micrograd_from_scratch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 3 * x**2 - 4 * x + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(3.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f9ea04c640>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.arange(-5, 5, 0.2)\n",
    "ys = f(xs)\n",
    "plt.plot(xs, ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02999999999997449"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h = 0.01\n",
    "x = 2 / 3\n",
    "(f(x + h) - f(x)) / h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d1 4.0\n",
      "d2 4.02\n",
      "slope 1.9999999999999574\n"
     ]
    }
   ],
   "source": [
    "a = 2.0\n",
    "b = -3.0\n",
    "c = 10.0\n",
    "\n",
    "d1 = a * b + c\n",
    "b += h\n",
    "d2 = a * b + c\n",
    "\n",
    "print(\"d1\", d1)\n",
    "print(\"d2\", d2)\n",
    "print(\"slope\", (d2 - d1) / h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Value:\n",
    "    def __init__(self, data, _children=(), _op=\"\", label=\"\") -> None:\n",
    "        self.data = data\n",
    "        self.grad = 0.0\n",
    "        self._backward = lambda: None\n",
    "        self._prev = set(_children)\n",
    "        self._op = _op\n",
    "        self.label = label\n",
    "\n",
    "    def __repr__(self) -> str:\n",
    "        return f\"Value(data={self.data})\"\n",
    "\n",
    "    def __add__(self, other):\n",
    "        # add constant\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "\n",
    "        out = Value(self.data + other.data, (self, other), \"+\")\n",
    "\n",
    "        def _backward():\n",
    "            # out with respect to self & other\n",
    "            self.grad += out.grad\n",
    "            other.grad += out.grad\n",
    "\n",
    "        out._backward = _backward\n",
    "        return out\n",
    "\n",
    "    def __mul__(self, other):\n",
    "        # add constant\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "\n",
    "        out = Value(self.data * other.data, (self, other), \"*\")\n",
    "\n",
    "        def _backward():\n",
    "            # out with respect to self & other\n",
    "            self.grad += other.data * out.grad\n",
    "            other.grad += self.data * out.grad\n",
    "\n",
    "        out._backward = _backward\n",
    "        return out\n",
    "\n",
    "    def __rmul__(self, other):\n",
    "        return self * other\n",
    "        # if we uses 'constant * Value', python will check Value to see if swap * can be applied\n",
    "\n",
    "    def __truediv__(self, other):\n",
    "        return self * other**-1\n",
    "\n",
    "    def __pow__(self, other):\n",
    "        assert isinstance(\n",
    "            other, (int, float)\n",
    "        ), \"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",
    "\n",
    "        # !self._backward = _backward\n",
    "        out._backward = _backward\n",
    "        return out\n",
    "\n",
    "    def __neg__(self):\n",
    "        return self * -1\n",
    "\n",
    "    def __sub__(self, other):\n",
    "        return self + (-other)\n",
    "\n",
    "    def exp(self):\n",
    "        # ! out = Value(math.exp(x), (self,), \"exp\") 你看看这是人吗\n",
    "        out = Value(math.exp(self.data), (self,), 'exp')\n",
    "        def _backward():\n",
    "            self.grad += out.data * out.grad\n",
    "\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",
    "\n",
    "        def _backward():\n",
    "            # out with respect to self & other\n",
    "            self.grad += (1 - t**2) * out.grad\n",
    "\n",
    "        out._backward = _backward\n",
    "\n",
    "        return out\n",
    "    def __radd__(self, other):\n",
    "        return self + other\n",
    "    \n",
    "    def backward(self):\n",
    "        self.grad = 1.0\n",
    "\n",
    "        topo = []\n",
    "        visited = set()\n",
    "\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",
    "\n",
    "        build_topo(self)\n",
    "\n",
    "        for node in reversed(topo):\n",
    "            node._backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graphviz import Digraph\n",
    "\n",
    "\n",
    "def trace(root):\n",
    "    nodes, edges = set(), set()\n",
    "\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",
    "\n",
