Neural Network with Derivatives.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f01cb0e7-db31-4865-b2b9-c732c46b6a24",
   "metadata": {},
   "source": [
    "# Neural Networks with Derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7591e9fe-adae-4f00-8659-eaa2219d2c06",
   "metadata": {},
   "source": [
    "# Installing Dependencies"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da314e45-ecda-4201-8248-9bf8a9fa05d3",
   "metadata": {},
   "source": [
    "- networkx is for visualizing graphs\n",
    "- numpy is for array manipulation\n",
    "- pandas is for data manipulations in form of tables\n",
    "- matplotlib is for plotting data and visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3d0d40dc-8361-4b68-89cb-1848319aed30",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: networkx in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (3.2.1)\n",
      "Requirement already satisfied: numpy in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (1.26.3)\n",
      "Requirement already satisfied: pandas in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (2.1.4)\n",
      "Requirement already satisfied: numpy<2,>=1.26.0 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from pandas) (1.26.3)\n",
      "Requirement already satisfied: python-dateutil>=2.8.2 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from pandas) (2.8.2)\n",
      "Requirement already satisfied: pytz>=2020.1 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from pandas) (2023.3.post1)\n",
      "Requirement already satisfied: tzdata>=2022.1 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from pandas) (2023.4)\n",
      "Requirement already satisfied: six>=1.5 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from python-dateutil>=2.8.2->pandas) (1.16.0)\n",
      "Requirement already satisfied: matplotlib in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (3.8.2)\n",
      "Requirement already satisfied: contourpy>=1.0.1 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (1.2.0)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (0.12.1)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (4.47.2)\n",
      "Requirement already satisfied: kiwisolver>=1.3.1 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (1.4.5)\n",
      "Requirement already satisfied: numpy<2,>=1.21 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (1.26.3)\n",
      "Requirement already satisfied: packaging>=20.0 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (23.2)\n",
      "Requirement already satisfied: pillow>=8 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (10.2.0)\n",
      "Requirement already satisfied: pyparsing>=2.3.1 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (3.1.1)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from matplotlib) (2.8.2)\n",
      "Requirement already satisfied: six>=1.5 in c:\\users\\avhis\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install networkx\n",
    "!pip install numpy\n",
    "!pip install pandas\n",
    "!pip install matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73d8c072-1c01-4a95-b936-e88928442efb",
   "metadata": {},
   "source": [
    "# Importing Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "abbe1632-1bad-4813-8704-7cfaf518f2ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22e2bb0c-f9b6-4d05-a487-7ca489bb520a",
   "metadata": {},
   "source": [
    "# Derivative:\n",
    "#### The derivative is a fundamental tool of calculus that **quantifies the sensitivity of change** of a **function's output with respect to its input**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9970fa6-546c-47a9-b601-63557fe8d75f",
   "metadata": {},
   "source": [
    "$$ L = \\lim_{{h \\to 0}} \\frac{{f(a + h) - f(a)}}{h} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14bfaa0f-2d6e-4e88-b2b3-d854678fdc0b",
   "metadata": {},
   "source": [
    "### Let's take a Simple Parabolic Function:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11c5cacb-6cac-4176-a4f6-63df8657ea60",
   "metadata": {},
   "source": [
    "$$ f(x) = ax^2 + bx + c $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "722c4500-c7da-4bf9-b291-1b28677ed275",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assuming random 'a', 'b' and 'c' values\n",
    "def f(x):\n",
    "    return 3*x**2 + 2*x + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "92c2acf9-30e8-4456-aad0-0dc408898bb7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "When x=-5.0; y=66.0\n",
      "When x=-4.75; y=59.1875\n",
      "When x=-4.5; y=52.75\n",
      "When x=-4.25; y=46.6875\n",
      "When x=-4.0; y=41.0\n",
      "When x=-3.75; y=35.6875\n",
      "When x=-3.5; y=30.75\n",
      "When x=-3.25; y=26.1875\n",
      "When x=-3.0; y=22.0\n",
      "When x=-2.75; y=18.1875\n",
      "When x=-2.5; y=14.75\n",
      "When x=-2.25; y=11.6875\n",
      "When x=-2.0; y=9.0\n",
      "When x=-1.75; y=6.6875\n",
      "When x=-1.5; y=4.75\n",
      "When x=-1.25; y=3.1875\n",
      "When x=-1.0; y=2.0\n",
      "When x=-0.75; y=1.1875\n",
      "When x=-0.5; y=0.75\n",
      "When x=-0.25; y=0.6875\n",
      "When x=0.0; y=1.0\n",
      "When x=0.25; y=1.6875\n",
      "When x=0.5; y=2.75\n",
      "When x=0.75; y=4.1875\n",
      "When x=1.0; y=6.0\n",
      "When x=1.25; y=8.1875\n",
      "When x=1.5; y=10.75\n",
      "When x=1.75; y=13.6875\n",
      "When x=2.0; y=17.0\n",
      "When x=2.25; y=20.6875\n",
      "When x=2.5; y=24.75\n",
      "When x=2.75; y=29.1875\n",
      "When x=3.0; y=34.0\n",
      "When x=3.25; y=39.1875\n",
      "When x=3.5; y=44.75\n",
      "When x=3.75; y=50.6875\n",
      "When x=4.0; y=57.0\n",
      "When x=4.25; y=63.6875\n",
      "When x=4.5; y=70.75\n",
      "When x=4.75; y=78.1875\n"
     ]
    }
   ],
   "source": [
    "xs = np.arange(-5,5,0.25) # Creates a list of numbers from -5 to +5 with a step of 0.25\n",
    "ys = f(xs)\n",
    "for i in range(len(xs)):\n",
    "    print(f\"When x={xs[i]}; y={ys[i]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5ee466bf-2cac-42f2-9287-dbd240e1d992",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ac0f177080>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the points on a graph gives us...\n",
    "plt.plot(xs,ys)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d97c0e9-8cac-4122-9b24-24f731135075",
   "metadata": {},
   "source": [
    "According to the definition of Derivatives, we have to check what is the sensitivity of 'x' if we bump the value with 'h'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "00edbeb0-ae40-4a1e-a5d5-adcfb6676eae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.383333333333333"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's take a very small value of h and check the sensitivity in both positive and negetive\n",
    "h = 0.1\n",
    "x = 1.0\n",
    "( f(x + h) / ( f(x) ) ) / h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4f9504b7-0a18-4d1b-9930-f921b7aa659a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-8.716666666666667"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's take a very small value of h and check the sensitivity in both positive and negetive\n",
    "h = -0.1\n",
    "x = 1.0\n",
    "( f(x + h) / ( f(x) ) ) / h"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c1d3937-f76f-4efd-8508-5361fb514623",
   "metadata": {},
   "source": [
