prompt 11, number of tensors: 366\n",
      "After loading prompt 12, number of tensors: 366\n",
      "After loading prompt 13, number of tensors: 366\n",
      "After loading prompt 14, number of tensors: 366\n",
      "After loading prompt 15, number of tensors: 366\n",
      "After loading prompt 16, number of tensors: 366\n",
      "After loading prompt 17, number of tensors: 366\n",
      "After loading prompt 18, number of tensors: 366\n",
      "After loading prompt 19, number of tensors: 366\n",
      "After loading prompt 20, number of tensors: 366\n",
      "After loading prompt 21, number of tensors: 366\n",
      "After loading prompt 22, number of tensors: 366\n",
      "After loading prompt 23, number of tensors: 366\n",
      "After loading prompt 24, number of tensors: 366\n",
      "After loading prompt 25, number of tensors: 366\n",
      "After loading prompt 26, number of tensors: 366\n",
      "After loading prompt 27, number of tensors: 366\n",
      "After loading prompt 28, number of tensors: 366\n",
      "After loading prompt 29, number of tensors: 366\n",
      "After loading prompt 30, number of tensors: 366\n",
      "After loading prompt 31, number of tensors: 366\n",
      "After loading prompt 32, number of tensors: 366\n",
      "After loading prompt 33, number of tensors: 366\n",
      "After loading prompt 34, number of tensors: 366\n",
      "After loading prompt 35, number of tensors: 366\n",
      "After loading prompt 36, number of tensors: 366\n",
      "After loading prompt 37, number of tensors: 366\n",
      "After loading prompt 38, number of tensors: 366\n",
      "After loading prompt 39, number of tensors: 366\n",
      "After loading prompt 40, number of tensors: 366\n",
      "After loading prompt 41, number of tensors: 366\n",
      "After loading prompt 42, number of tensors: 366\n",
      "After loading prompt 43, number of tensors: 366\n",
      "After loading prompt 44, number of tensors: 366\n",
      "After loading prompt 45, number of tensors: 366\n",
      "After loading prompt 46, number of tensors: 366\n",
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      "After loading prompt 26, number of tensors: 366\n",
      "After loading prompt 27, number of tensors: 366\n",
      "After loading prompt 28, number of tensors: 366\n",
      "After loading prompt 29, number of tensors: 366\n",
      "After loading prompt 30, number of tensors: 366\n",
      "After loading prompt 31, number of tensors: 366\n",
      "After loading prompt 32, number of tensors: 366\n",
      "After loading prompt 33, number of tensors: 366\n",
      "After loading prompt 34, number of tensors: 366\n",
      "After loading prompt 35, number of tensors: 366\n",
      "After loading prompt 36, number of tensors: 366\n",
      "After loading prompt 37, number of tensors: 366\n",
      "After loading prompt 38, number of tensors: 366\n",
      "After loading prompt 39, number of tensors: 366\n",
      "After loading prompt 40, number of tensors: 366\n",
      "After loading prompt 41, number of tensors: 366\n",
      "After loading prompt 42, number of tensors: 366\n",
      "After loading prompt 43, number of tensors: 366\n",
      "After loading prompt 44, number of tensors: 366\n",
      "After loading prompt 45, number of tensors: 366\n",
      "After loading prompt 46, number of tensors: 366\n",
      "After loading prompt 47, number of tensors: 366\n",
      "After loading prompt 48, number of tensors: 366\n",
      "After loading prompt 49, number of tensors: 366\n",
      "After loading prompt 50, number of tensors: 366\n",
      "After loading prompt 51, number of tensors: 366\n",
      "After loading prompt 52, number of tensors: 366\n",
      "After loading prompt 53, number of tensors: 366\n",
      "After loading prompt 54, number of tensors: 366\n",
      "After loading prompt 55, number of tensors: 366\n",
      "After loading prompt 56, number of tensors: 366\n",
      "After loading prompt 57, number of tensors: 366\n",
      "After loading prompt 58, number of tensors: 366\n",
      "After loading prompt 59, number of tensors: 366\n",
      "After loading prompt 60, number of tensors: 366\n",
      "After loading prompt 61, number of tensors: 366\n",
      "After loading prompt 62, number of tensors: 366\n",
      "After loading prompt 63, number of tensors: 366\n",
      "After loading prompt 64, number of tensors: 366\n",
