microsoft/AI-For-Beginners
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lessons/3-NeuralNetworks/05-Frameworks/IntroKerasTF.ipynb
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| 1 | { |
| 2 | "cells": [ |
| 3 | { |
| 4 | "cell_type": "markdown", |
| 5 | "metadata": { |
| 6 | "id": "En2vX4FuwHlu" |
| 7 | }, |
| 8 | "source": [ |
| 9 | "## Introduction to Tensorflow and Keras\n", |
| 10 | "\n", |
| 11 | "> This notebook is a part of [AI for Beginners Curricula](http://github.com/microsoft/ai-for-beginners). Visit the repository for complete set of learning materials.\n", |
| 12 | "\n", |
| 13 | "### Neural Frameworks\n", |
| 14 | "\n", |
| 15 | "We have learnt that to train neural networks you need:\n", |
| 16 | "* Quickly multiply matrices (tensors)\n", |
| 17 | "* Compute gradients to perform gradient descent optimization\n", |
| 18 | "\n", |
| 19 | "What neural network frameworks allow you to do:\n", |
| 20 | "* Operate with tensors on whatever compute is available, CPU or GPU, or even TPU\n", |
| 21 | "* Automatically compute gradients (they are explicitly programmed for all built-in tensor functions)\n", |
| 22 | "\n", |
| 23 | "Optionally:\n", |
| 24 | "* Neural Network constructor / higher level API (describe network as a sequence of layers)\n", |
| 25 | "* Simple training functions (`fit`, as in Scikit Learn)\n", |
| 26 | "* A number of optimization algorithms in addition to gradient descent\n", |
| 27 | "* Data handling abstractions (that will ideally work on GPU, too)" |
| 28 | ] |
| 29 | }, |
| 30 | { |
| 31 | "cell_type": "markdown", |
| 32 | "metadata": { |
| 33 | "id": "8cACQoFMwHl3" |
| 34 | }, |
| 35 | "source": [ |
| 36 | "### Most Popular Frameworks\n", |
| 37 | "\n", |
| 38 | "* Tensorflow 1.x - first widely available framework (Google). Allowed to define static computation graph, push it to GPU, and explicitly evaluate it\n", |
| 39 | "* PyTorch - a framework from Facebook that is growing in popularity\n", |
| 40 | "* Keras - higher level API on top of Tensorflow/PyTorch to unify and simplify using neural networks (Francois Chollet)\n", |
| 41 | "* Tensorflow 2.x + Keras - new version of Tensorflow with integrated Keras functionality, which supports **dynamic computation graph**, allowing to perform tensor operations very similar to numpy (and PyTorch)\n", |
| 42 | "\n", |
| 43 | "We will consider Tensorflow 2.x and Keras. Make sure you have version 2.x.x of Tensorflow installed:\n", |
| 44 | "```\n", |
| 45 | "pip install tensorflow\n", |
| 46 | "```\n", |
| 47 | "or\n", |
| 48 | "```\n", |
| 49 | "conda install tensorflow\n", |
| 50 | "```" |
| 51 | ] |
| 52 | }, |
| 53 | { |
| 54 | "cell_type": "code", |
| 55 | "execution_count": 1, |
| 56 | "metadata": { |
| 57 | "colab": { |
| 58 | "base_uri": "https://localhost:8080/" |
| 59 | }, |
| 60 | "id": "xwqVx9-bwHl3", |
| 61 | "outputId": "2aa591b4-b647-441f-9c8e-4e0da2d517a0", |
| 62 | "tags": [] |
| 63 | }, |
| 64 | "outputs": [ |
| 65 | { |
| 66 | "name": "stdout", |
| 67 | "output_type": "stream", |
| 68 | "text": [ |
| 69 | "2.7.0\n" |
| 70 | ] |
| 71 | } |
| 72 | ], |
| 73 | "source": [ |
| 74 | "import tensorflow as tf\n", |
| 75 | "import numpy as np\n", |
| 76 | "print(tf.__version__)" |
| 77 | ] |
| 78 | }, |
| 79 | { |
| 80 | "cell_type": "markdown", |
| 81 | "metadata": { |
| 82 | "id": "6tp2xGV7wHl4" |
| 83 | }, |
| 84 | "source": [ |
| 85 | "## Basic Concepts: Tensor\n", |
| 86 | "\n", |
| 87 | "**Tensor** is a multi-dimensional array. It is very convenient to use tensors to represent different types of data:\n", |
| 88 | "* 400x400 - black-and-white picture\n", |
| 89 | "* 400x400x3 - color picture \n", |
| 90 | "* 16x400x400x3 - minibatch of 16 color pictures\n", |
| 91 | "* 25x400x400x3 - one second of 25-fps video\n", |
| 92 | "* 8x25x400x400x3 - minibatch of 8 1-second videos" |
| 93 | ] |
| 94 | }, |
| 95 | { |
| 96 | "cell_type": "markdown", |
| 97 | "metadata": { |
| 98 | "id": "qG2bsaR7wHl4" |
| 99 | }, |
| 100 | "source": [ |
| 101 | "### Simple Tensors\n", |
| 102 | "\n", |
| 103 | "You can easily create simple tensors from lists of np-arrays, or generate random ones:" |
| 104 | ] |
| 105 | }, |
| 106 | { |
| 107 | "cell_type": "code", |
| 108 | "execution_count": 2, |
| 109 | "metadata": { |
| 110 | "colab": { |
| 111 | "base_uri": "https://localhost:8080/" |
| 112 | }, |
| 113 | "id": "ybpnk08HwHl4", |
| 114 | "outputId": "fad9ed4a-df82-44a0-84ea-324bc71ea46f", |
| 115 | "trusted": true |
| 116 | }, |
| 117 | "outputs": [ |
| 118 | { |
| 119 | "name": "stdout", |
| 120 | "output_type": "stream", |
| 121 | "text": [ |
| 122 | "tf.Tensor(\n", |
| 123 | "[[1 2]\n", |
| 124 | " [3 4]], shape=(2, 2), dtype=int32)\n", |
| 125 | "tf.Tensor(\n", |
| 126 | "[[-0.33552304 -1.8252622 -1.8532339 ]\n", |
| 127 | " [ 1.0871267 -1.2779568 0.5240014 ]\n", |
| 128 | " [-0.12793781 -1.8618349 -0.9020286 ]\n", |
| 129 | " [ 0.5948797 0.11144501 -2.0396452 ]\n", |
| 130 | " [ 0.47620854 1.1726047 -0.4405675 ]\n", |
| 131 | " [-0.27211484 -0.08985762 -0.03376012]\n", |
| 132 | " [ 0.64274263 0.53368104 -0.9006528 ]\n", |
| 133 | " [-0.43745974 -1.0081122 -0.13442488]\n", |
| 134 | " [ 0.36497566 1.3221073 -1.8739727 ]\n", |
| 135 | " [ 0.94821155 -0.02817811 1.3563292 ]], shape=(10, 3), dtype=float32)\n" |
| 136 | ] |
| 137 | } |
| 138 | ], |
| 139 | "source": [ |
| 140 | "a = tf.constant([[1,2],[3,4]])\n", |
| 141 | "print(a)\n", |
| 142 | "a = tf.random.normal(shape=(10,3))\n", |
| 143 | "print(a)" |
| 144 | ] |
| 145 | }, |
| 146 | { |
| 147 | "cell_type": "markdown", |
| 148 | "metadata": { |
| 149 | "id": "AXFMsV3r09Ux" |
| 150 | }, |
| 151 | "source": [ |
| 152 | "You can use arithmetic operations on tensors, which are performed element-wise, as in numpy. Tensors are automatically expanded to required dimension, if needed. To extract numpy-array from tensor, use `.numpy()`:" |
| 153 | ] |
| 154 | }, |
| 155 | { |
| 156 | "cell_type": "code", |
| 157 | "execution_count": 3, |
| 158 | "metadata": { |
| 159 | "colab": { |
| 160 | "base_uri": "https://localhost:8080/" |
| 161 | }, |
| 162 | "id": "e5Nu5Xgj1DnQ", |
| 163 | "outputId": "0dfc8758-4ffd-4968-c7bf-6ba8d435df2e" |
| 164 | }, |
| 165 | "outputs": [ |
| 166 | { |
| 167 | "name": "stdout", |
| 168 | "output_type": "stream", |
| 169 | "text": [ |
| 170 | "tf.Tensor(\n", |
| 171 | "[[ 0. 0. 0. ]\n", |
| 172 | " [ 1.4226497 0.54730535 2.3772354 ]\n", |
| 173 | " [ 0.20758523 -0.03657269 0.9512053 ]\n", |
| 174 | " [ 0.93040276 1.9367073 -0.18641126]\n", |
| 175 | " [ 0.8117316 2.9978669 1.4126664 ]\n", |
| 176 | " [ 0.0634082 1.7354046 1.8194739 ]\n", |
| 177 | " [ 0.97826564 2.3589432 0.9525811 ]\n", |
| 178 | " [-0.1019367 0.81715 1.718809 ]\n", |
| 179 | " [ 0.7004987 3.1473694 -0.02073872]\n", |
| 180 | " [ 1.2837346 1.7970841 3.2095633 ]], shape=(10, 3), dtype=float32)\n", |
| 181 | "[0.71496403 0.16117539 0.15672949]\n" |
| 182 | ] |
| 183 | } |
| 184 | ], |
| 185 | "source": [ |
| 186 | "print(a-a[0])\n", |
| 187 | "print(tf.exp(a)[0].numpy())" |
| 188 | ] |
| 189 | }, |
| 190 | { |
| 191 | "cell_type": "markdown", |
| 192 | "metadata": { |
| 193 | "id": "uQ5zN6cVyrG7" |
| 194 | }, |