    "Let's try a different scenario where we use mathematical expressions to understand derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "39d05555-97ba-4b92-b9aa-e2eed6be25d6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expression before bumping: 9.5; Expression after bumping: 9.501; Slope 0.9999999999994458\n"
     ]
    }
   ],
   "source": [
    "# Let's say we have an expression with values\n",
    "\n",
    "j = 5.0\n",
    "k = -0.1\n",
    "l = 10.0\n",
    "\n",
    "h = 0.001\n",
    "\n",
    "expressionBeforeBumping = j * k + l\n",
    "l += h # Here the value of l is bumped up in the positive direction\n",
    "expressionAfterBumping = j * k + l\n",
    "slope = (expressionAfterBumping - expressionBeforeBumping)/h\n",
    "\n",
    "print(f\"Expression before bumping: {expressionBeforeBumping};\", f\"Expression after bumping: {expressionAfterBumping};\", f\"Slope {slope}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "028d2f99-83ad-4a85-a1af-7cb4e3c84e64",
   "metadata": {},
   "source": [
    "# Why are Derivatives Important?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1b1b3ca-9bd9-41cd-adb9-940cefb5159a",
   "metadata": {},
   "source": [
    "Eventually, when we arrive at the important parts like gradient descent algorithm, we will be requiring derivatives.\n",
    "\n",
    "**What is \"Gradient\" you ask?**\n",
    "\n",
    "Imagine a car being dropped on a parabolic slope. You want the car to 'eventually' stop at a particular point. So you start applying brakes (basically a force in the opposite direction) of the movement.\n",
    "\n",
    "This force in the opposite direction is known as a gradient.\n",
    "\n",
    "**What is the relationship between a 'derivative' and a 'gradient'?**\n",
    "\n",
    "A 'Gradient' is a 'Derivative' with known direction.\n",
    "In Derivatives we check the sensitivity in all directions for a value.\n",
    "But in Gradients we know the direction we want to push, we just have to tinker with the value."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb2871d1-a5aa-4744-969b-b227ea1c4e44",
   "metadata": {},
   "source": [
    "# Mathematical Example"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4cd89fb-18ff-47ec-8220-dca9494bd524",
   "metadata": {},
   "source": [
    "#### Let's take a more complicated mathematical expression and try to evaluate it with gradients:\n",
    "\n",
    "Let's assume random values as 'r'\n",
    "\n",
    "1. A = r\n",
    "2. B = r\n",
    "3. C = A * B\n",
    "4. D = r\n",
    "5. E = C + D\n",
    "6. F = r\n",
    "7. L = E * F\n",
    "\n",
    "Where **L** is the result of this expression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "704dba60-3e26-48e6-8884-5d952b112f91",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's construct a Value class to store all the expressions for simpler calculations\n",
    "class Value:\n",
    "    # Constructor\n",
    "    def __init__(self , data,_children=(), label='', _op=''):\n",
    "        self.data = data\n",
    "        self.label = label\n",
    "        # Used for Graph Construction\n",
    "        self._prev = set(_children)\n",
    "        self._op = _op if _op else label\n",
    "    # For Printing Without Print Statements | Representation\n",
    "    def __repr__(self):\n",
    "        return f\"Value(data={self.data})\"\n",
    "    def __add__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        return Value(self.data + other.data, (self, other), '+')\n",
    "    def __mul__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        return Value(self.data * other.data, (self, other), '*')\n",
    "    # other + self\n",
    "    def __radd__(self, other):\n",
    "        return self + other\n",
    "    # other * self\n",
    "    def __rmul__(self, other):\n",
    "        return self * other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "46d98b12-b378-4564-a8b8-b4ce3d0e0f46",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = Value(3, label='a')\n",
    "b = Value(-2, label='b')\n",
    "c = a * b\n",
    "d = Value(5, label='d')\n",
    "e = c + d\n",
    "f = Value(-10, label='f')\n",
    "L = e * f\n",
    "\n",
    "c.label = 'c'\n",
    "e.label = 'e'\n",
    "L.label = 'L'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cfa5e2e-3f62-45ba-9d39-4e1b0954e4fa",
   "metadata": {},
   "source": [
    "Let's visualize our expression in form of expression graphs now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e50a24e9-f4f2-4db1-bd55-2ab0b6b8e219",
   "metadata": {},
   "outputs": [],
   "source": [
    "def trace(root):\n",
    "    nodes, edges = set(), set()\n",
    "    def build(v):\n",
    "        if v not in nodes:\n",
    "            nodes.add(v)\n",
    "            for child in v._prev:\n",
    "                edges.add((child, v))\n",
    "                build(child)\n",
    "    build(root)\n",
    "    return nodes, edges\n",
    "\n",
    "def draw_networkx(root, rankdir='LR'):\n",
    "    assert rankdir in ['LR', 'TB']\n",
    "    nodes, edges = trace(root)\n",
    "    \n",
    "    G = nx.DiGraph()\n",
    "    \n",
    "    for n in nodes:\n",
    "        label = \"{label} \\n d={data:.4f}\".format(label=n.label, data=n.data)\n",
    "        G.add_node(str(id(n)), label=label)\n",
    "        if n._op:\n",
    "            G.add_node(str(id(n)) + n._op, label=n._op)\n",
    "            G.add_edge(str(id(n)) + n._op, str(id(n)))\n",
    "    \n",
    "    for n1, n2 in edges:\n",
    "        G.add_edge(str(id(n1)), str(id(n2)) + n2._op)\n",
    "    \n",
    "    pos = None\n",
    "    if rankdir == 'LR':\n",
    "        pos = nx.spring_layout(G, seed=4)\n",
    "    \n",
    "    labels = nx.get_node_attributes(G, 'label')\n",
    "    nx.draw(G, pos=pos, with_labels=True, labels=labels, font_size=6, font_weight='bold')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f8da8d5f-ba26-43c7-8d14-f4dd30d444f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_networkx(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d639e5d2-4e01-40d2-aea6-69fe60bcdae5",
   "metadata": {},
   "source": [
    "Now the expression brings us to our next question...\n",
    "\n",
    "We know that L = E * F\n",
    "\n",
    "What is the **derivative of L**?\n",
    "\n",
    "Or more specifically\n",
    "\n",
    "What is the result of\n",
    "\n",
    "$$ \\frac{dL}{de} $$\n",
    "\n",
    "?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a37193af-b71b-44a4-bd29-8201762f2436",
   "metadata": {},
   "source": [
    "If we take the formula for our good old derivatives... \n",
    "We get:\n",
    "$$ ((f(x+h) - f(x)) / h) $$\n",
    "\n",
    "Substituting the values from the formula L = E * F\n",
    "\n",
    "Because we are trying to understand that if we nudge the value of e by a certain amount 'h' how sensitive 'L' is:\n",
    "\n",
    "=> $$ ((e+h)*f - (e*f)) / h $$\n",
    "=> $$ (e*f) + (h*f) - (e*f) / h $$\n",
    "=> $$ (h*f) / h $$\n",
    "=> $$ f $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a5ca3736-04ce-4a18-8b7e-399342e0674e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's modify our Value Class\n",
    "\n",
    "class Value:\n",
    "    # Constructor\n",
    "    def __init__(self, data, _children=(), label='', _op=''):\n",
    "        self.data = data\n",
    "        self.label = label\n",
    "        self.grad = 0\n",
    "        self._backward = lambda: None\n",
    "        # Used for Graph Construction\n",
    "        self._prev = set(_children)\n",
    "        self._op = _op if _op else label\n",
    "\n",
    "    def backward(self):\n",
