gradient_meets_attention.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "989d4e0b",
   "metadata": {},
   "source": [
    "# Gradient meets attention\n",
    "Generates Figure 5 of the paper Attention Meets Post-hoc Interpretability: A Mathematical Perspective."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "93ea7683",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pickle\n",
    "import itertools \n",
    "\n",
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import torch.nn.functional as F\n",
    "\n",
    "import numpy as np\n",
    "import math\n",
    "\n",
    "import matplotlib.pyplot as plt \n",
    "import matplotlib.colors as colors\n",
    "\n",
    "from lime import lime_text\n",
    "\n",
    "import re"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "edf52f41",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rc('pdf', fonttype=42)\n",
    "plt.rc('ps', fonttype=42)\n",
    "plt.rcParams.update({'font.size': 18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4576a53f",
   "metadata": {},
   "outputs": [],
   "source": [
    "SEED = 42\n",
    "torch.manual_seed(SEED)\n",
    "np.random.seed(SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a8978ec8",
   "metadata": {},
   "outputs": [],
   "source": [
    "from models.utils import get_g_values\n",
    "from models.utils import scaled_dot_product\n",
    "from data.dataset import Dataset\n",
    "import params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bc8c7b05",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"C:/Users/gianl/Anaconda3/bin\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c387dd06",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using device: cpu\n",
      "Model loaded successfully from: .\\models\\saved\\IMDB\\multi_head_e\\model\n"
     ]
    }
   ],
   "source": [
    "# Check if CUDA is available and set device accordingly\n",
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
    "print(f\"Using device: {device}\")\n",
    "\n",
    "# Define model name and path\n",
    "model_name = 'multi_head_e\\\\model'\n",
    "model_path = os.path.join('.', 'models', 'saved', 'IMDB', model_name)\n",
    "\n",
    "# Load the classifier model\n",
    "with open(os.path.join(model_path, 'classifier.pkl'), 'rb') as inp:\n",
    "    classifier = pickle.load(inp)\n",
    "print(f\"Model loaded successfully from: {model_path}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d1d25c6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.64168686,  0.58398646]], dtype=float32)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example = \"attention based explanations are popular but questionable\"\n",
    "\n",
    "classifier.predict_proba([example])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f98bc9ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'attention based explanations are popular but questionable'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6f256d09",
   "metadata": {},
   "outputs": [],
   "source": [
    "unk_string = ' '.join([params.MASK for i in range(params.MAX_LEN-1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "914601b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-1.9244,  2.2145]], grad_fn=<MmBackward0>)\n",
      "tensor([[ 0.7073, -0.7996]], grad_fn=<MmBackward0>)\n",
      "tensor([[-2.8908,  3.1665]], grad_fn=<MmBackward0>)\n",
      "tensor([[ 1.8753, -2.5159]], grad_fn=<MmBackward0>)\n",
      "tensor([[-1.4783,  0.8150]], grad_fn=<MmBackward0>)\n",
      "tensor([[-0.1392,  0.6234]], grad_fn=<MmBackward0>)\n"
     ]
    }
   ],
   "source": [
    "# Preprocess the input sentence\n",
    "x = torch.stack([classifier.preprocess(example)])\n",
    "\n",
    "v, q, k, attention, g_u = [], [], [], [], []\n",
    "W_k, W_q, W_v, W, q_cls = [], [], [], [], []\n",
    "\n",
    "    \n",
    "emb = classifier.embedding(x.to(torch.int64))\n",
    "e = classifier.pe(emb)\n",
    "\n",
    "for h in range(params.NUM_HEADS):\n",
    "    # Transform the sentence embedding using the embedding layer\n",
    "    head = classifier.heads[h]\n",
    "\n",
    "\n",
    "    # Extract query, key, and value representations from the embedding\n",
    "    q.append(head.query(e))\n",
    "    k.append(head.key(e))\n",
    "    v.append(head.value(e))\n",
    "\n",
    "    W_k.append(head.key(torch.eye(e.shape[-1])))\n",
    "    W_q.append(head.query(torch.eye(e.shape[-1])))\n",
    "    W_v.append(head.value(torch.eye(e.shape[-1])))\n",
    "    W.append(head.classifier(torch.eye(v[h].shape[-1]))[:, 1])\n",
    "    q_cls.append(q[h][:, classifier.cls_pos, :])\n",