      "After loading prompt 65, number of tensors: 366\n",
      "After loading prompt 66, number of tensors: 366\n",
      "After loading prompt 67, number of tensors: 366\n",
      "After loading prompt 68, number of tensors: 366\n",
      "After loading prompt 69, number of tensors: 366\n",
      "After loading prompt 70, number of tensors: 366\n",
      "After loading prompt 71, number of tensors: 366\n",
      "After loading prompt 72, number of tensors: 366\n",
      "After loading prompt 73, number of tensors: 366\n",
      "After loading prompt 74, number of tensors: 366\n",
      "After loading prompt 75, number of tensors: 366\n",
      "After loading prompt 76, number of tensors: 366\n",
      "After loading prompt 77, number of tensors: 366\n",
      "After loading prompt 78, number of tensors: 366\n",
      "After loading prompt 79, number of tensors: 366\n",
      "After loading prompt 80, number of tensors: 366\n",
      "After loading prompt 81, number of tensors: 366\n",
      "After loading prompt 82, number of tensors: 366\n",
      "After loading prompt 83, number of tensors: 366\n",
      "After loading prompt 84, number of tensors: 366\n",
      "After loading prompt 85, number of tensors: 366\n",
      "After loading prompt 86, number of tensors: 366\n",
      "After loading prompt 87, number of tensors: 366\n",
      "After loading prompt 88, number of tensors: 366\n",
      "After loading prompt 89, number of tensors: 366\n",
      "After loading prompt 90, number of tensors: 366\n",
      "After loading prompt 91, number of tensors: 366\n",
      "After loading prompt 92, number of tensors: 366\n",
      "After loading prompt 93, number of tensors: 366\n",
      "After loading prompt 94, number of tensors: 366\n",
      "After loading prompt 95, number of tensors: 366\n",
      "After loading prompt 96, number of tensors: 366\n",
      "After loading prompt 97, number of tensors: 366\n",
      "After loading prompt 98, number of tensors: 366\n",
      "After loading prompt 99, number of tensors: 366\n"
     ]
    }
   ],
   "source": [
    "subj_embeddings_male = [embeddings_from_prompt_list(model, sublist, use_tqdm=False, print_tensors_count=True)\n",
    "                        for sublist in subj_prompts_male]\n",
    "subj_embeddings_female = [embeddings_from_prompt_list(model, sublist, use_tqdm=False, print_tensors_count=True)\n",
    "                        for sublist in subj_prompts_female]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dba06ebc-c9a4-4e65-9b2d-c8f585974cbf",
   "metadata": {},
   "source": [
    "## LayerNorm $W$ variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "2a0a2c39-2d27-44e6-a8eb-00c59c0c346e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007827168"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variances = []\n",
    "for layer in model.transformer.h:\n",
    "    variances.append(layer.ln_1.weight.detach().cpu().numpy().var())\n",
    "    variances.append(layer.ln_2.weight.detach().cpu().numpy().var())\n",
    "variances.append(model.transformer.ln_f.weight.detach().cpu().numpy().var())\n",
    "np.mean(variances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "86cdd0a9-63db-4c15-b4b4-54398268a2af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "368.2572"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean([np.linalg.norm(subj_embeddings_female[0]['layers'][1]['ln_2_in'][0], axis=1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "c6767f0e-aab2-477f-8561-c07215b46e95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0538908"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(subj_embeddings_female[0]['layers'][1]['ln_2_in']).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "ffcade58-f520-4f97-a5ae-b92ea78aa105",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.2019696, 3.9285078, 2.6398177, 3.7392533, 2.7157164, 3.0362577,\n",
       "       4.078494 , 2.5403502, 3.649878 , 3.7672796], dtype=float32)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ln_1_norms[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "a4a6fb18-3fcc-4c3c-a0ed-5b3c1e727408",
   "metadata": {},
   "outputs": [],
   "source": [
    "all_norms = []\n",
    "for layer in range(len(model.transformer.h)):\n",
    "    ln_1_norms = []\n",
    "    ln_2_norms = []\n",
    "    for i in range(len(subj_embeddings_female)):\n",
    "        for j in range(3):\n",