    "        # Topological Sort, Sorting for Directed Acyclic Graph\n",
    "        topo = []\n",
    "        visited = set()\n",
    "        def build_topo(v):\n",
    "            if v not in visited:\n",
    "                visited.add(v)\n",
    "                for child in v._prev:\n",
    "                    build_topo(child)\n",
    "                topo.append(v)\n",
    "        build_topo(self)\n",
    "\n",
    "        # Freshly starting back propagation with its value as 1\n",
    "        self.grad = 1\n",
    "\n",
    "        # Backpropagation for Other Nodes\n",
    "        for vertex in topo:\n",
    "            vertex._backward()\n",
    "        \n",
    "    # For Printing Without Print Statements | Representation\n",
    "    def __repr__(self):\n",
    "        return f\"Value(data={self.data})\"\n",
    "    def __add__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        return Value(self.data + other.data, (self, other), '+')\n",
    "    def __mul__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data * other.data, (self, other), '*')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += other.data * out.grad\n",
    "            other.grad += self.data * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    # other + self\n",
    "    def __radd__(self, other):\n",
    "        return self + other\n",
    "    # other * self\n",
    "    def __rmul__(self, other):\n",
    "        return self * other"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "863cdd58-949f-40f4-a3b9-bae500f1d79c",
   "metadata": {},
   "source": [
    "We can manually back propagate and set the gradient to be interchanged with the data of the adjacent class for the moment...\n",
    "Cause we cannot do L.backward() at the moment, as we only implemented the derivative function of the multiplication method..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b73142e8-2107-443a-be9d-1574a8a20d51",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's modify our draw network to represent the gradients as well...\n",
    "\n",
    "def trace(root):\n",
    "    nodes, edges = set(), set()\n",
    "    def build(v):\n",
    "        if v not in nodes:\n",
    "            nodes.add(v)\n",
    "            for child in v._prev:\n",
    "                edges.add((child, v))\n",
    "                build(child)\n",
    "    build(root)\n",
    "    return nodes, edges\n",
    "\n",
    "def draw_networkx(root, rankdir='LR'):\n",
    "    assert rankdir in ['LR', 'TB']\n",
    "    nodes, edges = trace(root)\n",
    "    \n",
    "    G = nx.DiGraph()\n",
    "    \n",
    "    for n in nodes:\n",
    "        label = \"{label} \\n d={data:.4f} \\n g={grad:.4f}\".format(label=n.label, data=n.data, grad=n.grad)\n",
    "        G.add_node(str(id(n)), label=label)\n",
    "        if n._op:\n",
    "            G.add_node(str(id(n)) + n._op, label=n._op)\n",
    "            G.add_edge(str(id(n)) + n._op, str(id(n)))\n",
    "    \n",
    "    for n1, n2 in edges:\n",
    "        G.add_edge(str(id(n1)), str(id(n2)) + n2._op)\n",
    "    \n",
    "    pos = None\n",
    "    if rankdir == 'LR':\n",
    "        pos = nx.spring_layout(G, seed=4)\n",
    "    \n",
    "    labels = nx.get_node_attributes(G, 'label')\n",
    "    nx.draw(G, pos=pos, with_labels=True, labels=labels, font_size=6, font_weight='bold')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a3ce28b4-c7b2-4ad0-98cb-9683f9311206",
   "metadata": {},
   "outputs": [],
   "source": [
    "# draw_networkx(L) Won't Work"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "50fff2eb-9d91-47bb-b8d4-1b407066c218",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Manually Setting Gradient for Expression L = E * F\n",
    "L.grad = 1\n",
    "\n",
    "e.grad = f.data\n",
    "\n",
    "f.grad = e.data\n",
    "\n",
    "# All other nodes, required for drawing graph otherwise would throw an error expecting for gradient value\n",
    "a.grad = 0\n",
    "b.grad = 0\n",
    "c.grad = 0\n",
    "d.grad = 0\n",
    "\n",
    "draw_networkx(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64e45ccf-52a5-46ed-ba38-04946dcfea52",
   "metadata": {},
   "source": [
    "Now the next question that comes to the mind is...\n",
    "\n",
    "**What is the result of**\n",
    "\n",
    "$$ \\frac{dL}{dd} $$\n",
    "\n",
    "?\n",
    "\n",
    "Which follows up with\n",
    "\n",
    "$$ \\frac{de}{dd} $$\n",
    "\n",
    "Because we are now **know how L is sensitive to e**, we are now trying to **understand how L is sensitive to d**\n",
    "\n",
    "We Know:\n",
    "E = C + D\n",
    "\n",
    "Lets take our old derivative formula again:\n",
    "\n",
    "$$ ((f(x+h) - f(x)) / h) $$\n",
    "\n",
    "Substituting the values from the formula: E = C + D\n",
    "\n",
    "Because we are trying to understand that if we nudge the value of d by a certain amount 'h' how sensitive 'e' is:\n",
    "\n",
    "=> $$ (((d+h)+c) - (d+c)) / h $$\n",
    "=> $$ (d + h + c - d - c) / h $$\n",
    "=> $$ (h) / h $$\n",
    "=> $$ 1 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e2bb48c-eeea-48ee-aaea-f7e0d8a67b05",
   "metadata": {},
   "source": [
    "Now let's follow up with another mathematical section of the derivatives known as\n",
    "\n",
    "# Chain Rule\n",
    "\n",
    "The expression evaluates to :\n",
    "\n",
    "$$ \\frac{dz}{dx} = \\frac{dz}{dy} * \\frac{dy}{dx} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cefde2e-b93c-4a74-b764-5930e21e3b42",
   "metadata": {},
   "source": [
    "So,\n",
    "\n",
    "We **WANT**:\n",
    "$$ \\frac{dL}{dd} $$\n",
    "\n",
    "We **KNOW**:\n",
    "$$ \\frac{dL}{de} $$\n",
    "$$ \\frac{de}{dd} $$\n",
    "\n",
    "Applying Chain Rule:\n",
    "\n",
    "$$ \\frac{dz}{dx} = \\frac{dz}{dy} * \\frac{dy}{dx} $$\n",
    "\n",
    "We Substitute the values of:\n",
    "- z with L\n",
    "- y with e\n",
    "- x with d\n",
    "\n",
    "We get:\n",
    "$$ \\frac{dL}{dd} = \\frac{dL}{de} * \\frac{de}{dd} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "611472ca-39d2-44f9-b006-e010478d5948",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Manually Setting Gradient for Expression E = C + D\n",
    "\n",
    "# Old Expression\n",
    "L.grad = 1\n",
    "e.grad = f.data\n",
    "f.grad = e.data\n",
    "\n",
    "# New Expression\n",
    "c.grad = e.grad\n",
    "d.grad = e.grad\n",
    "\n",
    "# All other nodes\n",
    "a.grad = 0\n",
    "b.grad = 0\n",
    "\n",
    "draw_networkx(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fec01145-0adb-4089-8acf-7b2f6d216ccc",
   "metadata": {},
   "source": [
    "Once again,\n",
    "\n",
    "We **WANT**:\n",
    "$$ \\frac{dL}{da} $$\n",
    "\n",
    "We **KNOW**:\n",
    "$$ \\frac{dL}{de} $$ Our Global Derivative\n",
    "\n",
    "Applying Chain Rule:\n",
    "\n",
    "$$ \\frac{dz}{dx} = \\frac{dz}{dy} * \\frac{dy}{dx} $$\n",
    "\n",
    "We get:\n",
    "$$ \\frac{dL}{da} = \\frac{dL}{de} * \\frac{de}{dd} $$\n",
    "\n",
    "Where,\n",
    "$$ \\frac{dL}{de} $$ Is our **Global Derivative**\n",
    "$$ \\frac{dc}{da} $$ Is our **Local Derivative**\n",
    "\n",
    "To our good old,\n",
    "C = A * B\n",
    "\n",
    "We ask what is:\n",
    "$$ \\frac{dc}{da} $$\n",
    "\n",
    "So with the perspective of **Global Derivative** & **Local Derivative**,\n",
    "\n",
    "We get:\n",
