micrograd_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c9e28332",
   "metadata": {},
   "outputs": [],
   "source": [
    "from micrograd.engine import Value\n",
    "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, format='svg', rankdir='LR'):\n",
    "    \"\"\"\n",
    "    format: png | svg | ...\n",
    "    rankdir: TB (top to bottom graph) | LR (left to right)\n",
    "    \"\"\"\n",
    "    assert rankdir in ['LR', 'TB']\n",
    "    nodes, edges = trace(root)\n",
    "    dot = Digraph(format=format, graph_attr={'rankdir': rankdir}) #, node_attr={'rankdir': 'TB'})\n",
    "    \n",
    "    for n in nodes:\n",
    "        dot.node(name=str(id(n)), label = \"{ data %.4f | grad %.4f }\" % (n.data, n.grad), shape='record')\n",
    "        if n._op:\n",
    "            dot.node(name=str(id(n)) + n._op, label=n._op)\n",
    "            dot.edge(str(id(n)) + n._op, str(id(n)))\n",
    "    \n",
    "    for n1, n2 in edges:\n",
    "        dot.edge(str(id(n1)), str(id(n2)) + n2._op)\n",
    "    \n",
    "    return dot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "7a922235",
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import uniform\n",
    "import numpy as np\n",
    "from tqdm import tqdm\n",
    "from sklearn import datasets\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "f84ff146",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def linear_dataset(count=300, y_intercept=-30, slope=4, spread=15.0):\n",
    "    X = np.array([i+(uniform(-spread, spread)) for i in range(count)])\n",
    "    y = np.array([y_intercept+i*slope+(uniform(-spread, spread)) for i in range(count)])\n",
    "    return X, y\n",
    "\n",
    "data_X, data_y = linear_dataset(10, -45.0, -3, 5)\n",
    "m = len(data_X); print(m)\n",
    "\n",
    "data_X = data_X.reshape(-1)\n",
    "\n",
    "plt.scatter(data_X, data_y)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "id": "64b3b558",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Value(data=-7.2283753990102175, grad=0),\n",
       " Value(data=-10.649678205375455, grad=0))"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = Value(0) # target weight is 1\n",
    "b = Value(0) # target bias is   0\n",
    "\n",
    "lr = 0.0001\n",
    "losses = []\n",
    "\n",
    "for i in range(2500):\n",
    "    forward = data_X * w + b\n",
    "    loss = (1/m)*np.sum((forward-data_y)**2)\n",
    "    losses.append(loss)\n",
    "    loss.backward()\n",
    "\n",
    "    w += -lr * w.grad\n",
    "    b += -lr * b.grad\n",
    "    \n",
    "plt.plot([i.data for i in losses])\n",
    "w, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "3c723d23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 0)"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.grad, b.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "id": "4826a9fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fe3b6d4c9d0>"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([i.data for i in data_X * w + b], data_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1dfbf51d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}