    "\n",
    "    # Calculate scaled dot-product attention\n",
    "    values, alpha, g = scaled_dot_product(q[h], k[h], v[h], return_g=True, scale=True)\n",
    "    \n",
    "    attention.append(alpha)\n",
    "    g_u.append(g[:, classifier.cls_pos, :])\n",
    "    \n",
    "    # Extract attention-weighted values for the classifier layer\n",
    "    cls_values = values[:, classifier.cls_pos, :]\n",
    "\n",
    "    # Pass the attention-weighted values through the classifier to obtain predictions\n",
    "    output = head.classifier(cls_values)\n",
    "\n",
    "    print(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0eda1899",
   "metadata": {},
   "outputs": [],
   "source": [
    "d_k = params.ATTN_DIM\n",
    "n_heads = params.NUM_HEADS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9ca19a58",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Preprocess the \"UNK\" token\n",
    "x_unk = torch.stack([classifier.preprocess(unk_string)])\n",
    "\n",
    "v_unk, q_unk, k_unk, g_unk = [], [], [], []\n",
    "\n",
    "# Convert the \"UNK\" token to embedding representation\n",
    "emb = classifier.embedding(x_unk.to(torch.int64))\n",
    "e_unk = classifier.pe(emb)\n",
    "\n",
    "for h in range(params.NUM_HEADS):\n",
    "\n",
    "    # Extract the hidden state (h) from the \"UNK\" token embedding\n",
    "    v_unk.append(classifier.heads[h].value(e_unk)) \n",
    "    q_unk.append(classifier.heads[h].query(e_unk))\n",
    "    k_unk.append(classifier.heads[h].key(e_unk)) \n",
    "    \n",
    "    d_k = q_unk[h].size()[-1]\n",
    "    attn_logits = torch.matmul(q[h], k_unk[h].transpose(-2, -1)) / math.sqrt(d_k)\n",
    "    g_unk.append(torch.exp(attn_logits)[:, classifier.cls_pos, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3551540d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fd5434fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "grad_theory = []\n",
    "for h in range(n_heads):\n",
    "    grad_head = []\n",
    "\n",
    "    for t in range(params.MAX_LEN):     \n",
    "        p1 = torch.matmul(q_cls[h], W_k[h].T) / math.sqrt(d_k) * torch.matmul(v[h][:, t, :], W[h])\n",
    "        p2 = torch.matmul(W[h], W_v[h].T)\n",
    "        n1 = torch.sum(torch.stack([attention[h][:, classifier.cls_pos, s] * \n",
    "                                         torch.matmul(q_cls[h], W_k[h].T) / math.sqrt(d_k) * \n",
    "                                         torch.matmul(v[h][:, s, :], W[h])\n",
    "                                         for s in range(params.MAX_LEN)]), dim=0)\n",
    "\n",
    "        grad_head.append((attention[h][:, classifier.cls_pos, t]) * (p1 + p2 - n1))\n",
    "        \n",
    "    grad_theory.append(torch.cat(grad_head))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "340b22e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([6, 256, 128])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.stack(grad_theory).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5b41d122",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "905f23f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-1.0511e-01, -2.9445e-02,  5.7189e-02,  ...,  7.9856e-02,\n",
       "         -9.5229e-02, -3.0264e-01],\n",
       "        [ 4.4375e-04, -2.3625e-04, -1.1520e-03,  ...,  8.6789e-03,\n",
       "          6.3203e-03,  6.8574e-04],\n",
       "        [ 2.7160e-02,  1.7591e-02, -4.2354e-02,  ...,  9.9584e-02,\n",
       "          4.4732e-02, -4.5896e-02],\n",
       "        ...,\n",
       "        [ 2.3949e-04,  1.9903e-04,  1.5449e-04,  ..., -2.9668e-04,\n",
       "         -1.4545e-04,  1.2914e-04],\n",
       "        [ 1.9137e-04,  1.6650e-04,  1.4803e-04,  ..., -2.7715e-04,\n",
       "         -1.2557e-04,  1.7253e-04],\n",
       "        [ 1.9224e-04,  1.6840e-04,  2.5337e-04,  ..., -3.4953e-04,\n",
       "         -1.6771e-04,  3.1299e-04]], grad_fn=<MeanBackward1>)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.mean(torch.stack(grad_theory), dim=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d9540258",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c1094909",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-0.6417,  0.5840]], grad_fn=<DivBackward0>)\n",
      "tensor([[-1.0361e-01, -2.2006e-02,  6.3245e-02,  ...,  5.0508e-02,\n",
      "         -1.3956e-01, -3.1812e-01],\n",
      "        [ 4.4375e-04, -2.3625e-04, -1.1520e-03,  ...,  8.6789e-03,\n",
      "          6.3203e-03,  6.8574e-04],\n",
      "        [ 2.7160e-02,  1.7591e-02, -4.2354e-02,  ...,  9.9584e-02,\n",
      "          4.4732e-02, -4.5896e-02],\n",