    "$$ Current Gradient = Global Derivative * Local Derivative $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0145b279-b5df-4ec4-9ea4-9a4b0ccffe14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Manually Setting Gradient for Expression C = A * B\n",
    "\n",
    "# Old Expression\n",
    "L.grad = 1\n",
    "e.grad = f.data\n",
    "f.grad = e.data\n",
    "c.grad = e.grad\n",
    "d.grad = e.grad\n",
    "\n",
    "# New Expression\n",
    "a.grad = (c.grad * b.data)\n",
    "b.grad = (c.grad * a.data)\n",
    "\n",
    "draw_networkx(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7c081fbd-da41-460c-9598-ac9233668e74",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's modify our Value Class again after getting the idea of global and local derivatives\n",
    "\n",
    "class Value:\n",
    "    # Constructor\n",
    "    def __init__(self, data, _children=(), label='', _op=''):\n",
    "        self.data = data\n",
    "        self.label = label\n",
    "        self.grad = 0\n",
    "        self._backward = lambda: None\n",
    "        # Used for Graph Construction\n",
    "        self._prev = set(_children)\n",
    "        self._op = _op if _op else label\n",
    "\n",
    "    def backward(self):\n",
    "        # Topological Sort, Sorting for Directed Acyclic Graph\n",
    "        topo = []\n",
    "        visited = set()\n",
    "        def build_topo(v):\n",
    "            if v not in visited:\n",
    "                visited.add(v)\n",
    "                for child in v._prev:\n",
    "                    build_topo(child)\n",
    "                topo.append(v)\n",
    "        build_topo(self)\n",
    "\n",
    "        # Freshly starting back propagation with its value as 1\n",
    "        self.grad = 1\n",
    "\n",
    "        # Backpropagation for Other Nodes\n",
    "        for vertex in topo:\n",
    "            vertex._backward()\n",
    "        \n",
    "    # For Printing Without Print Statements | Representation\n",
    "    def __repr__(self):\n",
    "        return f\"Value(data={self.data})\"\n",
    "    def __add__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data + other.data, (self, other), '+')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += out.grad\n",
    "            other.grad += out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def __mul__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data * other.data, (self, other), '*')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += other.data * out.grad\n",
    "            other.grad += self.data * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    # other + self\n",
    "    def __radd__(self, other):\n",
    "        return self + other\n",
    "    # other * self\n",
    "    def __rmul__(self, other):\n",
    "        return self * other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b3bdd2ba-3928-41f3-a2c0-408a6a57a506",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Redefining our expression\n",
    "\n",
    "a = Value(3, label='a')\n",
    "b = Value(-2, label='b')\n",
    "d = Value(5, label='d')\n",
    "f = Value(-10, label='f')\n",
    "\n",
    "# Forward Pass\n",
    "c = a * b\n",
    "e = c + d\n",
    "L = e * f\n",
    "\n",
    "c.label = 'c'\n",
    "e.label = 'e'\n",
    "L.label = 'L'\n",
    "\n",
    "# Backward Pass\n",
    "L.backward()\n",
    "e.backward()\n",
    "c.backward()\n",
    "\n",
    "draw_networkx(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c0aaef5-3c97-4090-afd7-f9bc3c364ed6",
   "metadata": {},
   "source": [
    "So we know how **forward pass** and **backward pass** works now\n",
    "\n",
    "Let's now move on to something called a \n",
    "# Neuron"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2c2334b-cbf1-478c-8529-29211f96d040",
   "metadata": {},
   "source": [
    "So what is a **Neuron**? Or more specifically an **Artificial Neuron**?\n",
    "\n",
    "An artificial neuron is a mathematical function:\n",
    "\n",
    "$$\n",
    "y_k = \\varphi\\left(\\sum_{j=0}^{m} w_{kj}x_j\\right)\n",
    "$$\n",
    "\n",
    "Let's Visualize this \\\n",
    "![Artificial Neuron](https://i.stack.imgur.com/7mTvt.jpg)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae1cb532-d86e-4b54-b632-3710f9f6232e",
   "metadata": {},
   "source": [
    "So in simple terms an Artificial Neuron is a mathematical expression, \\\n",
    "That takes multiple inputs of say 'x' \\\n",
    "These inputs have their own weights, say 'w' \\\n",
    "And all this inputs have a common bias, say 'b' \\\n",
    "These inputs are then passed through a summation function \\\n",
    "The output of these summed inputs is then passed through an activation function \\\n",
    "which acts as a threshold function to limit the output to a certain value.\n",
    "\n",
    "Which evaluates to the expression:\n",
    "\n",
    "$$\n",
    "\\text{Summation Function} = x_1w_1 + x_2w_2 + \\ldots + x_nw_n + b\n",
    "$$\n",
    "\n",
    "Then,\n",
    "$$\n",
    "\\text{Neuron Output} =f(\\text{Summation Function})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aafa7e2b-7e3c-4c06-9d3e-f07a3a5ad2fd",
   "metadata": {},
   "source": [
    "So let's now practice with a neuron expression\n",
    "Let's take a simple expression:\n",
    "\n",
    "Summation Function = (x1w1 + x2w2 + b)\n",
    "Neuron Output = (Summation Function) -> tanh(Summation Function)\n",
    "\n",
    "Where tanh() is our activation function of choice."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef98104f-c1ac-4029-be02-985e20c64a3f",
   "metadata": {},
   "source": [
    "**How does tanh() work?**\n",
    "\n",
    "![](https://images.squarespace-cdn.com/content/v1/5acbdd3a25bf024c12f4c8b4/1524687495762-MQLVJGP4I57NT34XXTF4/TanhFunction.jpg)\n",
    "\n",
    "We can see it returns a value between -1 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "86f59154-5d00-4c72-8afa-ff124adc758d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# So, let's take our simple expression\n",
    "\n",
    "# Inputs\n",
    "x1 = Value(1, label='x1')\n",
    "x2 = Value(2, label='x2')\n",
    "\n",
    "# Weights\n",
    "w1 = Value(-3, label='w1')\n",
    "w2 = Value(0, label='w2')\n",
    "\n",
    "# Inputs\n",
    "b = Value(6.9, label='b')\n",
    "\n",
    "# Forward Pass\n",
    "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
    "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
    "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1x2w2'\n",
    "n = x1w1x2w2 + b; n.label = 'n'\n",
    "# n.tanh()\n",
    "# tanh is not implemented yet... so lets do that next\n",
    "\n",
    "draw_networkx(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bee1fdc-4bd0-451d-8725-4fbe12dd7213",
   "metadata": {},
   "source": [
    "So Let's Now Construct Tanh()\n",
    "\n",
    "\n",
    "According to the definition tanh() formulates to:\n",
    "$$ \\tanh x = \\frac{\\sinh x}{\\cosh x} = \\frac{e^x - e^{-x}}{e^x + e^{-x}} = \\frac{e^{2x} - 1}{e^{2x} + 1} $$\n",
    "\n",
    "We see that, in order to use the tanh method we need to implement **exponentiation** as well..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f77e281-9b65-46ba-8810-d4f534a55ccf",
   "metadata": {},
   "source": [
    "Now what is the **exponentiation function**?\n",
    "\n",
    "It evaluates to:\n",
    "$$ e^x = 1 + x + \\frac{x^2}{2!} + \\frac{x^3}{3!} + \\frac{x^4}{4!} + \\ldots $$\r\n",
    "![Exponentiation Function](https://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Exp_series.gif/220px-Exp_series.gif)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6da32b6-da58-4d48-9d38-02907fae4c68",