| 195 | "source": [ |
| 196 | "## Variables\n", |
| 197 | "\n", |
| 198 | "Variables are useful to represent tensor values that can be modified using `assign` and `assign_add`. They are often used to represent neural network weights.\n", |
| 199 | "\n", |
| 200 | "As an example, here is a silly way to get a sum of all rows of tensor `a`:" |
| 201 | ] |
| 202 | }, |
| 203 | { |
| 204 | "cell_type": "code", |
| 205 | "execution_count": 4, |
| 206 | "metadata": { |
| 207 | "colab": { |
| 208 | "base_uri": "https://localhost:8080/" |
| 209 | }, |
| 210 | "id": "7pu0UZ-_yqfB", |
| 211 | "outputId": "6708c83e-02e6-4442-8757-45918eb1fbc2" |
| 212 | }, |
| 213 | "outputs": [ |
| 214 | { |
| 215 | "name": "stdout", |
| 216 | "output_type": "stream", |
| 217 | "text": [ |
| 218 | "<tf.Variable 'Variable:0' shape=(3,) dtype=float32, numpy=array([ 2.9411097, -2.9513645, -6.2979555], dtype=float32)>\n" |
| 219 | ] |
| 220 | } |
| 221 | ], |
| 222 | "source": [ |
| 223 | "s = tf.Variable(tf.zeros_like(a[0]))\n", |
| 224 | "for i in a:\n", |
| 225 | " s.assign_add(i)\n", |
| 226 | "\n", |
| 227 | "print(s)" |
| 228 | ] |
| 229 | }, |
| 230 | { |
| 231 | "cell_type": "markdown", |
| 232 | "metadata": { |
| 233 | "id": "rIh1EHcezlNo" |
| 234 | }, |
| 235 | "source": [ |
| 236 | "Much better way to do it:" |
| 237 | ] |
| 238 | }, |
| 239 | { |
| 240 | "cell_type": "code", |
| 241 | "execution_count": 5, |
| 242 | "metadata": { |
| 243 | "colab": { |
| 244 | "base_uri": "https://localhost:8080/" |
| 245 | }, |
| 246 | "id": "aQIdWZ1kzn6P", |
| 247 | "outputId": "1c123d9a-ecd2-4f2e-828e-5ade85ac8f63" |
| 248 | }, |
| 249 | "outputs": [ |
| 250 | { |
| 251 | "data": { |
| 252 | "text/plain": [ |
| 253 | "<tf.Tensor: shape=(3,), dtype=float32, numpy=array([ 2.9411097, -2.9513645, -6.2979555], dtype=float32)>" |
| 254 | ] |
| 255 | }, |
| 256 | "execution_count": 5, |
| 257 | "metadata": {}, |
| 258 | "output_type": "execute_result" |
| 259 | } |
| 260 | ], |
| 261 | "source": [ |
| 262 | "tf.reduce_sum(a,axis=0)" |
| 263 | ] |
| 264 | }, |
| 265 | { |
| 266 | "cell_type": "markdown", |
| 267 | "metadata": { |
| 268 | "id": "U-auwezDwHl6" |
| 269 | }, |
| 270 | "source": [ |
| 271 | "## Computing Gradients\n", |
| 272 | "\n", |
| 273 | "For back propagation, you need to compute gradients. This is done using `tf.GradientTape()` idiom:\n", |
| 274 | " * Add `with tf.GradientTape` block around our computations\n", |
| 275 | " * Mark those tensors with respect to which we need to compute gradients by calling `tape.watch` (all variables are watched automatically)\n", |
| 276 | " * Compute whatever we need (build computational graph)\n", |
| 277 | " * Obtain gradients using `tape.gradient` " |
| 278 | ] |
| 279 | }, |
| 280 | { |
| 281 | "cell_type": "code", |
| 282 | "execution_count": 6, |
| 283 | "metadata": { |
| 284 | "colab": { |
| 285 | "base_uri": "https://localhost:8080/" |
| 286 | }, |
| 287 | "id": "m8vFOXr7wHl6", |
| 288 | "outputId": "860ac72e-50c7-4ff2-f258-747f27194f90", |
| 289 | "trusted": true |
| 290 | }, |
| 291 | "outputs": [ |
| 292 | { |
| 293 | "name": "stdout", |
| 294 | "output_type": "stream", |
| 295 | "text": [ |
| 296 | "tf.Tensor(\n", |
| 297 | "[[ 0.40935674 -0.3495818 ]\n", |
| 298 | " [ 0.94165146 -0.33209163]], shape=(2, 2), dtype=float32)\n" |
| 299 | ] |
| 300 | } |
| 301 | ], |
| 302 | "source": [ |
| 303 | "a = tf.random.normal(shape=(2, 2))\n", |
| 304 | "b = tf.random.normal(shape=(2, 2))\n", |
| 305 | "\n", |
| 306 | "with tf.GradientTape() as tape:\n", |
| 307 | " tape.watch(a) # Start recording the history of operations applied to `a`\n", |
| 308 | " c = tf.sqrt(tf.square(a) + tf.square(b)) # Do some math using `a`\n", |
| 309 | " # What's the gradient of `c` with respect to `a`?\n", |
| 310 | " dc_da = tape.gradient(c, a)\n", |
| 311 | " print(dc_da)" |
| 312 | ] |
| 313 | }, |
| 314 | { |
| 315 | "cell_type": "markdown", |
| 316 | "metadata": { |
| 317 | "id": "8sfjBMBu59B5" |
| 318 | }, |
| 319 | "source": [ |
| 320 | "## Example 1: Linear Regression\n", |
| 321 | "\n", |
| 322 | "Now we know enough to solve the classical problem of **Linear regression**. Let's generate small synthetic dataset:" |
| 323 | ] |
| 324 | }, |
| 325 | { |
| 326 | "cell_type": "code", |
| 327 | "execution_count": 7, |
| 328 | "metadata": { |
| 329 | "id": "j723455WwHl7", |
| 330 | "trusted": true |
| 331 | }, |
| 332 | "outputs": [], |
| 333 | "source": [ |
| 334 | "import matplotlib.pyplot as plt\n", |
| 335 | "from sklearn.datasets import make_classification, make_regression\n", |
| 336 | "from sklearn.model_selection import train_test_split\n", |
| 337 | "import random" |
| 338 | ] |
| 339 | }, |
| 340 | { |
| 341 | "cell_type": "code", |
| 342 | "execution_count": 8, |
| 343 | "metadata": { |
| 344 | "colab": { |
| 345 | "base_uri": "https://localhost:8080/", |
| 346 | "height": 282 |
| 347 | }, |
| 348 | "id": "WJNK_J6v6I-Z", |
| 349 | "outputId": "eb4a66a6-6b9a-4c8a-bc24-d81eeb2d3f27" |
| 350 | }, |
| 351 | "outputs": [ |
| 352 | { |
| 353 | "data": { |
| 354 | "text/plain": [ |
| 355 | "<matplotlib.collections.PathCollection at 0x12892776880>" |
| 356 | ] |
| 357 | }, |
| 358 | "execution_count": 8, |
| 359 | "metadata": {}, |
| 360 | "output_type": "execute_result" |
| 361 | }, |
| 362 | { |
| 363 | "data": { |
| 364 | "image/png": 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", |
| 365 | "text/plain": [ |
| 366 | "<Figure size 432x288 with 1 Axes>" |
| 367 | ] |
| 368 | }, |
| 369 | "metadata": { |
| 370 | "needs_background": "light" |
| 371 | }, |
| 372 | "output_type": "display_data" |
| 373 | } |
| 374 | ], |
| 375 | "source": [ |
| 376 | "np.random.seed(13) # pick the seed for reproducability - change it to explore the effects of random variations\n", |
| 377 | "\n", |
| 378 | "train_x = np.linspace(0, 3, 120)\n", |
| 379 | "train_labels = 2 * train_x + 0.9 + np.random.randn(*train_x.shape) * 0.5\n", |
| 380 | "\n", |
| 381 | "plt.scatter(train_x,train_labels)" |
| 382 | ] |
| 383 | }, |
| 384 | { |
| 385 | "cell_type": "markdown", |
| 386 | "metadata": { |
| 387 | "id": "Ng4rZmGc6oxk" |
| 388 | }, |
| 389 | "source": [ |
| 390 | "Linear regression is defined by a straight line $f_{W,b}(x) = Wx+b$, where $W, b$ are model parameters that we need to find. An error on our dataset $\\{x_i,y_u\\}_{i=1}^N$ (also called **loss function**) can be defined as mean square error:\n", |
| 391 | "$$\n", |
| 392 | "\\mathcal{L}(W,b) = {1\\over N}\\sum_{i=1}^N (f_{W,b}(x_i)-y_i)^2\n", |
| 393 | "$$\n", |
| 394 | "\n", |
| 395 | "Let's define our model and loss function:" |
| 396 | ] |
| 397 | }, |
| 398 | { |
| 399 | "cell_type": "code", |
| 400 | "execution_count": 9, |
| 401 | "metadata": { |
| 402 | "id": "QxhI4GlB6aiH" |
| 403 | }, |
| 404 | "outputs": [], |
| 405 | "source": [ |
| 406 | "input_dim = 1\n", |
| 407 | "output_dim = 1\n", |
| 408 | "learning_rate = 0.1\n", |
| 409 | "\n", |
| 410 | "# This is our weight matrix\n", |
| 411 | "w = tf.Variable([[100.0]])\n", |
| 412 | "# This is our bias vector\n", |
| 413 | "b = tf.Variable(tf.zeros(shape=(output_dim,)))\n", |
| 414 | "\n", |
| 415 | "def f(x):\n", |
