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The spelled-out intro to neural networks - Part2.ipynb
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the-spelled-out-intro-to-neural-networks-part2.ipynb
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"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"authorship_tag": "ABX9TyM0ebgSYDW+zer6wVhAlOmS",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/theptrk/cc83bb92e91a48b8ae97902d8576940e/the-spelled-out-intro-to-neural-networks-part2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"source": [
"import math\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
],
"metadata": {
"id": "Kj58OFy0zLSD"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "2D5KnuHiy-dV"
},
"outputs": [],
"source": [
"class Value: \n",
"\n",
" def __init__(self, data, _children=(), _op='', label=''):\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):\n",
" return f\"Value(data={self.data})\"\n",
"\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 += 1 * out.grad \n",
" other.grad += 1 * out.grad \n",
" out._backward = _backward\n",
"\n",
" return out\n",
"\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",
"\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",
"\n",
" def __rmul__(self, other): # other * self\n",
" return self * other\n",
"\n",
" def __truediv__(self, other): # self / other\n",
" return self * other**-1\n",
"\n",
" def __neg__(self): # -self\n",
" return self * -1\n",
"\n",
" def __sub__(self, other): # self - other\n",
" return self + (-other)\n",
" \n",
" def __radd__(self, other): # other + self\n",
" return self + other\n",
"\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",
" self.grad += (1 - t**2) * out.grad \n",
" out._backward = _backward\n",
"\n",
" return out\n",
"\n",
" def exp(self):\n",
" x = self.data\n",
" out = Value(math.exp(x), (self, ), 'exp')\n",
" \n",
" def _backward():\n",
" self.grad += out.data * out.grad \n",
" # NOTE: in the video I incorrectly used = instead of +=. Fixed here.\n",
" out._backward = _backward\n",
" \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()"
]
},
{
"cell_type": "code",
"source": [
"a = Value(2.0)\n",
"a-1"
],
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"base_uri": "https://localhost:8080/"
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"id": "c31yZ_VEz3oS",
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{
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"Value(data=1.0)"
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}
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{
"cell_type": "code",
"source": [
"from graphviz import Digraph\n",
"\n",
"def trace(root):\n",
" # builds a set of all nodes and edges in a graph\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'}) # LR = left to right\n",
" \n",
" nodes, edges = trace(root)\n",
" for n in nodes:\n",
" uid = str(id(n))\n",
" # for any value in the graph, create a rectangular ('record') node for it\n",
" dot.node(name = uid, label = \"{%s | data %.4f | grad %.4f }\" % (n.label, n.data, n.grad ), shape='record')\n",
" if n._op:\n",
" # if this value is a result of some operation, create an op node for it\n",
" dot.node(name = uid + n._op, label = n._op)\n",
" # and connect this node to it\n",
" dot.edge(uid + n._op, uid)\n",
"\n",
" for n1, n2 in edges:\n",
" # connect n1 to the op node of n2\n",
" dot.edge(str(id(n1)), str(id(n2)) + n2._op)\n",
"\n",
" return dot"
],
"metadata": {
"id": "LPxCRM_-zDL3"
},
"execution_count": null,
"outputs": []
},
{
"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 = 'o'\n",
"o.backward()"
],
"metadata": {
"id": "qqN6MJ9EzHc-"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"draw_dot(o)\n"
],
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"base_uri": "https://localhost:8080/",
"height": 321
},
"id": "UH-OkYCB5CNi",
"outputId": "28918831-0a9b-484a-f20c-d3a1154847fa"
},
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}
]
},
{
"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",
"# ----\n",
"e = (2*n).exp()\n",
"o = (e - 1) / (e + 1)\n",
"# ----\n",
"o.label = 'o'\n",
"o.backward()\n",
"draw_dot(o)"
],
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"base_uri": "https://localhost:8080/",
"height": 356
},
"id": "so-iS4215CZE",
"outputId": "db5f403e-60fe-4d98-c0a8-acbd1f582b2c"
},
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{
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},
"metadata": {},
"execution_count": 9
}
]
},
{
"cell_type": "code",
"source": [
"import random\n",
"\n",
"class Neuron:\n",
" \n",
" def __init__(self, nin):\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",
" # w * x + b\n",
" sum_plus_bias = sum((wi*xi for wi, xi in zip(self.w, x)), self.b)\n",
" out = sum_plus_bias.tanh()\n",
" return out\n",
" \n",
" def parameters(self):\n",
" return self.w + [self.b]\n",
"\n",
"class Layer:\n",
" \n",
" def __init__(self, nin, nout):\n",
" self.neurons = [Neuron(nin) for _ in range(nout)]\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",
" return [p for neuron in self.neurons for p in neuron.parameters()]\n",
"\n",
"class MLP:\n",
" \n",
" def __init__(self, nin, nouts):\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()]"
],
"metadata": {
"id": "Y8a0bopQ5Izh"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"x = [2.0, 3.0, -1.0]\n",
"\n",
"# n = Neuron(3)\n",
"# n(x)\n",
"\n",
"# l = Layer(3,3)\n",
"# l(x)\n",
"\n",
"mlp = MLP(3, [4,4,1])\n",
"mlp(x)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "HcALFlENxvFc",
"outputId": "ea64d0ce-62b4-46d5-c934-0d39ac0f2590"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Value(data=-0.5901895180839163)"