   "metadata": {},
   "source": [
    "We can see that, in the exponentiation function the series can go upto $$ \\infty $$\n",
    "\n",
    "So we can define our own exponentiation function limiting the series to 'n' terms..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68ffe667-c719-40f7-a3d1-a2539383803d",
   "metadata": {},
   "source": [
    "Note:\n",
    "\n",
    "Derivative of tanh() according to Wikipedia is:\n",
    "$$ 1 - \\tanh^2 x $$\n",
    "\n",
    "Derivative of exp() according to Wikipedia is:\n",
    "$$ \\frac{d}{dx}e^x = e^x \\quad \\text{and} \\quad e^0 = 1 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d41fbf68-44c5-436e-bbd0-e5e697955b7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's modify our Value Class again to implement exp and tanh functionality\n",
    "\n",
    "class Value:\n",
    "    # Constructor\n",
    "    def __init__(self, data, _children=(), label='', _op=''):\n",
    "        self.data = data\n",
    "        self.label = label\n",
    "        self.grad = 0\n",
    "        self._backward = lambda: None\n",
    "        # Used for Graph Construction\n",
    "        self._prev = set(_children)\n",
    "        self._op = _op if _op else label\n",
    "\n",
    "    def backward(self):\n",
    "        # Topological Sort, Sorting for Directed Acyclic Graph\n",
    "        topo = []\n",
    "        visited = set()\n",
    "        def build_topo(v):\n",
    "            if v not in visited:\n",
    "                visited.add(v)\n",
    "                for child in v._prev:\n",
    "                    build_topo(child)\n",
    "                topo.append(v)\n",
    "        build_topo(self)\n",
    "\n",
    "        # Freshly starting back propagation with its value as 1\n",
    "        self.grad = 1\n",
    "\n",
    "        # Backpropagation for Other Nodes\n",
    "        for vertex in topo:\n",
    "            vertex._backward()\n",
    "        \n",
    "    # For Printing Without Print Statements | Representation\n",
    "    def __repr__(self):\n",
    "        return f\"Value(data={self.data}, label='{self.label}', grad={self.grad:.4f})\"\n",
    "    def __format__(self, format_spec):\n",
    "        if format_spec == '':\n",
    "            return str(self)\n",
    "        return self.data.__format__(format_spec)\n",
    "    def __add__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data + other.data, (self, other), '+')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += out.grad\n",
    "            other.grad += out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def __mul__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data * other.data, (self, other), '*')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += other.data * out.grad\n",
    "            other.grad += self.data * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def __pow__(self, other):\n",
    "        assert isinstance(other, (int, float)), \"only supporting int/float powers for now\"\n",
    "        out = Value(self.data**other, (self,), f'**{other}')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += (other * self.data**(other-1)) * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def exp(self, terms=10):\n",
    "        x = self.data\n",
    "        result = 1.0\n",
    "        factorial = 1.0\n",
    "    \n",
    "        for i in range(1, int(terms) + 1):\n",
    "            factorial *= i\n",
    "            result += (x**i) / factorial\n",
    "        out = Value(result, (self, ), 'exp')\n",
    "        \n",
    "        def _backward():\n",
    "            self.grad += out.data * out.grad\n",
    "        out._backward = _backward\n",
    "        \n",
    "        return out\n",
    "    def tanh(self):\n",
    "        x = self.data\n",
    "        t = (self.exp(2*x) - 1)/(self.exp(2*x) + 1)\n",
    "        out = Value(t, (self, ), 'tanh')\n",
    "    \n",
    "        def _backward():\n",
    "          self.grad += (1 - t**2) * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    # -self\n",
    "    def __neg__(self):\n",
    "        return self * -1\n",
    "    # other + self\n",
    "    def __radd__(self, other):\n",
    "        return self + other\n",
    "    # self - other\n",
    "    def __sub__(self, other): \n",
    "        return self + (-other)\n",
    "    # other - self\n",
    "    def __rsub__(self, other): \n",
    "        return other + (-self)\n",
    "    # other * self\n",
    "    def __rmul__(self, other):\n",
    "        return self * other\n",
    "    # self / other\n",
    "    def __truediv__(self, other):\n",
    "        return self * other**-1\n",
    "    # other / self\n",
    "    def __rtruediv__(self, other):\n",
    "        return other * self**-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f05dfb4a-8a5b-4145-be15-94d9d6dd90a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# So, let's take our simple expression\n",
    "\n",
    "# Inputs\n",
    "x1 = Value(1, label='x1')\n",
    "x2 = Value(2, label='x2')\n",
    "\n",
    "# Weights\n",
    "w1 = Value(-3, label='w1')\n",
    "w2 = Value(0, label='w2')\n",
    "\n",
    "# Inputs\n",
    "b = Value(6.9, label='b')\n",
    "\n",
    "# Forward Pass\n",
    "x1w1 = x1 * w1; x1w1.label = 'x1w1'\n",
    "x2w2 = x2 * w2; x2w2.label = 'x2w2'\n",
    "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1x2w2'\n",
    "n = x1w1x2w2 + b; n.label = 'n'\n",
    "o = n.tanh(); o.label = 'o'\n",
    "\n",
    "draw_networkx(o)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49601010-6e93-4bde-8258-18baaa771226",
   "metadata": {},
   "source": [
    "Now that we understand how neurons work, we can now move on to building the official Neuron class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "9bf2ecb4-a39d-44a8-bb0d-ced24b408a69",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random # Yes I did cheat a little bit, otherwise without 'random' my brain would pop like a popsickle\n",
    "\n",
    "class Neuron:\n",
    "    def __init__(self, numberOfInputs):\n",
    "        self.w = [Value(random.uniform(-1,1)) for _ in range(numberOfInputs)]\n",
    "        self.b = Value(random.uniform(-1,1))\n",
    "    # Method to use f(x) notation when we initialize the variable f with Neuron class as a Neuron object\n",
    "    def __call__(self, x):\n",
    "        activation = sum((wi*xi for wi,xi in zip(self.w, x)), self.b)\n",
    "        output = activation.tanh()\n",
    "        return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "453de058-3125-4e9f-8477-2c8830859601",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Value(data=Value(data=0.0, label='*', grad=0.0000), label='tanh', grad=0.0000)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Testing the initial Neuron class\n",
    "inputs = [6.0,9.0]\n",
    "testNeuron = Neuron(2)\n",
    "testNeuron(inputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaa89b64-77e2-490a-b6f3-8d536e6d9677",
   "metadata": {},
   "source": [
    "Let's now make a **Neuron Layer** which will eventually help us make a **Multi Layer Perceptron** or **MLP**\n",
    "\n",
    "Let's visualize a Neural Network with MLP: \\\n",
    "![MLP](https://editor.analyticsvidhya.com/uploads/84918Neural-network-architecture-diagram.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54b2b9f3-ca9c-41ed-8081-407c6cd25e7c",
   "metadata": {},
   "source": [
