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dwsgrad/micrograd.ipynb
Tanishq Dubey a7e452ea6d Initial Commit
2024-08-15 14:39:29 -04:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 4,
"id": "6ba1fbfd-0c9b-41cc-8c91-109b7e7c75ce",
"metadata": {},
"outputs": [],
"source": [
"import math\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import random\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "6c68e697-08a6-437a-b70b-10d07fc25303",
"metadata": {},
"outputs": [],
"source": [
"def f(x):\n",
" return 3*x**2 - 4*x + 5"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "329d0306-7585-43c3-809e-1881c04186eb",
"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,
"id": "d9fe6d4a-f217-4140-ab5d-aa94b2873f96",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7bab3c22a960>]"
]
},
"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, 0.25)\n",
"ys = f(xs)\n",
"ys\n",
"plt.plot(xs, ys)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "c529bf0b-bc62-44aa-972d-f3bc5f062281",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"14.000001158365194"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"h = 0.000000001\n",
"x = 3.0\n",
"(f(x + h) - f(x))/h"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9033878d-ae71-4347-ad2d-7b346cd7e3cc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.0\n"
]
}
],
"source": [
"a = 2.0\n",
"b = -3.0\n",
"c = 10.0\n",
"d = a*b + c\n",
"print(d)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "4552a24e-b104-48cb-8af7-d25810616d6e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"d1 4.0\n",
"d2 4.000002\n",
"slope 2.000000000279556\n"
]
}
],
"source": [
"h = 0.000001\n",
"\n",
"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": 99,
"id": "c8b07ebe-ddab-4b6d-bb8b-a57962122bca",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Value(data=-8.0)"
]
},
"execution_count": 99,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"class Value:\n",
"\n",
" def __init__(self, data, _children=(), _op='', label='', tag=''):\n",
" self.data = data\n",
" self.grad = 0.0\n",
" self._prev = set(_children)\n",
" self._backward = lambda: None\n",
" self._op = _op\n",
" self.label = label\n",
" self.tag = tag\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(float(other), label=f'const: {other}', tag=self.tag)\n",
" out = Value(self.data + other.data, (self, other), '+', tag=self.tag)\n",
"\n",
"\n",
" def _backward():\n",
" self.grad += 1.0 * out.grad\n",
" other.grad += 1.0 * out.grad\n",
" \n",
" out._backward = _backward\n",
" \n",
" return out\n",
"\n",
" def __radd__(self, other):\n",
" return self + other\n",
"\n",
" def __neg__(self):\n",
" return self * -1\n",
"\n",
" def __sub__(self, other):\n",
" return self + (-other)\n",
"\n",
" def __mul__(self, other):\n",
" other = other if isinstance(other, Value) else Value(float(other), label=f'const: {other}', tag=self.tag)\n",
" out = Value(self.data * other.data, (self, other), '*', tag=self.tag)\n",
"\n",
" def _backward():\n",
" self.grad += other.data * out.grad\n",
" other.grad += self.data * out.grad\n",
" \n",
" out._backward = _backward\n",
"\n",
" return out\n",
"\n",
" def __rmul__(self, other):\n",
" return self * other\n",
"\n",
" def __truediv__(self, other):\n",
" return self * other**-1\n",
"\n",
" def __pow__(self, other):\n",
" assert isinstance(other, (int, float))\n",
" other = float(other)\n",
" out = Value(self.data**other, (self,), f'**{other}', tag=self.tag)\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 tanh(self):\n",
" n = self.data\n",
" t = (math.exp(2 * n) - 1) / (math.exp(2 * n) + 1)\n",
" out = Value(t, (self, ), 'tanh', tag=self.tag)\n",
"\n",
" def _backward():\n",
" self.grad += (1 - t**2) * out.grad\n",
" \n",
" out._backward = _backward\n",
" \n",
" return out\n",
"\n",
" def exp(self):\n",
" n = self.data\n",
" out = Value(math.exp(n), (self, ), 'exp', tag=self.tag)\n",
"\n",
" def _backward():\n",
" self.grad += out.data * out.grad\n",