    "            ln_1_norms.append(np.linalg.norm(subj_embeddings_female[j][i]['layers'][layer]['ln_1_in'][0], axis=1))\n",
    "            ln_1_norms.append(np.linalg.norm(subj_embeddings_male[j][i]['layers'][layer]['ln_1_in'][0], axis=1))\n",
    "            ln_2_norms.append(np.linalg.norm(subj_embeddings_female[j][i]['layers'][layer]['ln_2_in'][0], axis=1))\n",
    "            ln_2_norms.append(np.linalg.norm(subj_embeddings_male[j][i]['layers'][layer]['ln_2_in'][0], axis=1))\n",
    "    all_norms.append(np.mean(np.concatenate(ln_1_norms)))\n",
    "    all_norms.append(np.mean(np.concatenate(ln_2_norms)))\n",
    "ln_f_norms = []\n",
    "for i in range(len(subj_embeddings_female)):\n",
    "    for j in range(3):\n",
    "        ln_f_norms.append(np.linalg.norm(subj_embeddings_female[j][i]['ln_f_in'][0], axis=1))\n",
    "        ln_f_norms.append(np.linalg.norm(subj_embeddings_male[j][i]['ln_f_in'][0], axis=1))\n",
    "all_norms.append(np.mean(np.concatenate(ln_f_norms)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "66063ef4-ed87-4324-a3ea-a2d379325fe0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.title(\"Mean norms of inputs to LayerNorm\")\n",
    "plt.xlabel(\"Layer\")\n",
    "plt.ylabel(\"Norm\")\n",
    "plt.plot(np.arange(0,24.5,0.5), all_norms, marker='o')\n",
    "plt.show()\n",
    "fig.savefig(\"layernorm_norms.pdf\", bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "5ef79ba8-6ee3-441b-9b8d-fc13722a4547",
   "metadata": {},
   "outputs": [],
   "source": [
    "mean_entries = []\n",
    "for layer in range(len(model.transformer.h)):\n",
    "    ln_1_norms = []\n",
    "    ln_2_norms = []\n",
    "    for i in range(len(subj_embeddings_female)):\n",
    "        for j in range(3):\n",
    "            ln_1_norms.append(np.mean(np.abs(subj_embeddings_female[j][i]['layers'][layer]['ln_1_in'][0])))\n",
    "            ln_1_norms.append(np.mean(np.abs(subj_embeddings_male[j][i]['layers'][layer]['ln_1_in'][0])))\n",
    "            ln_2_norms.append(np.mean(np.abs(subj_embeddings_female[j][i]['layers'][layer]['ln_2_in'][0])))\n",
    "            ln_2_norms.append(np.mean(np.abs(subj_embeddings_male[j][i]['layers'][layer]['ln_2_in'][0])))\n",
    "    mean_entries.append(np.mean(ln_1_norms))\n",
    "    mean_entries.append(np.mean(ln_2_norms))\n",
    "ln_f_norms = []\n",
    "for i in range(len(subj_embeddings_female)):\n",
    "    for j in range(3):\n",
    "        ln_f_norms.append(np.mean(np.abs(subj_embeddings_female[j][i]['ln_f_in'][0])))\n",
    "        ln_f_norms.append(np.mean(np.abs(subj_embeddings_male[j][i]['ln_f_in'][0])))\n",
    "mean_entries.append(np.mean(ln_f_norms))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "d58b87d8-2eb4-4564-ba5d-f805996645b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "variance_to_mean_entry_ratio = np.array(variances)/np.array(mean_entries)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "98a76a03-215c-43e2-8cfa-62db40caccb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07145301"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variance_to_mean_entry_ratio[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "201a11d8-e9ec-4b96-91fd-8d9c3f02fcfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.title(\"Ratio of LayerNorm weight entry variance to mean absolute embedding variance\")\n",
    "plt.ylabel(\"Ratio\")\n",
    "plt.xlabel(\"Layer\")\n",
    "plt.plot(np.arange(0,24.5,0.5), variance_to_mean_entry_ratio, marker='o')\n",
    "plt.show()\n",
    "fig.savefig(\"layernorm_variances.pdf\", bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba662664-d6be-4f9c-aaaf-913eb325a770",
   "metadata": {},
   "source": [
    "## Accuracies of `ln_f` approximations across prompt groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "b83d6605-f93c-4fd0-8b37-c91dde7eb937",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([50257])\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_24314/3127716323.py:23: UserWarning: The use of `x.T` on tensors of dimension other than 2 to reverse their shape is deprecated and it will throw an error in a future release. Consider `x.mT` to transpose batches of matrices or `x.permute(*torch.arange(x.ndim - 1, -1, -1))` to reverse the dimensions of a tensor. (Triggered internally at /opt/conda/conda-bld/pytorch_1682343997789/work/aten/src/ATen/native/TensorShape.cpp:3571.)\n",
      "  n = n.T.to(\"cuda\", dtype=torch.float32)\n"
     ]
    }