    "    build(root)\n",
    "    return nodes, edges\n",
    "\n",
    "\n",
    "def draw_dot(root):\n",
    "    dot = Digraph(format=\"svg\", graph_attr={\"rankdir\": \"LR\"})  # LR = left to right\n",
    "\n",
    "    nodes, edges = trace(root)\n",
    "    for n in nodes:\n",
    "        uid = str(id(n))\n",
    "        dot.node(\n",
    "            name=uid,\n",
    "            label=\"{ %s | data %.4f | grad %.4f}\" % (n.label, n.data, n.grad),\n",
    "            shape=\"record\",\n",
    "        )\n",
    "        if n._op:\n",
    "            dot.node(name=uid + n._op, label=n._op)\n",
    "            dot.edge(uid + n._op, uid)\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": 35,
   "metadata": {},
   "outputs": [
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    "# 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='o'\n",
    "draw_dot(o)\n",
    "o.backward()\n",
    "draw_dot(o)"
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   "cell_type": "code",
   "execution_count": 36,
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    "# inputs x1,x2\n",
    "x1 = Value(2.0, label='x1')\n",
    "x2 = Value(0.0, label='x2')\n",
    "# weights w1,w2\n",
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    "x1w1 = x1*w1; x1w1.label = 'x1*w1'\n",
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    "x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1*w1 + x2*w2'\n",
    "n = x1w1x2w2 + b; n.label = 'n'\n",
    "e = (2*n).exp();e.label='e'\n",
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    "o.backward()\n",
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    "# solving the bug\n",
    "# we use a variable more than once, so we can't just set the grad with '=', and uses '+=' instead\n",
    "a = Value(3.0, label='a')\n",
    "b = a + a;b.label='b'\n",
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  {
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   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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     "text": [
      "0.7071066904050358\n",
      "x2 0.5000001283844369\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(tensor([0.7071], dtype=torch.float64), 0.7071066904050358)"
      ]
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     "execution_count": 38,
     "metadata": {},
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   "source": [
    "import torch\n",
    "\n",
    "x1 = torch.Tensor([2.0]).double();  x1.requires_grad=True\n",
    "x2 = torch.Tensor([0.]).double(); x2.requires_grad=True\n",
    "w1 = torch.Tensor([-3.]).double();w1.requires_grad=True\n",
    "w2 = torch.Tensor([1.]).double();w2.requires_grad=True\n",
    "b = torch.Tensor([6.8813735870195432,]).double();b.requires_grad=True\n",
    "n = x1*w1 + x2*w2 + b\n",
    "o = torch.tanh(n)\n",
    "\n",
    "print(o.data.item())\n",
    "o.backward()\n",
    "print('x2', x2.grad.item())\n",
    "o.data, o.data.item()"
   ]
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   "source": [
    "import random\n",
    "from re import I\n",
    "\n",
    "\n",
    "class Neuron:\n",
    "    def __init__(self, nin) -> None:\n",
    "        self.w = [Value(random.uniform(-1, 1)) for _ in range(nin)]\n",
    "        self.b = Value(random.uniform(-1, 1))\n",
    "\n",
    "    def __call__(self, x):\n",
    "        act = sum((wi * xi for wi, xi in zip(self.w, x)), self.b)\n",
    "        out = act.tanh()\n",
    "        return out\n",
    "\n",
    "    def parameters(self):\n",
    "        return self.w + [self.b]\n",
    "\n",
    "class Layer:\n",
    "    def __init__(self, nin, nout) -> None:\n",
    "        self.neurons = [Neuron(nin) for _ in range(nout)]\n",
    "\n",
    "\n",
    "    def __call__(self, x):\n",
    "        outs = [n(x) for n in self.neurons]\n",
    "        return outs[0] if len(outs) == 1 else outs\n",
    "\n",
    "    def parameters(self,):\n",
    "        params = []\n",
    "        for neuron in self.neurons:\n",
    "            ps = neuron.parameters()\n",
    "            params.extend(ps)\n",
    "        return params\n",
    "\n",
    "class MLP:\n",
    "    def __init__(self, nin, nouts: list) -> None:\n",
    "        sz = [nin] + nouts\n",
    "        self.layers = [Layer(sz[i], sz[i + 1]) for i in range(len(nouts))]\n",
    "\n",