| 416 | " return tf.matmul(x,w) + b\n", |
| 417 | "\n", |
| 418 | "def compute_loss(labels, predictions):\n", |
| 419 | " return tf.reduce_mean(tf.square(labels - predictions))" |
| 420 | ] |
| 421 | }, |
| 422 | { |
| 423 | "cell_type": "markdown", |
| 424 | "metadata": { |
| 425 | "id": "JUxwj3367gD2" |
| 426 | }, |
| 427 | "source": [ |
| 428 | "We will train the model on a series of minibatches. We will use gradient descent, adjusting model parameters using the following formulae:\n", |
| 429 | "$$\n", |
| 430 | "\\begin{array}{l}\n", |
| 431 | "W^{(n+1)}=W^{(n)}-\\eta\\frac{\\partial\\mathcal{L}}{\\partial W} \\\\\n", |
| 432 | "b^{(n+1)}=b^{(n)}-\\eta\\frac{\\partial\\mathcal{L}}{\\partial b} \\\\\n", |
| 433 | "\\end{array}\n", |
| 434 | "$$" |
| 435 | ] |
| 436 | }, |
| 437 | { |
| 438 | "cell_type": "code", |
| 439 | "execution_count": 10, |
| 440 | "metadata": { |
| 441 | "id": "-991PErM7fJU" |
| 442 | }, |
| 443 | "outputs": [], |
| 444 | "source": [ |
| 445 | "def train_on_batch(x, y):\n", |
| 446 | " with tf.GradientTape() as tape:\n", |
| 447 | " predictions = f(x)\n", |
| 448 | " loss = compute_loss(y, predictions)\n", |
| 449 | " # Note that `tape.gradient` works with a list as well (w, b).\n", |
| 450 | " dloss_dw, dloss_db = tape.gradient(loss, [w, b])\n", |
| 451 | " w.assign_sub(learning_rate * dloss_dw)\n", |
| 452 | " b.assign_sub(learning_rate * dloss_db)\n", |
| 453 | " return loss" |
| 454 | ] |
| 455 | }, |
| 456 | { |
| 457 | "cell_type": "markdown", |
| 458 | "metadata": { |
| 459 | "id": "idr2VEWb9rr0" |
| 460 | }, |
| 461 | "source": [ |
| 462 | "Let's do the training. We will do several passes through the dataset (so-called **epochs**), divide it into minibatches and call the function defined above:" |
| 463 | ] |
| 464 | }, |
| 465 | { |
| 466 | "cell_type": "code", |
| 467 | "execution_count": 11, |
| 468 | "metadata": { |
| 469 | "id": "nOuu0qpx-wAp" |
| 470 | }, |
| 471 | "outputs": [], |
| 472 | "source": [ |
| 473 | "# Shuffle the data.\n", |
| 474 | "indices = np.random.permutation(len(train_x))\n", |
| 475 | "features = tf.constant(train_x[indices],dtype=tf.float32)\n", |
| 476 | "labels = tf.constant(train_labels[indices],dtype=tf.float32)" |
| 477 | ] |
| 478 | }, |
| 479 | { |
| 480 | "cell_type": "code", |
| 481 | "execution_count": 12, |
| 482 | "metadata": { |
| 483 | "colab": { |
| 484 | "base_uri": "https://localhost:8080/" |
| 485 | }, |
| 486 | "id": "3zdIf6c_85Ht", |
| 487 | "outputId": "43b04684-8b90-4c65-d5ff-20ebac61c73c" |
| 488 | }, |
| 489 | "outputs": [ |
| 490 | { |
| 491 | "name": "stdout", |
| 492 | "output_type": "stream", |
| 493 | "text": [ |
| 494 | "Epoch 0: last batch loss = 94.5247\n", |
| 495 | "Epoch 1: last batch loss = 9.3428\n", |
| 496 | "Epoch 2: last batch loss = 1.4166\n", |
| 497 | "Epoch 3: last batch loss = 0.5224\n", |
| 498 | "Epoch 4: last batch loss = 0.3807\n", |
| 499 | "Epoch 5: last batch loss = 0.3495\n", |
| 500 | "Epoch 6: last batch loss = 0.3413\n", |
| 501 | "Epoch 7: last batch loss = 0.3390\n", |
| 502 | "Epoch 8: last batch loss = 0.3384\n", |
| 503 | "Epoch 9: last batch loss = 0.3382\n" |
| 504 | ] |
| 505 | } |
| 506 | ], |
| 507 | "source": [ |
| 508 | "batch_size = 4\n", |
| 509 | "for epoch in range(10):\n", |
| 510 | " for i in range(0,len(features),batch_size):\n", |
| 511 | " loss = train_on_batch(tf.reshape(features[i:i+batch_size],(-1,1)),tf.reshape(labels[i:i+batch_size],(-1,1)))\n", |
| 512 | " print('Epoch %d: last batch loss = %.4f' % (epoch, float(loss)))" |
| 513 | ] |
| 514 | }, |
| 515 | { |
| 516 | "cell_type": "markdown", |
| 517 | "metadata": {}, |
| 518 | "source": [ |
| 519 | "We now have obtained optimized parameters $W$ and $b$. Note that their values are similar to the original values used when generating the dataset ($W=2, b=1$)" |
| 520 | ] |
| 521 | }, |
| 522 | { |
| 523 | "cell_type": "code", |
| 524 | "execution_count": 13, |
| 525 | "metadata": { |
| 526 | "colab": { |
| 527 | "base_uri": "https://localhost:8080/" |
| 528 | }, |
| 529 | "id": "US6q0nCBD-LL", |
| 530 | "outputId": "65a79620-a3eb-445b-aafb-60a60575ab0e" |
| 531 | }, |
| 532 | "outputs": [ |
| 533 | { |
| 534 | "data": { |
| 535 | "text/plain": [ |
| 536 | "(<tf.Variable 'Variable:0' shape=(1, 1) dtype=float32, numpy=array([[1.8616779]], dtype=float32)>,\n", |
| 537 | " <tf.Variable 'Variable:0' shape=(1,) dtype=float32, numpy=array([1.0710956], dtype=float32)>)" |
| 538 | ] |
| 539 | }, |
| 540 | "execution_count": 13, |
| 541 | "metadata": {}, |
| 542 | "output_type": "execute_result" |
| 543 | } |
| 544 | ], |
| 545 | "source": [ |
| 546 | "w,b" |
| 547 | ] |
| 548 | }, |
| 549 | { |
| 550 | "cell_type": "code", |
| 551 | "execution_count": 14, |
| 552 | "metadata": { |
| 553 | "colab": { |
| 554 | "base_uri": "https://localhost:8080/", |
| 555 | "height": 282 |
| 556 | }, |
| 557 | "id": "_e6xRMZFDnyI", |
| 558 | "outputId": "d202b7fe-4383-4d82-b98e-a20f3180093e" |
| 559 | }, |
| 560 | "outputs": [ |
| 561 | { |
| 562 | "data": { |
| 563 | "text/plain": [ |
| 564 | "[<matplotlib.lines.Line2D at 0x12892ae5eb0>]" |
| 565 | ] |
| 566 | }, |
| 567 | "execution_count": 14, |
| 568 | "metadata": {}, |
| 569 | "output_type": "execute_result" |
| 570 | }, |
| 571 | { |
| 572 | "data": { |
| 573 | "image/png": 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", |
| 574 | "text/plain": [ |
| 575 | "<Figure size 432x288 with 1 Axes>" |
| 576 | ] |
| 577 | }, |
| 578 | "metadata": { |
| 579 | "needs_background": "light" |
| 580 | }, |
| 581 | "output_type": "display_data" |
| 582 | } |
| 583 | ], |
| 584 | "source": [ |
| 585 | "plt.scatter(train_x,train_labels)\n", |
| 586 | "x = np.array([min(train_x),max(train_x)])\n", |
| 587 | "y = w.numpy()[0,0]*x+b.numpy()[0]\n", |
| 588 | "plt.plot(x,y,color='red')" |
| 589 | ] |
| 590 | }, |
| 591 | { |
| 592 | "cell_type": "markdown", |
| 593 | "metadata": { |
| 594 | "id": "0giuwC9GHzi8" |
| 595 | }, |
| 596 | "source": [ |
| 597 | "## Computational Graph and GPU Computations\n", |
| 598 | "\n", |
| 599 | "Whenever we compute tensor expression, Tensorflow builds a computational graph that can be computed on the available computing device, e.g. CPU or GPU. Since we were using arbitrary Python function in our code, they cannot be included as part of computational graph, and thus when running our code on GPU we would need to pass the data between CPU and GPU back and forth, and compute custom function on CPU.\n", |
| 600 | "\n", |
| 601 | "Tensorflow allows us to mark our Python function using `@tf.function` decorator, which will make this function a part of the same computational graph. This decorator can be applied to functions that use standard Tensorflow tensor operations. " |
| 602 | ] |
| 603 | }, |
| 604 | { |
| 605 | "cell_type": "code", |
| 606 | "execution_count": 15, |
| 607 | "metadata": { |
| 608 | "id": "HK7HPLz3Hyrl" |
| 609 | }, |
| 610 | "outputs": [], |
| 611 | "source": [ |
| 612 | "@tf.function\n", |
| 613 | "def train_on_batch(x, y):\n", |
| 614 | " with tf.GradientTape() as tape:\n", |
| 615 | " predictions = f(x)\n", |
| 616 | " loss = compute_loss(y, predictions)\n", |