    "Let's construct a Layer class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "fddd3fd1-079c-4bb6-b8dd-a5d352690a3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, numberOfInputs):\n",
    "        self.w = [Value(random.uniform(-1,1)) for _ in range(numberOfInputs)]\n",
    "        self.b = Value(random.uniform(-1,1))\n",
    "    # Method to use f(x) notation when we initialize the variable f with Neuron class as a Neuron object\n",
    "    def __call__(self, x):\n",
    "        activation = sum((wi*xi for wi,xi in zip(self.w, x)), self.b)\n",
    "        output = activation.tanh()\n",
    "        return output\n",
    "\n",
    "class Layer:\n",
    "    def __init__(self, numberOfInputs, numberOfOutputs):\n",
    "        self.neurons = [Neuron(numberOfInputs) for _ in range(numberOfOutputs)]\n",
    "    def __call__(self, x):\n",
    "        return [n(x) for n in self.neurons]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "b1a62137-38b3-472c-83c8-9c7b7021f68a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value(data=Value(data=0.0, label='*', grad=0.0000), label='tanh', grad=0.0000),\n",
       " Value(data=Value(data=0.8758937285024199, label='*', grad=0.0000), label='tanh', grad=0.0000),\n",
       " Value(data=Value(data=0.9470786783646301, label='*', grad=0.0000), label='tanh', grad=0.0000)]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Testing the initial Layer class\n",
    "inputs = [6.0,9.0]\n",
    "testLayer = Layer(2,3)\n",
    "testLayer(inputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e0f527d-7f01-4abf-8bb7-6eb1d3306859",
   "metadata": {},
   "source": [
    "We can now construct a MultiLayerPerceptron\n",
    "Let's construct our very own diagram as MLP example \\\n",
    "![MLP](https://editor.analyticsvidhya.com/uploads/84918Neural-network-architecture-diagram.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "9ff86564-7325-4b00-a610-6702b365c01f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Modified Value class to fix tanh error in computing int(terms)\n",
    "class Value:\n",
    "    # Constructor\n",
    "    def __init__(self, data, _children=(), label='', _op=''):\n",
    "        self.data = data\n",
    "        self.label = label\n",
    "        self.grad = 0\n",
    "        self._backward = lambda: None\n",
    "        # Used for Graph Construction\n",
    "        self._prev = set(_children)\n",
    "        self._op = _op if _op else label\n",
    "\n",
    "    def backward(self):\n",
    "        # Topological Sort, Sorting for Directed Acyclic Graph\n",
    "        topo = []\n",
    "        visited = set()\n",
    "        def build_topo(v):\n",
    "            if v not in visited:\n",
    "                visited.add(v)\n",
    "                for child in v._prev:\n",
    "                    build_topo(child)\n",
    "                topo.append(v)\n",
    "        build_topo(self)\n",
    "\n",
    "        # Freshly starting back propagation with its value as 1\n",
    "        self.grad = 1\n",
    "\n",
    "        # Backpropagation for Other Nodes\n",
    "        for vertex in topo:\n",
    "            vertex._backward()\n",
    "        \n",
    "    # For Printing Without Print Statements | Representation\n",
    "    def __repr__(self):\n",
    "        return f\"Value(data={self.data}, label='{self.label}', grad={self.grad:.4f})\"\n",
    "    def __format__(self, format_spec):\n",
    "        if format_spec == '':\n",
    "            return str(self)\n",
    "        return self.data.__format__(format_spec)\n",
    "    def __add__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data + other.data, (self, other), '+')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += out.grad\n",
    "            other.grad += out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def __mul__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data * other.data, (self, other), '*')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += other.data * out.grad\n",
    "            other.grad += self.data * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def __pow__(self, other):\n",
    "        assert isinstance(other, (int, float)), \"only supporting int/float powers for now\"\n",
    "        out = Value(self.data**other, (self,), f'**{other}')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += (other * self.data**(other-1)) * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def exp(self, terms=10):\n",
    "        x = self.data\n",
    "        result = 1.0\n",
    "        factorial = 1.0\n",
    "    \n",
    "        for i in range(1, int(terms) + 1):\n",
    "            factorial *= i\n",
    "            result += (x**i) / factorial\n",
    "    \n",
    "        out = Value(result, (self,), 'exp')\n",
    "    \n",
    "        def _backward():\n",
    "            self.grad += out.data * out.grad\n",
    "    \n",
    "        out._backward = _backward\n",
    "    \n",
    "        return out\n",
    "    def tanh(self):\n",
    "        x = self.data\n",
    "        exp_2x = self.exp(2*x)\n",
    "        t = (exp_2x - 1) / (exp_2x + 1)\n",
    "        out = Value(t.data, (self, ), 'tanh')\n",
    "    \n",
    "        def _backward():\n",
    "            self.grad += (1 - t.data**2) * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    # -self\n",
    "    def __neg__(self):\n",
    "        return self * -1\n",
    "    # other + self\n",
    "    def __radd__(self, other):\n",
    "        return self + other\n",
    "    # self - other\n",
    "    def __sub__(self, other): \n",
    "        return self + (-other)\n",
    "    # other - self\n",
    "    def __rsub__(self, other): \n",
    "        return other + (-self)\n",
    "    # other * self\n",
    "    def __rmul__(self, other):\n",
    "        return self * other\n",
    "    # self / other\n",
    "    def __truediv__(self, other):\n",
    "        return self * other**-1\n",
    "    # other / self\n",
    "    def __rtruediv__(self, other):\n",
    "        return other * self**-1\n",
    "        \n",
    "class Neuron:\n",
    "    def __init__(self, numberOfInputs):\n",
    "        self.w = [Value(random.uniform(-1,1)) for _ in range(numberOfInputs)]\n",
    "        self.b = Value(random.uniform(-1,1))\n",
    "    # Method to use f(x) notation when we initialize the variable f with Neuron class as a Neuron object\n",
    "    def __call__(self, x):\n",
    "        activation = sum((wi*xi for wi,xi in zip(self.w, x)), self.b)\n",
    "        output = activation.tanh()\n",
    "        return output\n",
    "\n",
    "class Layer:\n",
    "    def __init__(self, numberOfInputs, numberOfOutputs):\n",
    "        self.neurons = [Neuron(numberOfInputs) for _ in range(numberOfOutputs)]\n",
    "    def __call__(self, x):\n",
    "        return [n(x) for n in self.neurons]\n",
    "        \n",
    "class MultiLayerPerceptron:\n",
    "    def __init__(self, numberOfInputs, listOfNumberOfOutputsInEachLayer):\n",
    "        sz = [numberOfInputs] + listOfNumberOfOutputsInEachLayer\n",
    "        self.layers = [Layer(sz[i], sz[i+1]) for i in range(len(listOfNumberOfOutputsInEachLayer))]\n",
    "    def __call__(self, x):\n",
    "        for layer in self.layers:\n",
    "            x = layer(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "f0b7d28e-7831-491d-bfc7-036b28ba0328",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value(data=0.0, label='tanh', grad=0.0000),\n",