    "    def __call__(self, x):\n",
    "        for layer in self.layers:\n",
    "            x = layer(x)\n",
    "        return x\n",
    "\n",
    "    def parameters(self):\n",
    "        return [p for layer in self.layers for p in layer.parameters()]\n",
    "\n",
    "x = [2.0, 3.0, -1.0]\n",
    "n = MLP(3, [4, 4, 1])\n",
    "n(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
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       "<!-- 2171329986464*&#45;&gt;2171329986464 -->\n",
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       "<title>2171329986464*&#45;&gt;2171329986464</title>\n",
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x1f98d69b430>"
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     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw_dot(n(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = [\n",
    "  [2.0, 3.0, -1.0],\n",
    "  [3.0, -1.0, 0.5],\n",
    "  [0.5, 1.0, 1.0],\n",
    "  [1.0, 1.0, -1.0],\n",
    "]\n",
    "ys = [1.0, -1.0, -1.0, 1.0] # desired targets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 3.887860629232175\n",
      "1 1.426088029888975\n",
      "2 0.3283184899193125\n",
      "3 0.05618490691323136\n",
      "4 0.04558808219666432\n",
      "5 0.038258646695472256\n",
      "6 0.032897636798310495\n",
      "7 0.028812672698011788\n",
      "8 0.025600937917557874\n",
      "9 0.023012320472521615\n",
      "10 0.02088345449302606\n",
      "11 0.019103202582293297\n",
      "12 0.017593385001795855\n",
      "13 0.016297441991369326\n",
      "14 0.015173466999511652\n",
      "15 0.014189765641042419\n",
      "16 0.013321934236214649\n",
      "17 0.012550884841022632\n",
      "18 0.011861477847976445\n",
      "19 0.011241555054072457\n"
     ]
    }
   ],
   "source": [
    "for k in range(20):\n",
    "  \n",
    "  # forward pass\n",
    "  ypred = [n(x) for x in xs]\n",
    "  loss = sum((yout - ygt)**2 for ygt, yout in zip(ys, ypred))\n",
    "  \n",
    "  # backward pass\n",
    "  for p in n.parameters():\n",
    "    p.grad = 0.0\n",
    "  loss.backward()\n",
    "  \n",
    "  # update\n",
    "  for p in n.parameters():\n",
    "    p.data += -0.1 * p.grad\n",
    "  \n",
    "  print(k, loss.data)\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value(data=0.04440827891010124),\n",
       " Value(data=-0.31964960229673334),\n",
       " Value(data=-1.0752832162307964),\n",
       " Value(data=-0.08316228633375491),\n",
       " Value(data=-0.5104421706184485),\n",
       " Value(data=0.634665766113002),\n",
       " Value(data=-0.9597677525465169),\n",
       " Value(data=0.08917566020626158),\n",
       " Value(data=-0.13933529160731684),\n",
       " Value(data=-0.5208866909467486),\n",
       " Value(data=0.5634403115228721),\n",
       " Value(data=0.36348530701781573),\n",
       " Value(data=-0.6971579133933264),\n",
       " Value(data=-0.7305804568111471),\n",
       " Value(data=0.6690967760613348),\n",
       " Value(data=-0.2252690385568312),\n",
       " Value(data=-0.8325262292284608),\n",
       " Value(data=-0.652223371913184),\n",
       " Value(data=0.2792075951859609),\n",
       " Value(data=0.6856424784096985),\n",
       " Value(data=0.16404262096256284),\n",
       " Value(data=-0.0712420984169957),\n",
       " Value(data=0.9868625924571536),\n",
       " Value(data=-0.7653467252128915),\n",
       " Value(data=0.8335120361940493),\n",
       " Value(data=0.3721924036702012),\n",
       " Value(data=0.39714031501048924),\n",
       " Value(data=0.29863914127089675),\n",
       " Value(data=-0.6173954583459916),\n",
       " Value(data=0.020238009814836824),\n",
       " Value(data=0.21904947526267915),\n",
       " Value(data=-0.7715624918672221),\n",
       " Value(data=-0.9803274465681763),\n",
       " Value(data=-0.909452380674053),\n",
       " Value(data=-0.03145952265681987),\n",
       " Value(data=-0.6567973665818427),\n",
       " Value(data=-0.5736461705854559),\n",
       " Value(data=0.8786783448361338),\n",
       " Value(data=0.8552882390100106),\n",
       " Value(data=-0.37256077614735),\n",
       " Value(data=-0.3986438119247172)]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.parameters()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ypred"
   ]
  }
 ],
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