| 617 | " # Note that `tape.gradient` works with a list as well (w, b).\n", |
| 618 | " dloss_dw, dloss_db = tape.gradient(loss, [w, b])\n", |
| 619 | " w.assign_sub(learning_rate * dloss_dw)\n", |
| 620 | " b.assign_sub(learning_rate * dloss_db)\n", |
| 621 | " return loss" |
| 622 | ] |
| 623 | }, |
| 624 | { |
| 625 | "cell_type": "markdown", |
| 626 | "metadata": { |
| 627 | "id": "J7HusxWkGjLX" |
| 628 | }, |
| 629 | "source": [ |
| 630 | "The code has not changed, but if you were running this code on GPU and on larger dataset - you would have noticed the difference in speed. \n", |
| 631 | "\n", |
| 632 | "## Dataset API\n", |
| 633 | "\n", |
| 634 | "Tensorflow contains a convenient API to work with data. Let's try to use it. We will also train our model from scratch." |
| 635 | ] |
| 636 | }, |
| 637 | { |
| 638 | "cell_type": "code", |
| 639 | "execution_count": 16, |
| 640 | "metadata": { |
| 641 | "colab": { |
| 642 | "base_uri": "https://localhost:8080/" |
| 643 | }, |
| 644 | "id": "oYro9Lbr8q0M", |
| 645 | "outputId": "78c0a6de-71bd-4eef-8819-439495b28672" |
| 646 | }, |
| 647 | "outputs": [ |
| 648 | { |
| 649 | "name": "stdout", |
| 650 | "output_type": "stream", |
| 651 | "text": [ |
| 652 | "Epoch 0: last batch loss = 173.4585\n", |
| 653 | "Epoch 1: last batch loss = 13.8459\n", |
| 654 | "Epoch 2: last batch loss = 4.5407\n", |
| 655 | "Epoch 3: last batch loss = 3.7364\n", |
| 656 | "Epoch 4: last batch loss = 3.4334\n", |
| 657 | "Epoch 5: last batch loss = 3.1790\n", |
| 658 | "Epoch 6: last batch loss = 2.9458\n", |
| 659 | "Epoch 7: last batch loss = 2.7311\n", |
| 660 | "Epoch 8: last batch loss = 2.5332\n", |
| 661 | "Epoch 9: last batch loss = 2.3508\n" |
| 662 | ] |
| 663 | } |
| 664 | ], |
| 665 | "source": [ |
| 666 | "w.assign([[10.0]])\n", |
| 667 | "b.assign([0.0])\n", |
| 668 | "\n", |
| 669 | "# Create a tf.data.Dataset object for easy batched iteration\n", |
| 670 | "dataset = tf.data.Dataset.from_tensor_slices((train_x.astype(np.float32), train_labels.astype(np.float32)))\n", |
| 671 | "dataset = dataset.shuffle(buffer_size=1024).batch(256)\n", |
| 672 | "\n", |
| 673 | "for epoch in range(10):\n", |
| 674 | " for step, (x, y) in enumerate(dataset):\n", |
| 675 | " loss = train_on_batch(tf.reshape(x,(-1,1)), tf.reshape(y,(-1,1)))\n", |
| 676 | " print('Epoch %d: last batch loss = %.4f' % (epoch, float(loss)))" |
| 677 | ] |
| 678 | }, |
| 679 | { |
| 680 | "cell_type": "markdown", |
| 681 | "metadata": { |
| 682 | "id": "A10prCPowHl7" |
| 683 | }, |
| 684 | "source": [ |
| 685 | "## Example 2: Classification\n", |
| 686 | "\n", |
| 687 | "Now we will consider binary classification problem. A good example of such a problem would be a tumour classification between malignant and benign based on it's size and age.\n", |
| 688 | "\n", |
| 689 | "The core model is similar to regression, but we need to use different loss function. Let's start by generating sample data:\n" |
| 690 | ] |
| 691 | }, |
| 692 | { |
| 693 | "cell_type": "code", |
| 694 | "execution_count": 40, |
| 695 | "metadata": { |
| 696 | "id": "j0OTPkGpwHl7", |
| 697 | "scrolled": false, |
| 698 | "trusted": true |
| 699 | }, |
| 700 | "outputs": [], |
| 701 | "source": [ |
| 702 | "np.random.seed(0) # pick the seed for reproducibility - change it to explore the effects of random variations\n", |
| 703 | "\n", |
| 704 | "n = 100\n", |
| 705 | "X, Y = make_classification(n_samples = n, n_features=2,\n", |
| 706 | " n_redundant=0, n_informative=2, flip_y=0.05,class_sep=1.5)\n", |
| 707 | "X = X.astype(np.float32)\n", |
| 708 | "Y = Y.astype(np.int32)\n", |
| 709 | "\n", |
| 710 | "split = [ 70*n//100, (15+70)*n//100 ]\n", |
| 711 | "train_x, valid_x, test_x = np.split(X, split)\n", |
| 712 | "train_labels, valid_labels, test_labels = np.split(Y, split)" |
| 713 | ] |
| 714 | }, |
| 715 | { |
| 716 | "cell_type": "code", |
| 717 | "execution_count": 41, |
| 718 | "metadata": { |
| 719 | "id": "c-_BjSHPwHl8", |
| 720 | "scrolled": false, |
| 721 | "trusted": true |
| 722 | }, |
| 723 | "outputs": [], |
| 724 | "source": [ |
| 725 | "def plot_dataset(features, labels, W=None, b=None):\n", |
| 726 | " # prepare the plot\n", |
| 727 | " fig, ax = plt.subplots(1, 1)\n", |
| 728 | " ax.set_xlabel('$x_i[0]$ -- (feature 1)')\n", |
| 729 | " ax.set_ylabel('$x_i[1]$ -- (feature 2)')\n", |
| 730 | " colors = ['r' if l else 'b' for l in labels]\n", |
| 731 | " ax.scatter(features[:, 0], features[:, 1], marker='o', c=colors, s=100, alpha = 0.5)\n", |
| 732 | " if W is not None:\n", |
| 733 | " min_x = min(features[:,0])\n", |
| 734 | " max_x = max(features[:,1])\n", |
| 735 | " min_y = min(features[:,1])*(1-.1)\n", |
| 736 | " max_y = max(features[:,1])*(1+.1)\n", |
| 737 | " cx = np.array([min_x,max_x],dtype=np.float32)\n", |
| 738 | " cy = (0.5-W[0]*cx-b)/W[1]\n", |
| 739 | " ax.plot(cx,cy,'g')\n", |
| 740 | " ax.set_ylim(min_y,max_y)\n", |
| 741 | " fig.show()" |
| 742 | ] |
| 743 | }, |
| 744 | { |
| 745 | "cell_type": "code", |
| 746 | "execution_count": 42, |
| 747 | "metadata": { |
| 748 | "colab": { |
| 749 | "base_uri": "https://localhost:8080/", |
| 750 | "height": 283 |
| 751 | }, |
| 752 | "id": "tq0vFchQwHl8", |
| 753 | "outputId": "9a5aa6a0-c92f-4d72-9e78-c0f615804bff", |
| 754 | "scrolled": false, |
| 755 | "trusted": true |
| 756 | }, |
| 757 | "outputs": [ |
| 758 | { |
| 759 | "name": "stderr", |
| 760 | "output_type": "stream", |
| 761 | "text": [ |
| 762 | "C:\\Users\\dmitryso\\AppData\\Local\\Temp/ipykernel_66184/2721537645.py:17: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n", |
| 763 | " fig.show()\n" |
| 764 | ] |
| 765 | }, |
| 766 | { |
| 767 | "data": { |
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", |
| 769 | "text/plain": [ |
| 770 | "<Figure size 432x288 with 1 Axes>" |
| 771 | ] |
| 772 | }, |
| 773 | "metadata": { |
| 774 | "needs_background": "light" |
| 775 | }, |
| 776 | "output_type": "display_data" |
| 777 | } |
| 778 | ], |
| 779 | "source": [ |
| 780 | "plot_dataset(train_x, train_labels)" |
| 781 | ] |
| 782 | }, |
| 783 | { |
| 784 | "cell_type": "markdown", |
| 785 | "metadata": {}, |
| 786 | "source": [ |
| 787 | "## Normalizing Data\n", |
| 788 | "\n", |
| 789 | "Before training, it is common to bring our input features to the standard range of [0,1] (or [-1,1]). The exact reasons for that we will discuss later in the course, but in short the reason is the following. We want to avoid values that flow through our network getting too big or too small, and we normally agree to keep all values in the small range close to 0. Thus we initialize the weights with small random numbers, and we keep signals in the same range.\n", |
| 790 | "\n", |
| 791 | "When normalizing data, we need to subtract min value and divide by range. We compute min value and range using training data, and then normalize test/validation dataset using the same min/range values from the training set. This is because in real life we will only know the training set, and not all incoming new values that the network would be asked to predict. Occasionally, the new value may fall out of the [0,1] range, but that's not crucial. " |
| 792 | ] |
| 793 | }, |
| 794 | { |