" out._backward = _backward\n",
"\n",
" return out\n",
"\n",
" \n",
"\n",
" def backward(self):\n",
" self.grad = 1.0\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",
" for node in reversed(topo):\n",
" node._backward()\n",
"\n",
" \n",
"a = Value(2.0, label='a', tag='1,a')\n",
"b = Value(-3.0, label='b', tag='1,a')\n",
"c = Value(10.0, label='c', tag='2,a')\n",
"e = a*b; e.label = 'e'; e.tag='2,a'\n",
"d = e + c; d.label='d'; d.tag='3'\n",
"f = Value(-2.0, label='f', tag='3')\n",
"L = d * f; L.label='L'\n",
"L"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "72f770c5-27af-4f41-a4e3-4c234a03e0af",
"metadata": {},
"outputs": [],
"source": [
"from graphviz import Digraph\n",
"from collections import defaultdict\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",
"\n",
"def create_subgraph(dot, nodes, depth=0):\n",
" if nodes:\n",
" # Group nodes by the current tag at this depth\n",
" grouped_nodes = defaultdict(list)\n",
" for n in nodes:\n",
" tags = n.tag.split(',') if n.tag else []\n",
" if len(tags) > depth:\n",
" grouped_nodes[tags[depth]].append(n)\n",
" else:\n",
" grouped_nodes[None].append(n)\n",
" \n",
" # Create subgraphs for each tag\n",
" for tag, grouped in grouped_nodes.items():\n",
" if tag is not None:\n",
" with dot.subgraph(name='cluster_' + tag) as c:\n",
" c.attr(label=tag)\n",
" create_subgraph(c, grouped, depth + 1)\n",
" else:\n",
" for n in grouped:\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._op:\n",
" dot.node(name=uid + n._op, label=n._op)\n",
" dot.edge(uid + n._op, uid)\n",
"\n",
"def draw_dot(root):\n",
" dot = Digraph(format='svg', graph_attr={'rankdir': 'LR', \"beautify\": 'true'}, engine='dot')\n",
" \n",
" nodes, edges = trace(root)\n",
"\n",
" create_subgraph(dot, nodes)\n",
"\n",
" # Add edges\n",
" for n1, n2 in edges:\n",
" dot.edge(str(id(n1)), str(id(n2)) + n2._op)\n",
"\n",
" return dot"
]
},
{
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"execution_count": 181,
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"dL / dc\n",
"\n",
"dL / dD = -2\n",
"\n",
"dD / dC = 1.0\n",
"dD / dE = 1.0\n",
"\n",
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"\n",
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"dL / dC = dL/ dD * dD /dC\n",
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"\n",
"d = c + e\n",
"\n",
"\n",
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"\n",
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"\n",
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"(f(x+h) - f(x))/h\n",
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"L.grad = 1.0\n",
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"def lol():\n",
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" a = Value(2.0, label='a')\n",
" b = Value(-3.0, label='b')\n",
" c = Value(10.0,e label='c')\n",
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" L1 = L.data\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",
" L2 = L.data\n",
"\n",
" print((L2 - L1)/h)\n",
"\n",
"lol()"
]
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"# Inputs\n",
"x1 = Value(2.0, label='x1')\n",
"x2 = Value(0, label='x2')\n",
"# Weights\n",
"w1 = Value(-3.0, label='w1')\n",
"w2 = Value(1.0, label='w2')\n",
"\n",
"# Bias\n",
"b = Value(6.8813735870195432, label='b')\n",
"\n",
"# Cell body\n",
"## Weights\n",
"x1w1 = x1*w1; x1w1.label = 'x1 * w1'\n",
"x2w2 = x2*w2; x2w2.label = 'x2 * w2'\n",
"\n",
"## Sum\n",
"x1w1x2w2 = x1w1 + x2w2; x1w1x2w2.label = 'x1w1 + x2w2'\n",
"\n",
"## Add Bias\n",
"n = x1w1x2w2 + b; n.label = 'n'\n",
"\n",
"\n",
"\n",
"#---\n",
"e = (2*n).exp(); e.label = 'e'\n",
"o = (e - 1) / (e + 1); o.label = 'o'\n",
"#---\n",
"#o = n.tanh(); o.label = 'o'\n",
"\n",
"o.backward()\n",
"\n",
"draw_dot(o)"
]
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{
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"id": "5d9675c6-ccb7-4c30-814f-cc2fd8e16ebc",
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"o.grad = 1.0\n",