       " Value(data=0.0, label='tanh', grad=0.0000)]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Testing the initial MultiLayerPerceptron class\n",
    "inputs = [6.0,9.0,6.0,9.0]\n",
    "testMultiLayerPerceptron = MultiLayerPerceptron(3,[5,3,2])\n",
    "testMultiLayerPerceptron(inputs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "00201791-a91b-4eaa-a145-c9cf6530472c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value(data=0.0, label='tanh', grad=0.0000)]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets create a simpler neural network to eventually build the loss function\n",
    "inputs = [6.0,9.0]\n",
    "testMultiLayerPerceptron = MultiLayerPerceptron(3,[4,4,1])\n",
    "testMultiLayerPerceptron(inputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d91f2163-8d88-4164-8acc-685d94fe3e98",
   "metadata": {},
   "source": [
    "Now,\n",
    "\n",
    "**What is a loss function**?\n",
    "\n",
    "Loss function is a single number that is evaluated based on the individual losses of a neural network which says how good is our neural network.\n",
    "\n",
    "If loss is high, our neural network is performing bad.\n",
    "If loss is low, our neural network is performing good."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "018c9eee-20cc-4097-bdfa-f7cfa31a5b29",
   "metadata": {},
   "source": [
    "Before that let's define our **dataset** to train our network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "cef28e48-55c0-4f09-b724-d567faf5fb61",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's define four different input examples to the dataset\n",
    "xs = [\n",
    "  [1.0, 1.0, -1.],\n",
    "  [3.0, -1.0, 0.5],\n",
    "  [0.5, 1.0, 1.0],\n",
    "  [2.0, 3.0, -1.0],\n",
    "]\n",
    "# And their individual outputs as labels\n",
    "ys = [-1.0, 1.0, 1.0, -1.0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "930a82eb-d9eb-495d-ad49-db5bf990ca54",
   "metadata": {},
   "source": [
    "One of the most popular way to calculate loss is the **Mean Squared Error**\n",
    "\n",
    "$$ \\text{MSE} = \\frac{1}{n} \\sum_{i=1}^{n} \\left(Y_i - \\hat{Y_i}\\right)^2 $$\n",
    "\n",
    "Where,\n",
    "$$ \\text{MSE} = \\text{Mean Squared Error} $$\t\n",
    "$$ {n} = \\text{Number of data points} $$\n",
    "$$ Y_{i} = \\text{Observed Values or Actual Values} $$\n",
    "$$ \\hat{Y}_{i} = \\text{Predicted Values} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "57b3b7e8-5f40-4e4f-ae6d-f6a382efaa19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Value(data=4.0, label='+', grad=0.0000)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predicting Values from Data Examples\n",
    "ypred = [testMultiLayerPerceptron(inputs) for inputs in xs]\n",
    "# So eventually loss can be calculated as\n",
    "loss = sum((yout[0] - ygt)**2 for ygt, yout in zip(ys, ypred))\n",
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "32d8db30-c511-4b98-865e-5d7b7155d7ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We can now backpropagate from our loss element\n",
    "loss.backward()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f753a7b-a547-47e4-8d2f-d1caea7030ca",
   "metadata": {},
   "source": [
    "Let's now make a parameters attribute in each of these classes' definition to very handily set parameters in a batch\n",
    "\n",
    "For us, our parameters are:\n",
    " - For a Neuron -> The Weights and Biases\n",
    " - For a Layer -> The Parameters for all the Neurons in that Layer\n",
    " - For a Multi-Layer Perceptron -> The Parameters for all the Parameters in a Layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "66c653f5-4fb7-4d84-93fe-1b760c0ef6bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# So eventually our classes look like\n",
    "class Value:\n",
    "    # Constructor\n",
    "    def __init__(self, data, _children=(), label='', _op=''):\n",
    "        self.data = data\n",
    "        self.label = label\n",
    "        self.grad = 0\n",
    "        self._backward = lambda: None\n",
    "        # Used for Graph Construction\n",
    "        self._prev = set(_children)\n",
    "        self._op = _op if _op else label\n",
    "\n",
    "    def backward(self):\n",
    "        # Topological Sort, Sorting for Directed Acyclic Graph\n",
    "        topo = []\n",
    "        visited = set()\n",
    "        def build_topo(v):\n",
    "            if v not in visited:\n",
    "                visited.add(v)\n",
    "                for child in v._prev:\n",
    "                    build_topo(child)\n",
    "                topo.append(v)\n",
    "        build_topo(self)\n",
    "\n",
    "        # Freshly starting back propagation with its value as 1\n",
    "        self.grad = 1\n",
    "\n",
    "        # Backpropagation for Other Nodes\n",
    "        for vertex in topo:\n",
    "            vertex._backward()\n",
    "        \n",
    "    # For Printing Without Print Statements | Representation\n",
    "    def __repr__(self):\n",
    "        return f\"Value(data={self.data}, label='{self.label}', grad={self.grad:.4f})\"\n",
    "    def __format__(self, format_spec):\n",
    "        if format_spec == '':\n",
    "            return str(self)\n",
    "        return self.data.__format__(format_spec)\n",
    "    def __add__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data + other.data, (self, other), '+')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += out.grad\n",
    "            other.grad += out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def __mul__(self, other):\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "        out = Value(self.data * other.data, (self, other), '*')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += other.data * out.grad\n",
    "            other.grad += self.data * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def __pow__(self, other):\n",
    "        assert isinstance(other, (int, float)), \"only supporting int/float powers for now\"\n",
    "        out = Value(self.data**other, (self,), f'**{other}')\n",
    "\n",
    "        def _backward():\n",
    "            self.grad += (other * self.data**(other-1)) * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def exp(self, terms=10):\n",
    "        x = self.data\n",
    "        result = 1.0\n",
    "        factorial = 1.0\n",
    "    \n",
    "        for i in range(1, int(terms) + 1):\n",
    "            factorial *= i\n",
    "            result += (x**i) / factorial\n",
    "    \n",
    "        out = Value(result, (self,), 'exp')\n",
    "    \n",
    "        def _backward():\n",
    "            self.grad += out.data * out.grad\n",
    "    \n",
    "        out._backward = _backward\n",
    "    \n",
    "        return out\n",
    "    def tanh(self):\n",
    "        x = self.data\n",
    "        exp_2x = self.exp(2*x)\n",
    "        t = (exp_2x - 1) / (exp_2x + 1)\n",
    "        out = Value(t.data, (self, ), 'tanh')\n",
    "    \n",
    "        def _backward():\n",
    "            self.grad += (1 - t.data**2) * out.grad\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    # -self\n",
    "    def __neg__(self):\n",
    "        return self * -1\n",
    "    # other + self\n",
    "    def __radd__(self, other):\n",
    "        return self + other\n",
    "    # self - other\n",
    "    def __sub__(self, other): \n",
    "        return self + (-other)\n",
    "    # other - self\n",
    "    def __rsub__(self, other): \n",
    "        return other + (-self)\n",