   ],
   "source": [
    "subj_range_normal = make_range_normal([' she'], [' he'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "e5420878-d1dc-420b-94a5-425e18b40720",
   "metadata": {},
   "outputs": [],
   "source": [
    "zeros = torch.zeros(subj_range_normal.shape).to(\"cuda\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97c707b0-c77e-4369-af47-4c9985146f4e",
   "metadata": {},
   "source": [
    "### Subject prompt group 0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "6d3591de-cc4a-490a-acac-49b531a4aca3",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_ln_f_xpos_prompts0 = torch.from_numpy(\n",
    "    sum([x['ln_f_in'][:, -1, :] for x in subj_embeddings_female[0]])/len(subj_embeddings_female[0])\n",
    ").to(\"cuda\")[0]\n",
    "subj_ln_f_xneg_prompts0 = torch.from_numpy(\n",
    "    sum([x['ln_f_in'][:, -1, :] for x in subj_embeddings_male[0]])/len(subj_embeddings_female[0])\n",
    ").to(\"cuda\")[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "6e7c912d-c79a-4be0-8553-d25ce4f340f3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final loss: 7.581412830859335e-08\n",
      "Final t: tensor([0.4646], device='cuda:0', requires_grad=True)\n",
      "4.037406583279335e-06\n"
     ]
    }
   ],
   "source": [
    "subj_ln_f_affine_prompts0 = domain_boundary_intersection(subj_ln_f_xpos_prompts0, subj_ln_f_xneg_prompts0,\n",
    "                                                model.transformer.ln_f, subj_range_normal, zeros, lr=0.02, eps=0.0000001)\n",
    "subj_ln_f_normal_prompts0 = get_tangent_plane_given_point(subj_ln_f_affine_prompts0, model.transformer.ln_f, subj_range_normal, zeros)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "b15538ba-f8e6-4e3b-9875-bde1e6b38e8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_absolute_loss(f, embeddings_list, layer, sublayer, dom_normal, dom_affine, range_normal, range_affine, token=-1):\n",
    "    avg_diff_sum = 0\n",
    "    avg_diff_count = 0\n",
    "    for np_embeddings in embeddings_list:\n",
    "        embeddings = embeddings_np_to_torch(np_embeddings, free=False)\n",
    "        if layer is None:\n",
    "            my_point = embeddings[sublayer][:, token, :]\n",
    "        else:\n",
    "            my_point = embeddings['layers'][layer][sublayer][:, token, :]\n",
    "        with torch.no_grad():\n",
    "            avg_diff_sum += torch.abs(( (f(my_point) - range_affine) @ range_normal) - ((my_point-dom_affine) @ dom_normal)).item()\n",
    "        avg_diff_count += 1\n",
    "        free_embeddings(embeddings)\n",
    "    return avg_diff_sum/avg_diff_count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "0800acf0-1ece-48a6-81ed-8ea45d4a1bb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.050001001358032225"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[0]+subj_embeddings_male[0],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts0, subj_ln_f_affine_prompts0, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d89d6c49-e55f-445a-9b7b-0327f9167c0e",
   "metadata": {},
   "source": [
    "The above means that for prompts in \"Subject Prompt Group 0\", the tangent plane that we found for Subject Prompt Group 0 has an average absolute error of 0.05 logits. Not bad!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "944f9488-f58a-4f37-b44e-3a021d702488",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2946632385253906"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[1]+subj_embeddings_male[1],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts0, subj_ln_f_affine_prompts0, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c471eda-8b24-45ff-ab3e-1211be08c857",
   "metadata": {},
   "source": [
    "But for prompts in Subject Prompt Group 1, this jumps up to 0.295 logits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "33a05454-8d71-4c5e-b0a5-32b9760a0a50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2518632411956787"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[2]+subj_embeddings_male[2],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts0, subj_ln_f_affine_prompts0, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec982e6d-0c24-40d8-aaa6-242631668fc7",
   "metadata": {},
   "source": [
    "Suject Prompt Group 2. 0.252 logits."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f44b7176-76f5-4428-b815-99559e6a420f",
   "metadata": {},
   "source": [
