Part1_Micrograd_from_scratch.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPxd9Ivn9ZQ1qpKQ0bDEGB3"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SZaTU8panziH"
      },
      "outputs": [],
      "source": [
        "import math\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def f(x):\n",
        "  return 3*x**2 - 4*x + 5"
      ],
      "metadata": {
        "id": "lrv9rFsXq6F4"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "f(3.0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "neoYLSztrgHO",
        "outputId": "1fc9ac08-53f3-4c76-e01c-2bda506ad4b9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "20.0"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "xs = np.arange(-5, 5, 0.25)\n",
        "ys = f(xs)\n",
        "plt.plot(xs , ys)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "fiB6BY2urswm",
        "outputId": "98cce1d2-2810-42ee-bdb4-081757b2dabb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f9a787fc490>]"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "h = 0.00001\n",
        "x = -3.0\n",
        "(f(x + h) - f(x))/h"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VF2pamwvsmu9",
        "outputId": "6fed4483-77ef-4926-a589-e3f0ca01e130"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-21.999970000052823"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = 2.0\n",
        "b = -3.0\n",
        "c = 10\n",
        "d = a*b + c\n",
        "print(d)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "L1fuaxirtHPX",
        "outputId": "2bf3466e-4dc2-4f57-9c45-c265507a2b11"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "h = 0.0001\n",
        "\n",
        "a = 2.0\n",
        "b = -3.0\n",
        "c = 10.0\n",
        "\n",
        "d1 = a*b + c\n",
        "c += h\n",
        "d2 = a*b + c\n",
        "\n",
        "print('d1 =', d1)\n",
        "print('d2 =', d2)\n",
        "print('Slope =', (d2 - d1)/h)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dpUxpynruLWU",
        "outputId": "2336baec-83a0-4e38-f972-90f3b891aecc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "d1 = 4.0\n",
            "d2 = 4.0001\n",
            "Slope = 0.9999999999976694\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "class Value:\n",
        "\n",
        "  def __init__(self, data, _children=(), _operator='', label=''):\n",
        "    self.data = data\n",
        "    self.grad = 0.0\n",
        "    self._backward = lambda: None\n",
        "    self._prev = set(_children)\n",
        "    self._operator = _operator\n",
        "    self.label = label\n",
        "\n",
        "  def __repr__(self):\n",
        "    return f\"Value(data={self.data})\"\n",
        "\n",
        "  def __add__(self, other):\n",
        "    out = Value(self.data + other.data, (self, other), '+')\n",
        "    def _backward():\n",
        "      self.grad += 1.0 * out.grad\n",
        "      other.grad += 1.0 * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def __mul__(self, other):\n",
        "    out = Value(self.data * other.data, (self, other), '*')\n",
        "    def _backward():\n",
        "      self.grad += other.data * out.grad\n",
        "      other.grad += self.data * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def tanh(self):\n",
        "    x = self.data\n",
        "    t = (math.exp(2*x) - 1)/(math.exp(2*x) + 1)\n",
        "    out = Value(t, (self, ), 'tanh')\n",
        "    def _backward():\n",
        "      self.grad += (1 - t**2) * out.grad\n",
        "    out._backward = _backward\n",
        "    return out\n",
        "\n",
        "  def backward(self):\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",
        "    self.grad = 1.0\n",
        "    for node in reversed(topo):\n",
        "      node._backward()\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "a = Value(2.0, label='a')\n",
        "b = Value(-3.0, label='b')\n",
        "c = Value(10.0, label='c')\n",
        "e = a*b; e.label = 'e'\n",
        "d = e + c; d.label = 'd'\n",
        "print('d =', d)\n",
        "print('last value d =', d._prev)\n",
        "print('Last operator d =', d._operator)\n",
        "\n",
        "f = Value(-2.0, label='f')\n",
        "L = d * f ; L.label = 'L'\n",
        "print('L =', L)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Nx1A6o0dxeZn",
        "outputId": "fa193288-b878-4fd3-90b5-5c8a534660e3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "d = Value(data=4.0)\n",
            "last value d = {Value(data=10.0), Value(data=-6.0)}\n",
            "Last operator d = +\n",
            "L = Value(data=-8.0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from graphviz import Digraph\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_dot(root):\n",
        "  dot = Digraph(format='svg', graph_attr={'rankdir': 'LR'})\n",
        "\n",
        "  nodes, edges = trace(root)\n",
        "  for n in nodes:\n",
        "    uid = str(id(n))\n",
        "    dot.node(name = uid, label = \"{%s | data %.4f | grad %.4f }\" % (n.label, n.data, n.grad), shape='record')\n",
        "    if n._operator:\n",
        "      dot.node(name = uid + n._operator, label = n._operator)\n",
        "      dot.edge(uid + n._operator, uid)\n",
        "\n",
        "  for n1, n2 in edges:\n",
        "    dot.edge(str(id(n1)), str(id(n2)) + n2._operator)\n",
        "\n",
        "  return dot\n"
      ],
      "metadata": {
        "id": "ZE2Ut2Gy2BWO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "L.backward()\n",
        "draw_dot(L)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 249
        },
        "id": "GgNVycrH2Eal",
        "outputId": "259a47df-0ffb-498a-f6d5-10a33131750c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def derivative():\n",
        "\n",
        "  h = 0.0001\n",
        "\n",
        "  a = Value(2.0, label='a')\n",
        "  b = Value(-3.0, label='b')\n",
        "  c = Value(10.0, label='c')\n",
        "  e = a*b; e.label = 'e'\n",
        "  d = e + c; d.label = 'd'\n",
        "  f = Value(-2.0, label='f')\n",
        "  L = d * f ; L.label = 'L'\n",
        "  L1 = L.data\n",
        "\n",
        "  a = Value(2.0, label='a')\n",
        "  b = Value(-3.0, label='b')\n",
        "  b.data += h\n",
        "  c = Value(10.0, label='c')\n",
        "  e = a*b; e.label = 'e'\n",
        "  d = e + c; d.label = 'd'\n",
        "  f = Value(-2.0, label='f')\n",
        "  L = d * f ; L.label = 'L'\n",
        "  L2 = L.data\n",
        "\n",
        "  print((L2 - L1) / h)\n",
        "\n",
        "derivative()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Zq5gbQv5AdIU",
        "outputId": "b12046ea-a2e2-47af-f608-1456452bd8f8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-4.000000000008441\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(np.arange(-5,5,0.2), np.tanh(np.arange(-5,5,0.2))); plt.grid();"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "7s9h7NRbNSRA",
        "outputId": "82103f16-c7f1-4555-fea6-00e5051507b9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# inputs x1,x2\n",
        "x1 = Value(2.0, label='x1')\n",
        "x2 = Value(0.0, label='x2')\n",
        "# weights w1,w2\n",
        "w1 = Value(-3.0, label='w1')\n",
        "w2 = Value(1.0, label='w2')\n",
        "# bias of the neuron\n",
        "b = Value(6.8813735870195432, label='b')\n",
        "# x1*w1 + x2*w2 + b\n",
        "x1w1 = x1*w1; x1w1.label = 'x1*w1'\n",
        "x2w2 = x2*w2; x2w2.label = 'x2*w2'\n",
        "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1*w1 + x2*w2'\n",
        "n = x1w1x2w2 + b; n.label = 'n'\n",
        "o = n.tanh(); o.label = 'out'\n"
      ],
      "metadata": {
        "id": "VmXUfJ9UNdKW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "o.backward()\n",
        "draw_dot(o)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "id": "dJSsk0l7Qb1L",
        "outputId": "53002d7a-3aa9-4873-8655-16e3f437f0ff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
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