      "        ...,\n",
      "        [ 2.3949e-04,  1.9903e-04,  1.5449e-04,  ..., -2.9668e-04,\n",
      "         -1.4545e-04,  1.2914e-04],\n",
      "        [ 1.9137e-04,  1.6650e-04,  1.4803e-04,  ..., -2.7715e-04,\n",
      "         -1.2557e-04,  1.7253e-04],\n",
      "        [ 1.9224e-04,  1.6840e-04,  2.5337e-04,  ..., -3.4953e-04,\n",
      "         -1.6771e-04,  3.1299e-04]])\n"
     ]
    }
   ],
   "source": [
    "grad = {}\n",
    "\n",
    "def get_gradient(name):\n",
    "    def hook(model, grad_input, grad_output):\n",
    "        grad[name] = grad_output[0].detach()\n",
    "    return hook\n",
    "        \n",
    "handle_gradient_pe = classifier.pe.register_full_backward_hook(get_gradient('pe'))\n",
    "\n",
    "Z = classifier(x)\n",
    "\n",
    "Z[0,1].backward()\n",
    "\n",
    "# Print output and gradients\n",
    "gradient_e = torch.squeeze(grad['pe'])\n",
    "print(Z)\n",
    "\n",
    "print(gradient_e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "af7a9480",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-1.0511e-01, -2.9445e-02,  5.7189e-02,  ...,  7.9856e-02,\n",
       "         -9.5229e-02, -3.0264e-01],\n",
       "        [ 4.4375e-04, -2.3625e-04, -1.1520e-03,  ...,  8.6789e-03,\n",
       "          6.3203e-03,  6.8574e-04],\n",
       "        [ 2.7160e-02,  1.7591e-02, -4.2354e-02,  ...,  9.9584e-02,\n",
       "          4.4732e-02, -4.5896e-02],\n",
       "        ...,\n",
       "        [ 2.3949e-04,  1.9903e-04,  1.5449e-04,  ..., -2.9668e-04,\n",
       "         -1.4545e-04,  1.2914e-04],\n",
       "        [ 1.9137e-04,  1.6650e-04,  1.4803e-04,  ..., -2.7715e-04,\n",
       "         -1.2557e-04,  1.7253e-04],\n",
       "        [ 1.9224e-04,  1.6840e-04,  2.5337e-04,  ..., -3.4953e-04,\n",
       "         -1.6771e-04,  3.1299e-04]], grad_fn=<MeanBackward1>)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.mean(torch.stack(grad_theory), dim=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eca7b242",
   "metadata": {},
   "source": [
    "## Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f43f9868",
   "metadata": {},
   "outputs": [],
   "source": [
    "grad_f_theory = torch.mean(torch.stack(grad_theory), dim=0).detach().numpy()\n",
    "grad_f_practice = gradient_e.detach().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "89e4f6d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['[CLS]', 'attention', 'based', 'explanations', 'are', 'popular', 'but', 'questionable']\n"
     ]
    }
   ],
   "source": [
    "tokens = classifier.tokenizer(example)\n",
    "labels = ['[CLS]'] + tokens \n",
    "num_tokens = 10\n",
    "print(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7541cd86",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_e = 80\n",
    "\n",
    "# Define a custom colormap for visualization\n",
    "cmap = colors.LinearSegmentedColormap.from_list(\"\", [\"red\",\"white\",\"green\"])\n",
    "\n",
    "# Compute the global minimum and maximum of the data\n",
    "gmin = min(grad_f_theory[1:num_tokens, :num_e].min(), grad_f_practice[1:num_tokens, :num_e].min())\n",
    "gmax = max(grad_f_theory[1:num_tokens, :num_e].max(), grad_f_practice[1:num_tokens, :num_e].max())\n",
    "\n",
    "# Define the color range for the colormap\n",
    "vmax = min(abs(gmax), abs(gmin)) \n",
    "vmin = -vmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "83b64a29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1728x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initialize a figure with a specific size\n",
    "fig = plt.figure(figsize=(24,10))\n",
    "\n",
    "# Create the first subplot for the theoretical gradient\n",
    "ax1 = fig.add_subplot(2, 1, 1)\n",
    "mappable = ax1.matshow(grad_f_theory[:num_tokens, :num_e], cmap=cmap, vmin=vmin, vmax=vmax)\n",
    "ax1.set_yticks(range(len(labels)))\n",
    "ax1.set_yticklabels(labels)\n",
    "ax1.set_title('Theory')\n",
    "\n",
    "# Create the second subplot for the practical gradient\n",
    "ax2 = fig.add_subplot(2, 1, 2)\n",
    "mappable = ax2.matshow(grad_f_practice[:num_tokens, :num_e], cmap=cmap, vmin=vmin, vmax=vmax)\n",
    "ax2.set_yticks(range(len(labels)))\n",
    "ax2.set_yticklabels(labels)\n",
    "ax2.set_title('Practice')\n",
    "\n",
    "# Save the figure as a PDF file with a tight layout\n",
    "plt.savefig('results/paper/gradient_meets_attention.pdf', bbox_inches='tight', transparent=True, pad_inches=0)\n",
    "\n",
    "# Display the figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "532c15ce",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}