    "### Subject prompt group 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "e0bdb62e-3323-4cfb-9923-269149a2b65b",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_ln_f_xpos_prompts1 = torch.from_numpy(\n",
    "    sum([x['ln_f_in'][:, -1, :] for x in subj_embeddings_female[1]])/len(subj_embeddings_female[1])\n",
    ").to(\"cuda\")[0]\n",
    "subj_ln_f_xneg_prompts1 = torch.from_numpy(\n",
    "    sum([x['ln_f_in'][:, -1, :] for x in subj_embeddings_male[1]])/len(subj_embeddings_female[1])\n",
    ").to(\"cuda\")[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "9092f1c4-b46b-4133-a9ec-b5479d56d0c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final loss: 4.8557811993532596e-08\n",
      "Final t: tensor([0.5460], device='cuda:0', requires_grad=True)\n",
      "4.790950352884238e-06\n"
     ]
    }
   ],
   "source": [
    "subj_ln_f_affine_prompts1 = domain_boundary_intersection(subj_ln_f_xpos_prompts1, subj_ln_f_xneg_prompts1,\n",
    "                                                model.transformer.ln_f, subj_range_normal, zeros, lr=0.02, eps=0.0000001)\n",
    "subj_ln_f_normal_prompts1 = get_tangent_plane_given_point(subj_ln_f_affine_prompts1, model.transformer.ln_f, subj_range_normal, zeros)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "37a09a4a-6e1b-47d9-9d78-79aa392a3a6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1448301076889038"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[0]+subj_embeddings_male[0],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts1, subj_ln_f_affine_prompts1, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "49607ef7-550a-4abb-b7bb-f4fe47b44f9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09488174915313721"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[1]+subj_embeddings_male[1],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts1, subj_ln_f_affine_prompts1, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "e06861b1-5962-4232-adc2-31edc81cad60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.13128716945648194"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[2]+subj_embeddings_male[2],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts1, subj_ln_f_affine_prompts1, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adbb7fad-6c10-41c3-abcc-224fd2cda8a2",
   "metadata": {},
   "source": [
    "### Subject prompt group 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "f48e902b-3e29-4dfd-9e8a-492d3e1cf303",
   "metadata": {},
   "outputs": [],
   "source": [
    "subj_ln_f_xpos_prompts2 = torch.from_numpy(\n",
    "    sum([x['ln_f_in'][:, -1, :] for x in subj_embeddings_female[2]])/len(subj_embeddings_female[2])\n",
    ").to(\"cuda\")[0]\n",
    "subj_ln_f_xneg_prompts2 = torch.from_numpy(\n",
    "    sum([x['ln_f_in'][:, -1, :] for x in subj_embeddings_male[2]])/len(subj_embeddings_female[2])\n",
    ").to(\"cuda\")[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "889bae93-7c66-4954-ab20-2e98bdee7436",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final loss: 6.809445096678246e-08\n",
      "Final t: tensor([0.4901], device='cuda:0', requires_grad=True)\n",
      "3.847786261701458e-05\n"
     ]
    }
   ],
   "source": [
    "subj_ln_f_affine_prompts2 = domain_boundary_intersection(subj_ln_f_xpos_prompts2, subj_ln_f_xneg_prompts2,\n",
    "                                                model.transformer.ln_f, subj_range_normal, zeros, lr=0.02, eps=0.0000001)\n",
    "subj_ln_f_normal_prompts2 = get_tangent_plane_given_point(subj_ln_f_affine_prompts2, model.transformer.ln_f, subj_range_normal, zeros)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "ba947a6c-6f5e-40f4-b030-9a1835c0e0be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.18031926155090333"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[0]+subj_embeddings_male[0],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts2, subj_ln_f_affine_prompts2, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "ce71063b-f6ee-49d1-8b65-21cfb7b3bc54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05655231475830078"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[1]+subj_embeddings_male[1],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts2, subj_ln_f_affine_prompts2, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "798bec07-dc39-4704-9272-57dc4f76a83d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05453193187713623"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_loss(model.transformer.ln_f, subj_embeddings_female[2]+subj_embeddings_male[2],\n",