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"cell_type": "code",
"execution_count": 78,
"id": "ffd9f7cb-908d-48aa-992d-8f936045c09c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The shape of training images: (60000, 784) and training labels: (60000,)\n",
"The shape of test images: (10000, 784) and test labels: (10000,)\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data_sources = {\n",
" \"training_images\": \"train-images-idx3-ubyte.gz\", # 60,000 training images.\n",
" \"test_images\": \"t10k-images-idx3-ubyte.gz\", # 10,000 test images.\n",
" \"training_labels\": \"train-labels-idx1-ubyte.gz\", # 60,000 training labels.\n",
" \"test_labels\": \"t10k-labels-idx1-ubyte.gz\", # 10,000 test labels.\n",
"}\n",
"\n",
"# Use responsibly! When running notebooks locally, be sure to keep local\n",
"# copies of the datasets to prevent unnecessary server requests\n",
"headers = {\n",
" \"User-Agent\": \"Mozilla/5.0 (X11; Linux x86_64; rv:10.0) Gecko/20100101 Firefox/10.0\"\n",
"}\n",
"request_opts = {\n",
" \"headers\": headers,\n",
" \"params\": {\"raw\": \"true\"},\n",
"}\n",
"\n",
"import requests\n",
"import os\n",
"\n",
"data_dir = \"../_data\"\n",
"os.makedirs(data_dir, exist_ok=True)\n",
"\n",
"base_url = \"https://github.com/rossbar/numpy-tutorial-data-mirror/blob/main/\"\n",
"\n",
"for fname in data_sources.values():\n",
" fpath = os.path.join(data_dir, fname)\n",
" if not os.path.exists(fpath):\n",
" print(\"Downloading file: \" + fname)\n",
" resp = requests.get(base_url + fname, stream=True, **request_opts)\n",
" resp.raise_for_status() # Ensure download was succesful\n",
" with open(fpath, \"wb\") as fh:\n",
" for chunk in resp.iter_content(chunk_size=128):\n",
" fh.write(chunk)\n",
"\n",
"import gzip\n",
"\n",
"mnist_dataset = {}\n",
"\n",
"# Images\n",
"for key in (\"training_images\", \"test_images\"):\n",
" with gzip.open(os.path.join(data_dir, data_sources[key]), \"rb\") as mnist_file:\n",
" mnist_dataset[key] = np.frombuffer(\n",
" mnist_file.read(), np.uint8, offset=16\n",
" ).reshape(-1, 28 * 28)\n",
"# Labels\n",
"for key in (\"training_labels\", \"test_labels\"):\n",
" with gzip.open(os.path.join(data_dir, data_sources[key]), \"rb\") as mnist_file:\n",
" mnist_dataset[key] = np.frombuffer(mnist_file.read(), np.uint8, offset=8)\n",
"\n",
"x_train, y_train, x_test, y_test = (\n",
" mnist_dataset[\"training_images\"],\n",
" mnist_dataset[\"training_labels\"],\n",
" mnist_dataset[\"test_images\"],\n",
" mnist_dataset[\"test_labels\"],\n",
")\n",
"\n",
"print(\n",
" \"The shape of training images: {} and training labels: {}\".format(\n",
" x_train.shape, y_train.shape\n",
" )\n",
")\n",
"print(\n",
" \"The shape of test images: {} and test labels: {}\".format(\n",
" x_test.shape, y_test.shape\n",
" )\n",
")\n",
"\n",
"# Take the 60,000th image (indexed at 59,999) from the training set,\n",
"# reshape from (784, ) to (28, 28) to have a valid shape for displaying purposes.\n",
"mnist_image = x_train[0, :].reshape(28, 28)\n",
"# Set the color mapping to grayscale to have a black background.\n",
"plt.imshow(mnist_image, cmap=\"gray\")\n",
"# Display the image.\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 74,
"id": "3f8f1165-2a02-4b6f-85e6-7c9bcee655ee",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 5 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"num_examples = 5\n",
"seed = 147197952744\n",
"rng = np.random.default_rng(seed)\n",
"\n",
"fig, axes = plt.subplots(1, num_examples)\n",
"for sample, ax in zip(rng.choice(x_train, size=num_examples, replace=False), axes):\n",
" ax.imshow(sample.reshape(28, 28), cmap=\"gray\")"
]
},
{
"cell_type": "code",
"execution_count": 102,
"id": "e37a04f2-52f2-4cbb-b186-92ffa23e2ed3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
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" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0.07058824, 0.85882353, 0.99215686, 0.99215686,\n",
" 0.99215686, 0.99215686, 0.99215686, 0.77647059, 0.71372549,\n",