    "    # other * self\n",
    "    def __rmul__(self, other):\n",
    "        return self * other\n",
    "    # self / other\n",
    "    def __truediv__(self, other):\n",
    "        return self * other**-1\n",
    "    # other / self\n",
    "    def __rtruediv__(self, other):\n",
    "        return other * self**-1\n",
    "        \n",
    "class Neuron:\n",
    "    def __init__(self, numberOfInputs):\n",
    "        self.w = [Value(random.uniform(-1,1)) for _ in range(numberOfInputs)]\n",
    "        self.b = Value(random.uniform(-1,1))\n",
    "    # Method to use f(x) notation when we initialize the variable f with Neuron class as a Neuron object\n",
    "    def __call__(self, x):\n",
    "        activation = sum((wi*xi for wi,xi in zip(self.w, x)), self.b)\n",
    "        output = activation.tanh()\n",
    "        return output\n",
    "    # The weights and biases in the Neuron\n",
    "    def parameters(self):\n",
    "        return self.w + [self.b]\n",
    "\n",
    "class Layer:\n",
    "    def __init__(self, numberOfInputs, numberOfOutputs):\n",
    "        self.neurons = [Neuron(numberOfInputs) for _ in range(numberOfOutputs)]\n",
    "    def __call__(self, x):\n",
    "        return [n(x) for n in self.neurons]\n",
    "    # The Parameters for all the Neurons in that Layer\n",
    "    def parameters(self):\n",
    "        return [p for n in self.neurons for p in n.parameters()]\n",
    "        \n",
    "class MultiLayerPerceptron:\n",
    "    def __init__(self, numberOfInputs, listOfNumberOfOutputsInEachLayer):\n",
    "        sz = [numberOfInputs] + listOfNumberOfOutputsInEachLayer\n",
    "        self.layers = [Layer(sz[i], sz[i+1]) for i in range(len(listOfNumberOfOutputsInEachLayer))]\n",
    "    def __call__(self, x):\n",
    "        for layer in self.layers:\n",
    "            x = layer(x)\n",
    "        return x\n",
    "    # The Parameters for all the Parameters in a Layer\n",
    "    def parameters(self):\n",
    "        return [p for layer in self.layers for p in layer.parameters()]\n",
    "    def __repr__(self):\n",
    "        return f\"MultiLayerPerceptron of [{', '.join(str(layer) for layer in self.layers)}]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "ed8d12b7-0c5f-4499-bdcf-00a3fb49d0fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value(data=0.0, label='tanh', grad=0.0000)]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets create a simpler neural network to eventually build the loss function\n",
    "inputs = [6.0,9.0]\n",
    "testMultiLayerPerceptron = MultiLayerPerceptron(3,[4,4,1])\n",
    "testMultiLayerPerceptron(inputs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "652002e9-0f7c-4716-8d93-1e5ad186535d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's define four different input examples to the dataset\n",
    "xs = [\n",
    "  [1.0, 1.0, -1.],\n",
    "  [3.0, -1.0, 0.5],\n",
    "  [0.5, 1.0, 1.0],\n",
    "  [2.0, 3.0, -1.0],\n",
    "]\n",
    "# And their individual outputs as labels\n",
    "ys = [-1.0, 1.0, 1.0, -1.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "21d0e642-1909-4f46-ad94-6165e8fa9ba4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Value(data=4.0, label='+', grad=0.0000)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predicting Values from Data Examples\n",
    "ypred = [testMultiLayerPerceptron(inputs) for inputs in xs]\n",
    "# So eventually loss can be calculated as\n",
    "loss = sum((yout[0] - ygt)**2 for ygt, yout in zip(ys, ypred))\n",
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "43d6a201-0b66-4fc0-bea4-9fd3f2c167a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We can now backpropagate from our loss element\n",
    "loss.backward()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb738c67-0d86-40f6-8ca4-e1d7b636f2c1",
   "metadata": {},
   "source": [
    "If we start nudging the data based on the gradient for all the parameters now,\n",
    "Our loss starts to effectively decrese now..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "7debda02-0c1b-47f8-b43d-ebb93e60409e",
   "metadata": {},
   "outputs": [],
   "source": [
    "for p in testMultiLayerPerceptron.parameters():\n",
    "    p.data += -0.1 * p.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "83ff04b4-576f-4a0a-80c6-58398ad3bdcd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.0000000000\n"
     ]
    }
   ],
   "source": [
    "# We can now run this same cell over and over to get a loss sequentially\n",
    "\n",
    "# Forward Pass\n",
    "ypred = [testMultiLayerPerceptron(inputs) for inputs in xs]\n",
    "loss = sum((yout[0] - ygt)**2 for ygt, yout in zip(ys, ypred))\n",
    "print(f\"{loss.data:.10f}\")\n",
    "\n",
    "# Backward Pass\n",
    "loss.backward()\n",
    "\n",
    "# Updating Data Values\n",
    "for p in testMultiLayerPerceptron.parameters():\n",
    "    p.data += -1 * p.grad"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e301bee-88fb-44b9-b849-63d7d761e39b",
   "metadata": {},
   "source": [
    "We can now eventually build a loop to iteratively come to gradient descent approach in a more natural manner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "0ad5ead7-d6f5-4168-8e7a-d1e7a2e0b1fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4.00000000000000000000\n",
      "1 4.00000000000000000000\n",
      "2 4.00000000000000000000\n",
      "3 4.00000000000000000000\n",
      "4 4.00000000000000000000\n",
      "5 4.00000000000000000000\n",
      "6 4.00000000000000000000\n",
      "7 4.00000000000000000000\n",
      "8 4.00000000000000000000\n",
      "9 4.00000000000000000000\n"
     ]
    }
   ],
   "source": [
    "passes = 10\n",
    "\n",
    "for index in range(passes):\n",
    "    # Forward Pass\n",
    "    ypred = [testMultiLayerPerceptron(inputs) for inputs in xs]\n",
    "    loss = sum((yout[0] - ygt)**2 for ygt, yout in zip(ys, ypred))\n",
    "    \n",
    "    # Backward Pass\n",
    "    loss.backward()\n",
    "    \n",
    "    # Updating Data Values\n",
    "    for p in testMultiLayerPerceptron.parameters():\n",
    "        p.data += -1 * p.grad\n",
    "\n",
    "    print(index,f\"{loss.data:.20f}\")"
   ]
  },
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   "id": "6896079d-0495-4033-9599-e519bd4975f3",
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   "source": [
    "In Conclusion,\n",
    "\n",
    "1. We saw how we can turn simple Values into mathematical expressions\n",
    "2. How their derivatives take place mathematically and practically\n",
    "3. Reused these Values to build Neurons\n",
    "4. Saw how these Neurons can form a Layer\n",
    "5. Saw how these Layers can be grouped to make a Multi Layer Perceptron\n",
    "6. Saw how we do a forward pass in these Neural Networks\n",
    "7. Saw how we calculate the loss function in these Neural Networks\n",
    "8. Saw how we do a backward pass in these Neural Networks\n",
    "9. Saw how update the data values in these Neural Networks\n",
    "10. Saw how we make a natural loop to do a forward pass, backward pass and updation of data values in a iterative manner"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e27de49c-4747-4fd1-822d-2d5c0a374c5e",
   "metadata": {},
   "source": [
    "I now also invite you all to contribute more to this notebook and eventually make improvements to the already written code...\n",
    "Happy Coding. :)"
   ]
  }
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