    "                   None, 'ln_f_in', subj_ln_f_normal_prompts2, subj_ln_f_affine_prompts2, subj_range_normal, zeros, -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "932fcea4-7f61-4cb1-a47c-c43b3a68f7bc",
   "metadata": {},
   "source": [
    "## Investigate feature vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "e9f2eee7-bf84-4fc7-b334-b4f39cf148f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999997019767761"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cossim(subj_ln_f_normal_prompts0, subj_ln_f_normal_prompts1).item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "99773617-d07b-4f1b-8376-3a96638c0562",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cossim 0 to 1 0.9999997019767761\n",
      "Cossim 1 to 2 0.9999980926513672\n",
      "Cossim 2 to 0 0.9999980330467224\n"
     ]
    }
   ],
   "source": [
    "print(\"Cossim 0 to 1\", cossim(subj_ln_f_normal_prompts0, subj_ln_f_normal_prompts1).item())\n",
    "print(\"Cossim 1 to 2\", cossim(subj_ln_f_normal_prompts1, subj_ln_f_normal_prompts2).item())\n",
    "print(\"Cossim 2 to 0\", cossim(subj_ln_f_normal_prompts0, subj_ln_f_normal_prompts2).item())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "id": "a59525cc-c016-427f-a3f6-0f1e5f5c90cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(0.2662, device='cuda:0'),\n",
       " tensor(0.2571, device='cuda:0'),\n",
       " tensor(0.2554, device='cuda:0'))"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.linalg.norm(subj_ln_f_normal_prompts0), torch.linalg.norm(subj_ln_f_normal_prompts1), torch.linalg.norm(subj_ln_f_normal_prompts2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "454ded02-0996-46da-852a-07bcde1f2521",
   "metadata": {},
   "source": [
    "### 17.14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "d882938d-8c66-4788-b3cd-70728fa250e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "attn17_14_subj_normal_prompts0 = get_attn_normal(model, 17, 14, subj_ln_f_normal_prompts0)\n",
    "attn17_14_subj_normal_prompts1 = get_attn_normal(model, 17, 14, subj_ln_f_normal_prompts1)\n",
    "attn17_14_subj_normal_prompts2 = get_attn_normal(model, 17, 14, subj_ln_f_normal_prompts2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "a0cac3f2-7611-4b04-95cd-2864bd104a7b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine similarity 0 to 1:  tensor(1., device='cuda:0', grad_fn=<DivBackward0>)\n",
      "Cosine similarity 1 to 2:  tensor(1.0000, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "Cosine similarity 2 to 0:  tensor(1., device='cuda:0', grad_fn=<DivBackward0>)\n"
     ]
    }
   ],
   "source": [
    "print(\"Cosine similarity 0 to 1: \", cossim(attn17_14_subj_normal_prompts0, attn17_14_subj_normal_prompts1))\n",
    "print(\"Cosine similarity 1 to 2: \", cossim(attn17_14_subj_normal_prompts2, attn17_14_subj_normal_prompts1))\n",
    "print(\"Cosine similarity 2 to 0: \", cossim(attn17_14_subj_normal_prompts0, attn17_14_subj_normal_prompts2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "3397f7ef-cb53-4ca2-8d7b-0ffb19cfb8d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(8.8101, device='cuda:0', grad_fn=<LinalgVectorNormBackward0>),\n",
       " tensor(8.5090, device='cuda:0', grad_fn=<LinalgVectorNormBackward0>),\n",
       " tensor(8.4536, device='cuda:0', grad_fn=<LinalgVectorNormBackward0>))"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.linalg.norm(attn17_14_subj_normal_prompts0),\\\n",
    "torch.linalg.norm(attn17_14_subj_normal_prompts1),\\\n",
    "torch.linalg.norm(attn17_14_subj_normal_prompts2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "2128477e-7152-4dbc-9c7d-96f99c37604e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0, 1 coupling:  tensor(0.9658, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "0, 2 coupling:  tensor(0.9595, device='cuda:0', grad_fn=<DivBackward0>)\n",
      "1, 2 coupling:  tensor(0.9935, device='cuda:0', grad_fn=<DivBackward0>)\n"
     ]
    }
   ],
   "source": [
    "print(\"0, 1 coupling: \", coupling_coeff(attn17_14_subj_normal_prompts0, attn17_14_subj_normal_prompts1))\n",
    "print(\"0, 2 coupling: \", coupling_coeff(attn17_14_subj_normal_prompts0, attn17_14_subj_normal_prompts2))\n",
    "print(\"1, 2 coupling: \", coupling_coeff(attn17_14_subj_normal_prompts1, attn17_14_subj_normal_prompts2))"
   ]
  }
 ],
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