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deep-learning-with-python-n…/chapter02_mathematical-building-blocks.ipynb
François Chollet 564df50076 Update notebooks for TF 2.6
2021-06-25 14:03:50 -07:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"This is a companion notebook for the book [Deep Learning with Python, Second Edition](https://www.manning.com/books/deep-learning-with-python-second-edition?a_aid=keras&a_bid=76564dff). For readability, it only contains runnable code blocks and section titles, and omits everything else in the book: text paragraphs, figures, and pseudocode.\n\n**If you want to be able to follow what's going on, I recommend reading the notebook side by side with your copy of the book.**\n\nThis notebook was generated for TensorFlow 2.6."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"# The mathematical building blocks of neural networks"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"## A first look at a neural network"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"**Loading the MNIST dataset in Keras**"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"from tensorflow.keras.datasets import mnist\n",
"(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"train_images.shape"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"len(train_labels)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"train_labels"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"test_images.shape"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"len(test_labels)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"test_labels"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"**The network architecture**"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"from tensorflow import keras\n",
"from tensorflow.keras import layers\n",
"model = keras.Sequential([\n",
" layers.Dense(512, activation=\"relu\"),\n",
" layers.Dense(10, activation=\"softmax\")\n",
"])"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"**The compilation step**"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"model.compile(optimizer=\"rmsprop\",\n",
" loss=\"sparse_categorical_crossentropy\",\n",
" metrics=[\"accuracy\"])"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"**Preparing the image data**"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"train_images = train_images.reshape((60000, 28 * 28))\n",
"train_images = train_images.astype(\"float32\") / 255\n",
"test_images = test_images.reshape((10000, 28 * 28))\n",
"test_images = test_images.astype(\"float32\") / 255"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"**\"Fitting\" the model**"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"model.fit(train_images, train_labels, epochs=5, batch_size=128)"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"**Using the model to make predictions**"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"test_digits = test_images[0:10]\n",
"predictions = model.predict(test_digits)\n",
"predictions[0]"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"predictions[0].argmax()"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"predictions[0][7]"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"test_labels[0]"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"**Evaluating the model on new data**"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"test_loss, test_acc = model.evaluate(test_images, test_labels)\n",
"print(f\"test_acc: {test_acc}\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"## Data representations for neural networks"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Scalars (rank-0 tensors)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"import numpy as np\n",
"x = np.array(12)\n",
"x"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x.ndim"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Vectors (rank-1 tensors)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x = np.array([12, 3, 6, 14, 7])\n",
"x"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x.ndim"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Matrices (rank-2 tensors)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x = np.array([[5, 78, 2, 34, 0],\n",
" [6, 79, 3, 35, 1],\n",
" [7, 80, 4, 36, 2]])\n",
"x.ndim"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Rank-3 tensors and higher-rank tensors"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x = np.array([[[5, 78, 2, 34, 0],\n",
" [6, 79, 3, 35, 1],\n",
" [7, 80, 4, 36, 2]],\n",
" [[5, 78, 2, 34, 0],\n",
" [6, 79, 3, 35, 1],\n",
" [7, 80, 4, 36, 2]],\n",
" [[5, 78, 2, 34, 0],\n",
" [6, 79, 3, 35, 1],\n",
" [7, 80, 4, 36, 2]]])\n",
"x.ndim"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Key attributes"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"from tensorflow.keras.datasets import mnist\n",
"(train_images, train_labels), (test_images, test_labels) = mnist.load_data()"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"train_images.ndim"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"train_images.shape"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"train_images.dtype"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"**Displaying the fourth digit**"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"digit = train_images[4]\n",
"plt.imshow(digit, cmap=plt.cm.binary)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"train_labels[4]"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Manipulating tensors in NumPy"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"my_slice = train_images[10:100]\n",
"my_slice.shape"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"my_slice = train_images[10:100, :, :]\n",
"my_slice.shape"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"my_slice = train_images[10:100, 0:28, 0:28]\n",
"my_slice.shape"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"my_slice = train_images[:, 14:, 14:]"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"my_slice = train_images[:, 7:-7, 7:-7]"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### The notion of data batches"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"batch = train_images[:128]"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"batch = train_images[128:256]"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"n = 3\n",