]
},
"metadata": {},
"execution_count": 56
}
]
},
{
"cell_type": "code",
"source": [
"draw_dot(mlp(x))"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "Y5iZ4EUpyCHY",
"outputId": "8be86a4d-5b10-45c1-de61-16e7e990f8fb"
},
"execution_count": null,
"outputs": [
{
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"data": {
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},
"metadata": {},
"execution_count": 57
}
]
},
{
"cell_type": "code",
"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"
],
"metadata": {
"id": "L8MajBLU2YcY"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"ypred = [mlp(x) for x in xs]\n",
"ypred"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "otta_vXK2rMA",
"outputId": "8dad155e-3cdf-43e3-a4ad-6d9ee16494cb"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[Value(data=0.8933124676756877),\n",
" Value(data=-0.6665567132670948),\n",
" Value(data=0.7973650834894992),\n",
" Value(data=0.853445732076444)]"
]
},
"metadata": {},
"execution_count": 142
}
]
},
{
"cell_type": "code",
"source": [
"[(yout-ygt)**2 for ygt, yout in zip(ys, ypred)]"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "irSY3DaA32di",
"outputId": "55272cf1-8d20-4d7f-9abe-dae70a961f96"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[Value(data=0.011382229553451176),\n",
" Value(data=0.11118442546724246),\n",
" Value(data=3.2305212433472144),\n",
" Value(data=0.021478153446609426)]"
]
},
"metadata": {},
"execution_count": 143
}
]
},
{
"cell_type": "code",
"source": [
"# mean squared error loss\n",
"# [(yout-ygt)**2 for ygt, yout in zip(ys, ypred)]\n",
"\n",
"# SUM OF mean squared error loss\n",
"loss = sum((yout-ygt)**2 for ygt, yout in zip(ys, ypred))\n",
"loss"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "Ly1sZXt923y8",
"outputId": "b48591b5-3b09-49c0-f8cd-fc687856b565"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Value(data=3.3745660518145173)"
]
},
"metadata": {},
"execution_count": 144
}
]
},
{
"cell_type": "code",
"source": [
"loss.backward()"
],
"metadata": {
"id": "eH4Lwe4f3nL-"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"mlp.layers[0].neurons[0].w[0].grad"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "04bBgi0a3p7O",
"outputId": "5f4ecb53-4bd2-44f3-f9b3-a76570affc86"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"-0.5818709982643476"
]
},
"metadata": {},
"execution_count": 146
}
]
},
{
"cell_type": "code",
"source": [
"mlp.layers[0].neurons[0].w[0].data"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "Hpd6yAWV5gRk",
"outputId": "d1be4d53-82b4-407c-f1df-e38da94dccca"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"-0.13239616527152753"
]
},
"metadata": {},
"execution_count": 147
}
]
},
{
"cell_type": "code",
"source": [
"len(mlp.parameters())"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "QCpAkcXe5Com",
"outputId": "7b6f4cae-18b8-4077-8a08-c0acacf5f36e"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"41"
]
},
"metadata": {},
"execution_count": 148
}
]
},
{
"cell_type": "code",
"source": [
"# draw_dot(loss)"
],
"metadata": {
"id": "eAWHL1k55bD0"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# nudge the data by the gradient\n",
"for p in mlp.parameters():\n",
" p.data += -0.01 * p.grad"
],
"metadata": {
"id": "9qLbhRyA5B-l"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"# see that data has changed\n",
"mlp.layers[0].neurons[0].w[0].data"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "EJChJ37m5BdL",
"outputId": "921c007b-e627-4e32-d229-c8de21f10475"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"-0.11494003532359712"
]
},
"metadata": {},
"execution_count": 160
}
]
},
{
"cell_type": "code",
"source": [
"ypred = [mlp(x) for x in xs]\n",
"loss = sum((yout-ygt)**2 for ygt, yout in zip(ys, ypred))\n",
"loss"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "WyY3L0ov5val",
"outputId": "1540d9e6-f6e4-44c7-adc7-9765361060c9"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Value(data=3.4008549616542587)"
]
},
"metadata": {},
"execution_count": 161
}
]
},
{
"cell_type": "code",
"source": [
"ypred"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "_ikWbpKi6VwJ",
"outputId": "a8e73d81-b7e9-4bd8-e202-efed0bc3971a"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[Value(data=0.8937246198020076),\n",
" Value(data=-0.6733700480680164),\n",
" Value(data=0.807136668351983),\n",
" Value(data=0.8691166870199393)]"
]
},
"metadata": {},
"execution_count": 162
}
]
},
{
"cell_type": "code",
"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\n"
],
"metadata": {
"id": "YOHAi_Sx8CpJ"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"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)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "bYCQ6q062kyB",
"outputId": "c242c586-5169-43ab-b982-8de50e7c1575"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"0 0.25464823757222455\n",
"1 0.2539637796344434\n",
"2 0.25328262383591993\n",
"3 0.25260474781875764\n",
"4 0.2519301294168201\n",
"5 0.2512587466537646\n",
"6 0.2505905777410996\n",
"7 0.24992560107626516\n",
"8 0.24926379524073206\n",
"9 0.24860513899813072\n",
"10 0.24794961129239326\n",
"11 0.24729719124592553\n",
"12 0.2466478581577937\n",
"13 0.24600159150193773\n",
"14 0.24535837092540047\n",
"15 0.24471817624658262\n",
"16 0.2440809874535133\n",
"17 0.24344678470214415\n",
"18 0.24281554831465985\n",
"19 0.24218725877781308\n"
]
}
]
},
{
"cell_type": "code",
"source": [],
"metadata": {
"id": "KiMnCIFE7Q3z"
},
"execution_count": null,
"outputs": []
}
]
}
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