" 0.96862745, 0.94509804, 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0.31372549, 0.61176471, 0.41960784, 0.99215686, 0.99215686,\n",
" 0.80392157, 0.04313725, 0. , 0.16862745, 0.60392157,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0.05490196,\n",
" 0.00392157, 0.60392157, 0.99215686, 0.35294118, 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0.54509804,\n",
" 0.99215686, 0.74509804, 0.00784314, 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0.04313725, 0.74509804, 0.99215686,\n",
" 0.2745098 , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0.1372549 , 0.94509804, 0.88235294, 0.62745098,\n",
" 0.42352941, 0.00392157, 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0.31764706, 0.94117647, 0.99215686, 0.99215686, 0.46666667,\n",
" 0.09803922, 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0.17647059,\n",
" 0.72941176, 0.99215686, 0.99215686, 0.58823529, 0.10588235,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0.0627451 , 0.36470588,\n",
" 0.98823529, 0.99215686, 0.73333333, 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0.97647059, 0.99215686,\n",
" 0.97647059, 0.25098039, 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0.18039216, 0.50980392,\n",
" 0.71764706, 0.99215686, 0.99215686, 0.81176471, 0.00784314,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0.15294118,\n",
" 0.58039216, 0.89803922, 0.99215686, 0.99215686, 0.99215686,\n",
" 0.98039216, 0.71372549, 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0.09411765, 0.44705882, 0.86666667, 0.99215686, 0.99215686,\n",
" 0.99215686, 0.99215686, 0.78823529, 0.30588235, 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0.09019608, 0.25882353, 0.83529412, 0.99215686,\n",
" 0.99215686, 0.99215686, 0.99215686, 0.77647059, 0.31764706,\n",
" 0.00784314, 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0.07058824, 0.67058824, 0.85882353,\n",
" 0.99215686, 0.99215686, 0.99215686, 0.99215686, 0.76470588,\n",
" 0.31372549, 0.03529412, 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0.21568627, 0.6745098 ,\n",
" 0.88627451, 0.99215686, 0.99215686, 0.99215686, 0.99215686,\n",
" 0.95686275, 0.52156863, 0.04313725, 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0.53333333, 0.99215686, 0.99215686, 0.99215686,\n",
" 0.83137255, 0.52941176, 0.51764706, 0.0627451 , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. , 0. ,\n",
" 0. , 0. , 0. , 0. ])"
]
},
"execution_count": 102,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.divide(x_train, 255.0)[0]"
]
},
{
"cell_type": "code",
"execution_count": 83,
"id": "099de0a6-a6c4-460a-994f-b64e6287f3e9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"np.uint8(0)"
]
},
"execution_count": 83,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_train[1]"
]
},
{
"cell_type": "code",
"execution_count": 103,
"id": "d767c65f-5167-45b1-9b18-2900163035df",
"metadata": {},
"outputs": [],
"source": [
"dataMap = {}\n",
"\n",
"for i in range(10):\n",
" a = [0] * 10\n",
" a[i] = 1\n",
" dataMap[i] = a\n",
"\n",
"\n",
"ys = []\n",
"for y in y_train:\n",
" ys.append(dataMap[y])\n",
"\n",
"xs = np.divide(x_train, 255.0).tolist()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d8ff11da-2715-4866-a13f-457d8e9c5b6d",
"metadata": {},
"outputs": [],
"source": [
"loss = Value(1000)\n",
"\n",
"n = MultiLayerPerceptron(784, [16, 10])\n",
"\n",
"while loss.data > 0.1:\n",
" ypred = [n(x) for x in xs]\n",
" loss = sum([(yout[0] - ygt)**2 for ygt, yout in zip(ys, ypred)])\n",
" for p in n.parameters():\n",
" p.grad = 0\n",
" loss.backward()\n",
" if loss.data < 0.1:\n",
" break\n",
" for p in n.parameters():\n",
" p.data += -0.05 * p.grad\n",
" print(loss.data)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ceab5f8e-49b0-457a-8499-abcb4b3123ec",
"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": "3.12.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
Reference in New Issue View Git Blame Copy Permalink