"batch = train_images[128 * n:128 * (n + 1)]"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Real-world examples of data tensors"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Vector data"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Timeseries data or sequence data"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Image data"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Video data"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"## The gears of neural networks: tensor operations"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Element-wise operations"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def naive_relu(x):\n",
" assert len(x.shape) == 2\n",
" x = x.copy()\n",
" for i in range(x.shape[0]):\n",
" for j in range(x.shape[1]):\n",
" x[i, j] = max(x[i, j], 0)\n",
" return x"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def naive_add(x, y):\n",
" assert len(x.shape) == 2\n",
" assert x.shape == y.shape\n",
" x = x.copy()\n",
" for i in range(x.shape[0]):\n",
" for j in range(x.shape[1]):\n",
" x[i, j] += y[i, j]\n",
" return x"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"import time\n",
"\n",
"x = np.random.random((20, 100))\n",
"y = np.random.random((20, 100))\n",
"\n",
"t0 = time.time()\n",
"for _ in range(1000):\n",
" z = x + y\n",
" z = np.maximum(z, 0.)\n",
"print(\"Took: {0:.2f} s\".format(time.time() - t0))"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"t0 = time.time()\n",
"for _ in range(1000):\n",
" z = naive_add(x, y)\n",
" z = naive_relu(z)\n",
"print(\"Took: {0:.2f} s\".format(time.time() - t0))"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Broadcasting"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"import numpy as np\n",
"X = np.random.random((32, 10))\n",
"y = np.random.random((10,))"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"y = np.expand_dims(y, axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"Y = np.concatenate([y] * 32, axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def naive_add_matrix_and_vector(x, y):\n",
" assert len(x.shape) == 2\n",
" assert len(y.shape) == 1\n",
" assert x.shape[1] == y.shape[0]\n",
" x = x.copy()\n",
" for i in range(x.shape[0]):\n",
" for j in range(x.shape[1]):\n",
" x[i, j] += y[j]\n",
" return x"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"import numpy as np\n",
"x = np.random.random((64, 3, 32, 10))\n",
"y = np.random.random((32, 10))\n",
"z = np.maximum(x, y)"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Tensor product"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x = np.random.random((32,))\n",
"y = np.random.random((32,))\n",
"z = np.dot(x, y)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def naive_vector_dot(x, y):\n",
" assert len(x.shape) == 1\n",
" assert len(y.shape) == 1\n",
" assert x.shape[0] == y.shape[0]\n",
" z = 0.\n",
" for i in range(x.shape[0]):\n",
" z += x[i] * y[i]\n",
" return z"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def naive_matrix_vector_dot(x, y):\n",
" assert len(x.shape) == 2\n",
" assert len(y.shape) == 1\n",
" assert x.shape[1] == y.shape[0]\n",
" z = np.zeros(x.shape[0])\n",
" for i in range(x.shape[0]):\n",
" for j in range(x.shape[1]):\n",
" z[i] += x[i, j] * y[j]\n",
" return z"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def naive_matrix_vector_dot(x, y):\n",
" z = np.zeros(x.shape[0])\n",
" for i in range(x.shape[0]):\n",
" z[i] = naive_vector_dot(x[i, :], y)\n",
" return z"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def naive_matrix_dot(x, y):\n",
" assert len(x.shape) == 2\n",
" assert len(y.shape) == 2\n",
" assert x.shape[1] == y.shape[0]\n",
" z = np.zeros((x.shape[0], y.shape[1]))\n",
" for i in range(x.shape[0]):\n",
" for j in range(y.shape[1]):\n",
" row_x = x[i, :]\n",
" column_y = y[:, j]\n",
" z[i, j] = naive_vector_dot(row_x, column_y)\n",
" return z"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Tensor reshaping"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"train_images = train_images.reshape((60000, 28 * 28))"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x = np.array([[0., 1.],\n",
" [2., 3.],\n",
" [4., 5.]])\n",
"x.shape"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x = x.reshape((6, 1))\n",
"x"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x = np.zeros((300, 20))\n",
"x = np.transpose(x)\n",
"x.shape"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Geometric interpretation of tensor operations"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### A geometric interpretation of deep learning"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"## The engine of neural networks: gradient-based optimization"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### What's a derivative?"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Derivative of a tensor operation: the gradient"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Stochastic gradient descent"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Chaining derivatives: the Backpropagation algorithm"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"#### The chain rule"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"#### Automatic differentiation with computation graphs"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"#### The Gradient Tape in TensorFlow"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"import tensorflow as tf\n",
"x = tf.Variable(0.)\n",
"with tf.GradientTape() as tape:\n",
" y = 2 * x + 3\n",
"grad_of_y_wrt_x = tape.gradient(y, x)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"x = tf.Variable(tf.random.uniform((2, 2)))\n",
"with tf.GradientTape() as tape:\n",
" y = 2 * x + 3\n",
"grad_of_y_wrt_x = tape.gradient(y, x)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"W = tf.Variable(tf.random.uniform((2, 2)))\n",
"b = tf.Variable(tf.zeros((2,)))\n",
"x = tf.random.uniform((2, 2))\n",
"with tf.GradientTape() as tape:\n",
" y = tf.matmul(x, W) + b\n",