| 795 | "cell_type": "code", |
| 796 | "execution_count": 43, |
| 797 | "metadata": {}, |
| 798 | "outputs": [], |
| 799 | "source": [ |
| 800 | "train_x_norm = (train_x-np.min(train_x)) / (np.max(train_x)-np.min(train_x))\n", |
| 801 | "valid_x_norm = (valid_x-np.min(train_x)) / (np.max(train_x)-np.min(train_x))\n", |
| 802 | "test_x_norm = (test_x-np.min(train_x)) / (np.max(train_x)-np.min(train_x))" |
| 803 | ] |
| 804 | }, |
| 805 | { |
| 806 | "cell_type": "markdown", |
| 807 | "metadata": { |
| 808 | "id": "SjPlpf2-wHl8" |
| 809 | }, |
| 810 | "source": [ |
| 811 | "## Training One-Layer Perceptron\n", |
| 812 | "\n", |
| 813 | "Let's use Tensorflow gradient computing machinery to train one-layer perceptron.\n", |
| 814 | "\n", |
| 815 | "Our neural network will have 2 inputs and 1 output. The weight matrix $W$ will have size $2\\times1$, and bias vector $b$ -- $1$.\n", |
| 816 | "\n", |
| 817 | "Core model will be the same as in previous example, but loss function will be a logistic loss. To apply logistic loss, we need to get the value of **probability** as the output of our network, i.e. we need to bring the output $z$ to the range [0,1] using `sigmoid` activation function: $p=\\sigma(z)$.\n", |
| 818 | "\n", |
| 819 | "If we get the probability $p_i$ for the i-th input value corresponding to the actual class $y_i\\in\\{0,1\\}$, we compute the loss as $\\mathcal{L_i}=-(y_i\\log p_i + (1-y_i)log(1-p_i))$. \n", |
| 820 | "\n", |
| 821 | "In Tensorflow, both those steps (applying sigmoid and then logistic loss) can be done using one call to `sigmoid_cross_entropy_with_logits` function. Since we are training our network in minibatches, we need to average out the loss across all elements of a minibatch using `reduce_mean`: " |
| 822 | ] |
| 823 | }, |
| 824 | { |
| 825 | "cell_type": "code", |
| 826 | "execution_count": 52, |
| 827 | "metadata": { |
| 828 | "id": "kdDxWeCqwHl8", |
| 829 | "trusted": true |
| 830 | }, |
| 831 | "outputs": [], |
| 832 | "source": [ |
| 833 | "W = tf.Variable(tf.random.normal(shape=(2,1)),dtype=tf.float32)\n", |
| 834 | "b = tf.Variable(tf.zeros(shape=(1,),dtype=tf.float32))\n", |
| 835 | "\n", |
| 836 | "learning_rate = 0.1\n", |
| 837 | "\n", |
| 838 | "@tf.function\n", |
| 839 | "def train_on_batch(x, y):\n", |
| 840 | " with tf.GradientTape() as tape:\n", |
| 841 | " z = tf.matmul(x, W) + b\n", |
| 842 | " loss = tf.reduce_mean(tf.nn.sigmoid_cross_entropy_with_logits(labels=y,logits=z))\n", |
| 843 | " dloss_dw, dloss_db = tape.gradient(loss, [W, b])\n", |
| 844 | " W.assign_sub(learning_rate * dloss_dw)\n", |
| 845 | " b.assign_sub(learning_rate * dloss_db)\n", |
| 846 | " return loss" |
| 847 | ] |
| 848 | }, |
| 849 | { |
| 850 | "cell_type": "markdown", |
| 851 | "metadata": { |
| 852 | "id": "zAAgw0h6KzUd" |
| 853 | }, |
| 854 | "source": [ |
| 855 | "We will use minibatches of 16 elements, and do a few epochs of training:" |
| 856 | ] |
| 857 | }, |
| 858 | { |
| 859 | "cell_type": "code", |
| 860 | "execution_count": 59, |
| 861 | "metadata": { |
| 862 | "colab": { |
| 863 | "base_uri": "https://localhost:8080/" |
| 864 | }, |
| 865 | "id": "PfyqjVb2wHl8", |
| 866 | "outputId": "308850b8-fe17-4cda-ac27-8bcda210f113", |
| 867 | "trusted": true |
| 868 | }, |
| 869 | "outputs": [ |
| 870 | { |
| 871 | "name": "stdout", |
| 872 | "output_type": "stream", |
| 873 | "text": [ |
| 874 | "Epoch 0: last batch loss = 0.3823\n", |
| 875 | "Epoch 1: last batch loss = 0.5243\n", |
| 876 | "Epoch 2: last batch loss = 0.4510\n", |
| 877 | "Epoch 3: last batch loss = 0.3261\n", |
| 878 | "Epoch 4: last batch loss = 0.4177\n", |
| 879 | "Epoch 5: last batch loss = 0.3323\n", |
| 880 | "Epoch 6: last batch loss = 0.6294\n", |
| 881 | "Epoch 7: last batch loss = 0.6334\n", |
| 882 | "Epoch 8: last batch loss = 0.2571\n", |
| 883 | "Epoch 9: last batch loss = 0.3425\n" |
| 884 | ] |
| 885 | } |
| 886 | ], |
| 887 | "source": [ |
| 888 | "# Create a tf.data.Dataset object for easy batched iteration\n", |
| 889 | "dataset = tf.data.Dataset.from_tensor_slices((train_x_norm.astype(np.float32), train_labels.astype(np.float32)))\n", |
| 890 | "dataset = dataset.shuffle(128).batch(2)\n", |
| 891 | "\n", |
| 892 | "for epoch in range(10):\n", |
| 893 | " for step, (x, y) in enumerate(dataset):\n", |
| 894 | " loss = train_on_batch(x, tf.expand_dims(y,1))\n", |
| 895 | " print('Epoch %d: last batch loss = %.4f' % (epoch, float(loss)))" |
| 896 | ] |
| 897 | }, |
| 898 | { |
| 899 | "cell_type": "markdown", |
| 900 | "metadata": { |
| 901 | "id": "s4_Atvn5K4K9" |
| 902 | }, |
| 903 | "source": [ |
| 904 | "To make sure our training worked, let's plot the line that separates two classes. Separation line is defined by the equation $W\\times x + b = 0.5$" |
| 905 | ] |
| 906 | }, |
| 907 | { |
| 908 | "cell_type": "code", |
| 909 | "execution_count": 60, |
| 910 | "metadata": { |
| 911 | "colab": { |
| 912 | "base_uri": "https://localhost:8080/", |
| 913 | "height": 283 |
| 914 | }, |
| 915 | "id": "PgRTHttLwHl9", |
| 916 | "outputId": "e4407e1b-edf5-48e5-fdc2-da28120a3c6b", |
| 917 | "trusted": true |
| 918 | }, |
| 919 | "outputs": [ |
| 920 | { |
| 921 | "name": "stderr", |
| 922 | "output_type": "stream", |
| 923 | "text": [ |
| 924 | "C:\\Users\\dmitryso\\AppData\\Local\\Temp/ipykernel_66184/2721537645.py:17: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n", |
| 925 | " fig.show()\n" |
| 926 | ] |
| 927 | }, |
| 928 | { |
| 929 | "data": { |
| 930 | "image/png": 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", |
| 931 | "text/plain": [ |
| 932 | "<Figure size 432x288 with 1 Axes>" |
| 933 | ] |
| 934 | }, |
| 935 | "metadata": { |
| 936 | "needs_background": "light" |
| 937 | }, |
| 938 | "output_type": "display_data" |
| 939 | } |
| 940 | ], |
| 941 | "source": [ |
| 942 | "plot_dataset(train_x,train_labels,W.numpy(),b.numpy())" |
| 943 | ] |
| 944 | }, |
| 945 | { |
| 946 | "cell_type": "markdown", |
| 947 | "metadata": {}, |
| 948 | "source": [ |
| 949 | "Let's see how our model behaves on the validation data." |
| 950 | ] |
| 951 | }, |
| 952 | { |
| 953 | "cell_type": "code", |
| 954 | "execution_count": 61, |
| 955 | "metadata": { |
| 956 | "colab": { |
| 957 | "base_uri": "https://localhost:8080/", |
| 958 | "height": 282 |
| 959 | }, |
| 960 | "id": "oEQswfCGrmHw", |
| 961 | "outputId": "3cf61882-60e1-4baa-8e51-0c31ea80875c" |
| 962 | }, |
| 963 | "outputs": [ |
| 964 | { |
| 965 | "data": { |
| 966 | "text/plain": [ |
| 967 | "<matplotlib.collections.PathCollection at 0x12892a01460>" |
| 968 | ] |
| 969 | }, |
| 970 | "execution_count": 61, |
| 971 | "metadata": {}, |
| 972 | "output_type": "execute_result" |
| 973 | }, |
| 974 | { |
| 975 | "data": { |
| 976 | "image/png": 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", |
| 977 | "text/plain": [ |
| 978 | "<Figure size 432x288 with 2 Axes>" |
| 979 | ] |
| 980 | }, |
| 981 | "metadata": { |
| 982 | "needs_background": "light" |
| 983 | }, |
| 984 | "output_type": "display_data" |
| 985 | } |
| 986 | ], |
| 987 | "source": [ |
| 988 | "pred = tf.matmul(test_x,W)+b\n", |
| 989 | "fig,ax = plt.subplots(1,2)\n", |