"grad_of_y_wrt_W_and_b = tape.gradient(y, [W, b])"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"## Looking back at our first example"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
"train_images = train_images.reshape((60000, 28 * 28))\n",
"train_images = train_images.astype(\"float32\") / 255\n",
"test_images = test_images.reshape((10000, 28 * 28))\n",
"test_images = test_images.astype(\"float32\") / 255"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"model = keras.Sequential([\n",
" layers.Dense(512, activation=\"relu\"),\n",
" layers.Dense(10, activation=\"softmax\")\n",
"])"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"model.compile(optimizer=\"rmsprop\",\n",
" loss=\"sparse_categorical_crossentropy\",\n",
" metrics=[\"accuracy\"])"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"model.fit(train_images, train_labels, epochs=5, batch_size=128)"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Reimplementing our first example from scratch in TensorFlow"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"#### A simple Dense class"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"import tensorflow as tf\n",
"\n",
"class NaiveDense:\n",
" def __init__(self, input_size, output_size, activation):\n",
" self.activation = activation\n",
"\n",
" w_shape = (input_size, output_size)\n",
" w_initial_value = tf.random.uniform(w_shape, minval=0, maxval=1e-1)\n",
" self.W = tf.Variable(w_initial_value)\n",
"\n",
" b_shape = (output_size,)\n",
" b_initial_value = tf.zeros(b_shape)\n",
" self.b = tf.Variable(b_initial_value)\n",
"\n",
" def __call__(self, inputs):\n",
" return self.activation(tf.matmul(inputs, self.W) + self.b)\n",
"\n",
" @property\n",
" def weights(self):\n",
" return [self.W, self.b]"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"#### A simple Sequential class"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"class NaiveSequential:\n",
" def __init__(self, layers):\n",
" self.layers = layers\n",
"\n",
" def __call__(self, inputs):\n",
" x = inputs\n",
" for layer in self.layers:\n",
" x = layer(x)\n",
" return x\n",
"\n",
" @property\n",
" def weights(self):\n",
" weights = []\n",
" for layer in self.layers:\n",
" weights += layer.weights\n",
" return weights"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"model = NaiveSequential([\n",
" NaiveDense(input_size=28 * 28, output_size=512, activation=tf.nn.relu),\n",
" NaiveDense(input_size=512, output_size=10, activation=tf.nn.softmax)\n",
"])\n",
"assert len(model.weights) == 4"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"#### A batch generator"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"import math\n",
"\n",
"class BatchGenerator:\n",
" def __init__(self, images, labels, batch_size=128):\n",
" assert len(images) == len(labels)\n",
" self.index = 0\n",
" self.images = images\n",
" self.labels = labels\n",
" self.batch_size = batch_size\n",
" self.num_batches = math.ceil(len(images) / batch_size)\n",
"\n",
" def next(self):\n",
" images = self.images[self.index : self.index + self.batch_size]\n",
" labels = self.labels[self.index : self.index + self.batch_size]\n",
" self.index += self.batch_size\n",
" return images, labels"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Running one training step"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def one_training_step(model, images_batch, labels_batch):\n",
" with tf.GradientTape() as tape:\n",
" predictions = model(images_batch)\n",
" per_sample_losses = tf.keras.losses.sparse_categorical_crossentropy(\n",
" labels_batch, predictions)\n",
" average_loss = tf.reduce_mean(per_sample_losses)\n",
" gradients = tape.gradient(average_loss, model.weights)\n",
" update_weights(gradients, model.weights)\n",
" return average_loss"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"learning_rate = 1e-3\n",
"\n",
"def update_weights(gradients, weights):\n",
" for g, w in zip(gradients, model.weights):\n",
" w.assign_sub(g * learning_rate)"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"from tensorflow.keras import optimizers\n",
"\n",
"optimizer = optimizers.SGD(learning_rate=1e-3)\n",
"\n",
"def update_weights(gradients, weights):\n",
" optimizer.apply_gradients(zip(gradients, weights))"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### The full training loop"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"def fit(model, images, labels, epochs, batch_size=128):\n",
" for epoch_counter in range(epochs):\n",
" print(f\"Epoch {epoch_counter}\")\n",
" batch_generator = BatchGenerator(images, labels)\n",
" for batch_counter in range(batch_generator.num_batches):\n",
" images_batch, labels_batch = batch_generator.next()\n",
" loss = one_training_step(model, images_batch, labels_batch)\n",
" if batch_counter % 100 == 0:\n",
" print(f\"loss at batch {batch_counter}: {loss:.2f}\")"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"from tensorflow.keras.datasets import mnist\n",
"(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
"\n",
"train_images = train_images.reshape((60000, 28 * 28))\n",
"train_images = train_images.astype(\"float32\") / 255\n",
"test_images = test_images.reshape((10000, 28 * 28))\n",
"test_images = test_images.astype(\"float32\") / 255\n",
"\n",
"fit(model, train_images, train_labels, epochs=10, batch_size=128)"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"### Evaluating the model"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"colab_type": "code"
},
"outputs": [],
"source": [
"predictions = model(test_images)\n",
"predictions = predictions.numpy()\n",
"predicted_labels = np.argmax(predictions, axis=1)\n",
"matches = predicted_labels == test_labels\n",
"print(f\"accuracy: {matches.mean():.2f}\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text"
},
"source": [
"## Chapter summary"
]
}
],
"metadata": {
"colab": {
"collapsed_sections": [],
"name": "chapter02_mathematical-building-blocks.i",
"private_outputs": false,
"provenance": [],
"toc_visible": true
},
"kernelspec": {
"display_name": "Python 3",
"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",
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"nbformat": 4,
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