| 990 | "ax[0].scatter(test_x[:,0],test_x[:,1],c=pred[:,0]>0.5)\n", |
| 991 | "ax[1].scatter(test_x[:,0],test_x[:,1],c=valid_labels)" |
| 992 | ] |
| 993 | }, |
| 994 | { |
| 995 | "cell_type": "markdown", |
| 996 | "metadata": {}, |
| 997 | "source": [ |
| 998 | "To compute the accuracy on the validation data, we can cast boolean type to float, and compute the mean:" |
| 999 | ] |
| 1000 | }, |
| 1001 | { |
| 1002 | "cell_type": "code", |
| 1003 | "execution_count": 62, |
| 1004 | "metadata": { |
| 1005 | "colab": { |
| 1006 | "base_uri": "https://localhost:8080/" |
| 1007 | }, |
| 1008 | "id": "HUjdeIefsIsg", |
| 1009 | "outputId": "f267f505-8ba4-43ef-9ebe-df124c3c05a1" |
| 1010 | }, |
| 1011 | "outputs": [ |
| 1012 | { |
| 1013 | "data": { |
| 1014 | "text/plain": [ |
| 1015 | "<tf.Tensor: shape=(), dtype=float32, numpy=0.46666667>" |
| 1016 | ] |
| 1017 | }, |
| 1018 | "execution_count": 62, |
| 1019 | "metadata": {}, |
| 1020 | "output_type": "execute_result" |
| 1021 | } |
| 1022 | ], |
| 1023 | "source": [ |
| 1024 | "tf.reduce_mean(tf.cast(((pred[0]>0.5)==test_labels),tf.float32))" |
| 1025 | ] |
| 1026 | }, |
| 1027 | { |
| 1028 | "cell_type": "markdown", |
| 1029 | "metadata": {}, |
| 1030 | "source": [ |
| 1031 | "Let's explain what goes on here:\n", |
| 1032 | "* `pred` is the values predicted by the network. They are not quite probabilities, because we have not used an activation function, but values greater than 0.5 correspond to class 1, and smaller - to class 0.\n", |
| 1033 | "* `pred[0]>0.5` creates a boolean tensor of results, where `True` corresponds to class 1, and `False` - to class 0\n", |
| 1034 | "* We compare that tensor to expected labels `valid_labels`, getting the boolean vector or correct predictions, where `True` corresponds to the correct prediction, and `False` - to incorrect one.\n", |
| 1035 | "* We convert that tensor to floating point using `tf.cast`\n", |
| 1036 | "* We then compute the mean value using `tf.reduce_mean` - that is exactly our desired accuracy " |
| 1037 | ] |
| 1038 | }, |
| 1039 | { |
| 1040 | "cell_type": "markdown", |
| 1041 | "metadata": { |
| 1042 | "id": "_95qF9lY2kHp" |
| 1043 | }, |
| 1044 | "source": [ |
| 1045 | "## Using TensorFlow/Keras Optimizers\n", |
| 1046 | "\n", |
| 1047 | "Tensorflow is closely integrated with Keras, which contains a lot of useful functionality. For example, we can use different **optimization algorithms**. Let's do that, and also print obtained accuracy during training." |
| 1048 | ] |
| 1049 | }, |
| 1050 | { |
| 1051 | "cell_type": "code", |
| 1052 | "execution_count": 63, |
| 1053 | "metadata": { |
| 1054 | "colab": { |
| 1055 | "base_uri": "https://localhost:8080/" |
| 1056 | }, |
| 1057 | "id": "ups7nlV22ofp", |
| 1058 | "outputId": "aa4dff06-82b9-4b2f-ca00-33970ea2b989" |
| 1059 | }, |
| 1060 | "outputs": [ |
| 1061 | { |
| 1062 | "name": "stdout", |
| 1063 | "output_type": "stream", |
| 1064 | "text": [ |
| 1065 | "Epoch 0: last batch loss = 4.7787, acc = 1.0000\n", |
| 1066 | "Epoch 1: last batch loss = 8.4343, acc = 0.5000\n", |
| 1067 | "Epoch 2: last batch loss = 8.3255, acc = 0.5000\n", |
| 1068 | "Epoch 3: last batch loss = 7.5579, acc = 0.5000\n", |
| 1069 | "Epoch 4: last batch loss = 6.5254, acc = 0.5000\n", |
| 1070 | "Epoch 5: last batch loss = 7.3800, acc = 0.5000\n", |
| 1071 | "Epoch 6: last batch loss = 7.7586, acc = 0.5000\n", |
| 1072 | "Epoch 7: last batch loss = 10.4724, acc = 0.0000\n", |
| 1073 | "Epoch 8: last batch loss = 9.4423, acc = 0.5000\n", |
| 1074 | "Epoch 9: last batch loss = 4.1888, acc = 1.0000\n", |
| 1075 | "Epoch 10: last batch loss = 11.2127, acc = 0.0000\n", |
| 1076 | "Epoch 11: last batch loss = 9.0417, acc = 0.5000\n", |
| 1077 | "Epoch 12: last batch loss = 7.9847, acc = 0.5000\n", |
| 1078 | "Epoch 13: last batch loss = 3.7879, acc = 1.0000\n", |
| 1079 | "Epoch 14: last batch loss = 6.8455, acc = 0.5000\n", |
| 1080 | "Epoch 15: last batch loss = 6.5204, acc = 0.5000\n", |
| 1081 | "Epoch 16: last batch loss = 9.2386, acc = 0.5000\n", |
| 1082 | "Epoch 17: last batch loss = 6.2447, acc = 0.5000\n", |
| 1083 | "Epoch 18: last batch loss = 3.9107, acc = 1.0000\n", |
| 1084 | "Epoch 19: last batch loss = 5.7645, acc = 1.0000\n" |
| 1085 | ] |
| 1086 | } |
| 1087 | ], |
| 1088 | "source": [ |
| 1089 | "optimizer = tf.keras.optimizers.Adam(0.01)\n", |
| 1090 | "\n", |
| 1091 | "W = tf.Variable(tf.random.normal(shape=(2,1)))\n", |
| 1092 | "b = tf.Variable(tf.zeros(shape=(1,),dtype=tf.float32))\n", |
| 1093 | "\n", |
| 1094 | "@tf.function\n", |
| 1095 | "def train_on_batch(x, y):\n", |
| 1096 | " vars = [W, b]\n", |
| 1097 | " with tf.GradientTape() as tape:\n", |
| 1098 | " z = tf.sigmoid(tf.matmul(x, W) + b)\n", |
| 1099 | " loss = tf.reduce_mean(tf.keras.losses.binary_crossentropy(z,y))\n", |
| 1100 | " correct_prediction = tf.equal(tf.round(y), tf.round(z))\n", |
| 1101 | " acc = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))\n", |
| 1102 | " grads = tape.gradient(loss, vars)\n", |
| 1103 | " optimizer.apply_gradients(zip(grads,vars))\n", |
| 1104 | " return loss,acc\n", |
| 1105 | "\n", |
| 1106 | "for epoch in range(20):\n", |
| 1107 | " for step, (x, y) in enumerate(dataset):\n", |
| 1108 | " loss,acc = train_on_batch(tf.reshape(x,(-1,2)), tf.reshape(y,(-1,1)))\n", |
| 1109 | " print('Epoch %d: last batch loss = %.4f, acc = %.4f' % (epoch, float(loss),acc))" |
| 1110 | ] |
| 1111 | }, |
| 1112 | { |
| 1113 | "cell_type": "markdown", |
| 1114 | "metadata": { |
| 1115 | "id": "dvAiaj_JndyP" |
| 1116 | }, |
| 1117 | "source": [ |
| 1118 | "**Task 1**: Plot the graphs of loss function and accuracy on training and validation data during training\n", |
| 1119 | "\n", |
| 1120 | "**Task 2**: Try to solve MNIST classificiation problem using this code. Hint: use `softmax_crossentropy_with_logits` or `sparse_softmax_cross_entropy_with_logits` as loss function. In the first case you need to feed expected output values in *one hot encoding*, and in the second case - as integer class number." |
| 1121 | ] |
| 1122 | }, |
| 1123 | { |
| 1124 | "cell_type": "markdown", |
| 1125 | "metadata": { |
| 1126 | "id": "995iCprDrgYQ" |
| 1127 | }, |
| 1128 | "source": [ |
| 1129 | "## Keras\n", |
| 1130 | "### Deep Learning for Humans\n", |
| 1131 | "\n", |
| 1132 | "* Keras is a library originally developed by Francois Chollet to work on top of Tensorflow, CNTK and Theano, to unify all lower-level frameworks. You can still install Keras as a separate library, but it is not advised to do so. \n", |
| 1133 | "* Now Keras is included as part of Tensorflow library\n", |
| 1134 | "* You can easily construct neural networks from layers\n", |
| 1135 | "* Contains `fit` function to do all training, plus a lot of functions to work with typical data (pictures, text, etc.)\n", |
| 1136 | "* A lot of samples\n", |
| 1137 | "* Functional API vs. Sequential API\n", |
| 1138 | "\n", |
| 1139 | "Keras provides higher level abstractions for neural networks, allowing us to operate in terms of layers, models and optimizers, and not in terms of tensors and gradients. \n", |
| 1140 | "\n", |
| 1141 | "Classical Deep Learning book from the creator of Keras: [Deep Learning with Python](https://www.manning.com/books/deep-learning-with-python)\n", |
| 1142 | "\n", |
| 1143 | "### Functional API\n", |
| 1144 | "\n", |
| 1145 | "When using functional API, we define the **input** to the network as `keras.Input`, and then compute the **output** by passing it through a series of computations. Finally, we define **model** as an object that transforms input into output.\n", |
| 1146 | "\n", |
| 1147 | "Once we obtained **model** object, we need to:\n", |
| 1148 | "* **Compile it**, by specifying loss function and the optimizer that we want to use with our model\n", |
| 1149 | "* **Train it** by calling `fit` function with the training (and possibly validation) data" |
| 1150 | ] |
| 1151 | }, |
| 1152 | { |
| 1153 | "cell_type": "code", |
| 1154 | "execution_count": 64, |
| 1155 | "metadata": { |
| 1156 | "colab": { |
| 1157 | "base_uri": "https://localhost:8080/" |
| 1158 | }, |
| 1159 | "id": "QJWplVfy34Eo", |
| 1160 | "outputId": "9be976f2-4f9a-495c-bddc-a7f9ec30989a" |
| 1161 | }, |
| 1162 | "outputs": [ |
| 1163 | { |
| 1164 | "name": "stdout", |
| 1165 | "output_type": "stream", |
| 1166 | "text": [ |
| 1167 | "Model: \"model\"\n", |
| 1168 | "_________________________________________________________________\n", |
| 1169 | " Layer (type) Output Shape Param # \n", |
| 1170 | "=================================================================\n", |
| 1171 | " input_1 (InputLayer) [(None, 2)] 0 \n", |
| 1172 | " \n", |
| 1173 | " dense (Dense) (None, 1) 3 \n", |
| 1174 | " \n", |
| 1175 | "=================================================================\n", |
| 1176 | "Total params: 3\n", |
| 1177 | "Trainable params: 3\n", |
| 1178 | "Non-trainable params: 0\n", |
| 1179 | "_________________________________________________________________\n", |
| 1180 | "Epoch 1/15\n", |
| 1181 | "9/9 [==============================] - 1s 2ms/step - loss: 0.7812 - accuracy: 0.2857\n", |
| 1182 | "Epoch 2/15\n", |
| 1183 | "9/9 [==============================] - 0s 2ms/step - loss: 0.7142 - accuracy: 0.4000\n", |
| 1184 | "Epoch 3/15\n", |
| 1185 | "9/9 [==============================] - 0s 2ms/step - loss: 0.6683 - accuracy: 0.6143\n", |
| 1186 | "Epoch 4/15\n", |
| 1187 | "9/9 [==============================] - 0s 2ms/step - loss: 0.6221 - accuracy: 0.8429\n", |
| 1188 | "Epoch 5/15\n", |
| 1189 | "9/9 [==============================] - 0s 2ms/step - loss: 0.5843 - accuracy: 0.8857\n", |
| 1190 | "Epoch 6/15\n", |
| 1191 | "9/9 [==============================] - 0s 2ms/step - loss: 0.5447 - accuracy: 0.9429\n", |
| 1192 | "Epoch 7/15\n", |
| 1193 | "9/9 [==============================] - 0s 2ms/step - loss: 0.5135 - accuracy: 0.9286\n", |
| 1194 | "Epoch 8/15\n", |
| 1195 | "9/9 [==============================] - 0s 2ms/step - loss: 0.4878 - accuracy: 0.9429\n", |
| 1196 | "Epoch 9/15\n", |
| 1197 | "9/9 [==============================] - 0s 2ms/step - loss: 0.4679 - accuracy: 0.9429\n", |
| 1198 | "Epoch 10/15\n", |
| 1199 | "9/9 [==============================] - 0s 2ms/step - loss: 0.4446 - accuracy: 0.9429\n", |
| 1200 | "Epoch 11/15\n", |
| 1201 | "9/9 [==============================] - 0s 2ms/step - loss: 0.4349 - accuracy: 0.8714\n", |
| 1202 | "Epoch 12/15\n", |
| 1203 | "9/9 [==============================] - 0s 2ms/step - loss: 0.4156 - accuracy: 0.9286\n", |
| 1204 | "Epoch 13/15\n", |
| 1205 | "9/9 [==============================] - 0s 2ms/step - loss: 0.4019 - accuracy: 0.9429\n", |
| 1206 | "Epoch 14/15\n", |
| 1207 | "9/9 [==============================] - 0s 2ms/step - loss: 0.3908 - accuracy: 0.9286\n", |
| 1208 | "Epoch 15/15\n", |
| 1209 | "9/9 [==============================] - 0s 2ms/step - loss: 0.3777 - accuracy: 0.9286\n" |
| 1210 | ] |
| 1211 | } |
| 1212 | ], |
| 1213 | "source": [ |
| 1214 | "inputs = tf.keras.Input(shape=(2,))\n", |
| 1215 | "z = tf.keras.layers.Dense(1,kernel_initializer='glorot_uniform',activation='sigmoid')(inputs)\n", |
| 1216 | "model = tf.keras.models.Model(inputs,z)\n", |
| 1217 | "\n", |
| 1218 | "model.compile(tf.keras.optimizers.Adam(0.1),'binary_crossentropy',['accuracy'])\n", |
| 1219 | "model.summary()\n", |
| 1220 | "h = model.fit(train_x_norm,train_labels,batch_size=8,epochs=15)" |
| 1221 | ] |
| 1222 | }, |
| 1223 | { |
| 1224 | "cell_type": "code", |
| 1225 | "execution_count": 65, |
| 1226 | "metadata": { |
| 1227 | "colab": { |
| 1228 | "base_uri": "https://localhost:8080/", |
| 1229 | "height": 282 |
| 1230 | }, |
| 1231 | "id": "K2Kf60IrZcqs", |
| 1232 | "outputId": "b60b868d-3562-4715-f5d5-1f9764e45f09" |
| 1233 | }, |
| 1234 | "outputs": [ |
| 1235 | { |
| 1236 | "data": { |
| 1237 | "text/plain": [ |
| 1238 | "[<matplotlib.lines.Line2D at 0x12894b95250>]" |
| 1239 | ] |
| 1240 | }, |
| 1241 | "execution_count": 65, |
| 1242 | "metadata": {}, |
| 1243 | "output_type": "execute_result" |
| 1244 | }, |
| 1245 | { |
| 1246 | "data": { |
| 1247 | "image/png": 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", |
| 1248 | "text/plain": [ |
| 1249 | "<Figure size 432x288 with 1 Axes>" |
| 1250 | ] |
| 1251 | }, |
| 1252 | "metadata": { |
| 1253 | "needs_background": "light" |
| 1254 | }, |
| 1255 | "output_type": "display_data" |
| 1256 | } |
| 1257 | ], |
| 1258 | "source": [ |
| 1259 | "plt.plot(h.history['accuracy'])" |
| 1260 | ] |
| 1261 | }, |
| 1262 | { |
| 1263 | "cell_type": "markdown", |
| 1264 | "metadata": { |
| 1265 | "id": "iJruFXmb_dur" |
| 1266 | }, |
| 1267 | "source": [ |
| 1268 | "### Sequential API\n", |
| 1269 | "\n", |
| 1270 | "Alternatively, we can start thinking of a model as of a **sequence of layers**, and just specify those layers by adding them to the `model` object:" |
| 1271 | ] |
| 1272 | }, |
| 1273 | { |
| 1274 | "cell_type": "code", |
| 1275 | "execution_count": 66, |
| 1276 | "metadata": { |
| 1277 | "colab": { |
| 1278 | "base_uri": "https://localhost:8080/" |
| 1279 | }, |
| 1280 | "id": "iWc_kSr8_YXt", |
| 1281 | "outputId": "345dbe65-629d-468f-ed75-1d412c966340" |
| 1282 | }, |
| 1283 | "outputs": [ |
| 1284 | { |
| 1285 | "name": "stdout", |
| 1286 | "output_type": "stream", |
| 1287 | "text": [ |
| 1288 | "Model: \"sequential\"\n", |
| 1289 | "_________________________________________________________________\n", |
| 1290 | " Layer (type) Output Shape Param # \n", |
| 1291 | "=================================================================\n", |
| 1292 | " dense_1 (Dense) (None, 5) 15 \n", |
| 1293 | " \n", |
| 1294 | " dense_2 (Dense) (None, 1) 6 \n", |
| 1295 | " \n", |
| 1296 | "=================================================================\n", |
| 1297 | "Total params: 21\n", |
| 1298 | "Trainable params: 21\n", |
| 1299 | "Non-trainable params: 0\n", |
| 1300 | "_________________________________________________________________\n", |
| 1301 | "Epoch 1/15\n", |
| 1302 | "9/9 [==============================] - 1s 64ms/step - loss: 0.6994 - accuracy: 0.5000 - val_loss: 0.6719 - val_accuracy: 0.4667\n", |
| 1303 | "Epoch 2/15\n", |
| 1304 | "9/9 [==============================] - 0s 6ms/step - loss: 0.6635 - accuracy: 0.5429 - val_loss: 0.6531 - val_accuracy: 0.4667\n", |
| 1305 | "Epoch 3/15\n", |
| 1306 | "9/9 [==============================] - 0s 5ms/step - loss: 0.6469 - accuracy: 0.5857 - val_loss: 0.5775 - val_accuracy: 1.0000\n", |
| 1307 | "Epoch 4/15\n", |
| 1308 | "9/9 [==============================] - 0s 4ms/step - loss: 0.5639 - accuracy: 0.9143 - val_loss: 0.5395 - val_accuracy: 0.7333\n", |
| 1309 | "Epoch 5/15\n", |
| 1310 | "9/9 [==============================] - 0s 5ms/step - loss: 0.5236 - accuracy: 0.7143 - val_loss: 0.4498 - val_accuracy: 0.9333\n", |
| 1311 | "Epoch 6/15\n", |
| 1312 | "9/9 [==============================] - 0s 5ms/step - loss: 0.4573 - accuracy: 0.8714 - val_loss: 0.3584 - val_accuracy: 1.0000\n", |
| 1313 | "Epoch 7/15\n", |
| 1314 | "9/9 [==============================] - 0s 5ms/step - loss: 0.3867 - accuracy: 0.8714 - val_loss: 0.2989 - val_accuracy: 0.9333\n", |
| 1315 | "Epoch 8/15\n", |
| 1316 | "9/9 [==============================] - 0s 7ms/step - loss: 0.3388 - accuracy: 0.8857 - val_loss: 0.2204 - val_accuracy: 1.0000\n", |
| 1317 | "Epoch 9/15\n", |
| 1318 | "9/9 [==============================] - 0s 6ms/step - loss: 0.2815 - accuracy: 0.9429 - val_loss: 0.1957 - val_accuracy: 1.0000\n", |
| 1319 | "Epoch 10/15\n", |
| 1320 | "9/9 [==============================] - 0s 6ms/step - loss: 0.2692 - accuracy: 0.8857 - val_loss: 0.1323 - val_accuracy: 1.0000\n", |
| 1321 | "Epoch 11/15\n", |
| 1322 | "9/9 [==============================] - 0s 5ms/step - loss: 0.2591 - accuracy: 0.9429 - val_loss: 0.1105 - val_accuracy: 1.0000\n", |
| 1323 | "Epoch 12/15\n", |
| 1324 | "9/9 [==============================] - 0s 6ms/step - loss: 0.2229 - accuracy: 0.9286 - val_loss: 0.1051 - val_accuracy: 1.0000\n", |
| 1325 | "Epoch 13/15\n", |
| 1326 | "9/9 [==============================] - 0s 5ms/step - loss: 0.2146 - accuracy: 0.9143 - val_loss: 0.0919 - val_accuracy: 1.0000\n", |
| 1327 | "Epoch 14/15\n", |
| 1328 | "9/9 [==============================] - 0s 5ms/step - loss: 0.2031 - accuracy: 0.9429 - val_loss: 0.0859 - val_accuracy: 1.0000\n", |
| 1329 | "Epoch 15/15\n", |
| 1330 | "9/9 [==============================] - 0s 5ms/step - loss: 0.1997 - accuracy: 0.9429 - val_loss: 0.0829 - val_accuracy: 1.0000\n" |
| 1331 | ] |
| 1332 | }, |
| 1333 | { |
| 1334 | "data": { |
| 1335 | "text/plain": [ |
| 1336 | "<keras.callbacks.History at 0x12894cfba30>" |
| 1337 | ] |
| 1338 | }, |
| 1339 | "execution_count": 66, |
| 1340 | "metadata": {}, |
| 1341 | "output_type": "execute_result" |
| 1342 | } |
| 1343 | ], |
| 1344 | "source": [ |
| 1345 | "model = tf.keras.models.Sequential()\n", |
| 1346 | "model.add(tf.keras.layers.Dense(5,activation='sigmoid',input_shape=(2,)))\n", |
| 1347 | "model.add(tf.keras.layers.Dense(1,activation='sigmoid'))\n", |
| 1348 | "\n", |
| 1349 | "model.compile(tf.keras.optimizers.Adam(0.1),'binary_crossentropy',['accuracy'])\n", |
| 1350 | "model.summary()\n", |
| 1351 | "model.fit(train_x_norm,train_labels,validation_data=(test_x_norm,test_labels),batch_size=8,epochs=15)" |
| 1352 | ] |
| 1353 | }, |
| 1354 | { |
| 1355 | "cell_type": "markdown", |
| 1356 | "metadata": { |
| 1357 | "id": "BmHNhUU8bqEX" |
| 1358 | }, |
| 1359 | "source": [ |
| 1360 | "## Classification Loss Functions\n", |
| 1361 | "\n", |
| 1362 | "It is important to correctly specify loss function and activation function on the last layer of the network. The main rules are the following:\n", |
| 1363 | "* If the network has one output (**binary classification**), we use **sigmoid** activation function, for **multiclass classification** - **softmax**\n", |
| 1364 | "* If the output class is represented as one-hot-encoding, the loss function will be **cross entropy loss** (categorical cross-entropy), if the output contains class number - **sparse categorical cross-entropy**. For **binary classification** - use **binary cross-entropy** (same as **log loss**)\n", |
| 1365 | "* **Multi-label classification** is when we can have an object belonging to several classes at the same time. In this case, we need to encode labels using one-hot encoding, and use **sigmoid** as activation function, so that each class probability is between 0 and 1.\n", |
| 1366 | "\n", |
| 1367 | "| Classification | Label Format | Activation Function | Loss |\n", |
| 1368 | "|---------------|-----------------------|-----------------|----------|\n", |
| 1369 | "| Binary | Probability of 1st class | sigmoid | binary crossentropy |\n", |
| 1370 | "| Binary | One-hot encoding (2 outputs) | softmax | categorical crossentropy |\n", |
| 1371 | "| Multiclass | One-hot encoding | softmax | categorical crossentropy |\n", |
| 1372 | "| Multiclass | Class Number | softmax | sparse categorical crossentropy |\n", |
| 1373 | "| Multilabel | One-hot encoding | sigmoid | categorical crossentropy |\n", |
| 1374 | "\n", |
| 1375 | "> Binary classification can also be handled as a special case of multi-class classification with two outputs. In this case, we need to use **softmax**.\n" |
| 1376 | ] |
| 1377 | }, |
| 1378 | { |
| 1379 | "cell_type": "markdown", |
| 1380 | "metadata": { |
| 1381 | "id": "gZ-kWx84bMDH" |
| 1382 | }, |
| 1383 | "source": [ |
| 1384 | "**Task 3**: \n", |
| 1385 | "Use Keras to train MNIST classifier:\n", |
| 1386 | "* Notice that Keras contains some standard datasets, including MNIST. To use MNIST from Keras, you only need a couple of lines of code (more information [here](https://www.tensorflow.org/api_docs/python/tf/keras/datasets/mnist))\n", |
| 1387 | "* Try several network configuration, with different number of layers/neurons, activation functions.\n", |
| 1388 | "\n", |
| 1389 | "What is the best accuracy you were able to achieve?" |
| 1390 | ] |
| 1391 | }, |
| 1392 | { |
| 1393 | "cell_type": "markdown", |
| 1394 | "metadata": { |
| 1395 | "id": "yX6hqiafwHl9" |
| 1396 | }, |
| 1397 | "source": [ |
| 1398 | "## Takeaways\n", |
| 1399 | "\n", |
| 1400 | "* Tensorflow allows you to operate on tensors at low level, you have most flexibility.\n", |
| 1401 | "* There are convenient tools to work with data (`td.Data`) and layers (`tf.layers`)\n", |
| 1402 | "* For beginners/typical tasks, it is recommended to use **Keras**, which allows to construct networks from layers\n", |
| 1403 | "* If non-standard architecture is needed, you can implement your own Keras layer, and then use it in Keras models\n", |
| 1404 | "* It is a good idea to look at PyTorch as well and compare approaches. \n", |
| 1405 | "\n", |
| 1406 | "A good sample notebook from the creator of Keras on Keras and Tensorflow 2.0 can be found [here](https://t.co/k694J95PI8)." |
| 1407 | ] |
| 1408 | } |
| 1409 | ], |
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| 1414 | "name": "IntroKerasTF.ipynb", |
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| 1421 | "display_name": "Python 3.8.12 64-bit (conda)", |
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| 1426 | "name": "ipython", |
| 1427 | "version": 3 |
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| 1430 | "mimetype": "text/x-python", |
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| 1432 | "nbconvert_exporter": "python", |
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