{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ " # Lecture 13: Training deep neural networks" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "![](https://www.tensorflow.org/images/colab_logo_32px.png)\n", "[Run in colab](https://colab.research.google.com/drive/1ftihrW-_2cIzCkA3TYScFgoOe1bQwTrT)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:55.831361Z", "iopub.status.busy": "2024-01-10T00:22:55.830970Z", "iopub.status.idle": "2024-01-10T00:22:55.838672Z", "shell.execute_reply": "2024-01-10T00:22:55.838114Z" }, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last executed: 2024-01-10 00:22:55\n" ] } ], "source": [ "import datetime\n", "now = datetime.datetime.now()\n", "print(\"Last executed: \" + now.strftime(\"%Y-%m-%d %H:%M:%S\"))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:55.878794Z", "iopub.status.busy": "2024-01-10T00:22:55.878339Z", "iopub.status.idle": "2024-01-10T00:22:56.288229Z", "shell.execute_reply": "2024-01-10T00:22:56.287528Z" }, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "# Common imports\n", "import numpy as np\n", "import os\n", "\n", "# to make this notebook's output stable across runs\n", "def reset_state(seed=42):\n", " tf.keras.backend.clear_session()\n", " tf.random.set_seed(seed)\n", " np.random.seed(seed)\n", "\n", "# To plot pretty figures\n", "%matplotlib inline\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "mpl.rc('axes', labelsize=14)\n", "mpl.rc('xtick', labelsize=12)\n", "mpl.rc('ytick', labelsize=12)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Vanishing and exploding gradients" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Training typically relies on gradients.\n", "\n", "*Vanishing gradients problem*: For deep networks, gradients in lower layers can become very small. Hence, corresponding weights are not updated during training.\n", "\n", "*Exploding gradients problem*: In some situations (typically recurrent neural networks) gradients can become very large. Hence, weight updates are very large and the training algorithm may not converge.\n", "\n", "In general deep neural networks can suffer from *unstable gradients*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Problematic activation functions\n", "\n", "One common cause of vanishing gradients in the past was the use of the sigmoid activation function (and unit Gaussian initialisation)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:56.291811Z", "iopub.status.busy": "2024-01-10T00:22:56.291496Z", "iopub.status.idle": "2024-01-10T00:22:56.295905Z", "shell.execute_reply": "2024-01-10T00:22:56.295221Z" } }, "outputs": [], "source": [ "def logit(z):\n", " return 1 / (1 + np.exp(-z))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:56.299923Z", "iopub.status.busy": "2024-01-10T00:22:56.298543Z", "iopub.status.idle": "2024-01-10T00:22:56.599443Z", "shell.execute_reply": "2024-01-10T00:22:56.598785Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "z = np.linspace(-5, 5, 200)\n", " \n", "plt.figure(figsize=(8,4))\n", "plt.plot([-5, 5], [0, 0], 'k-')\n", "plt.plot([-5, 5], [1, 1], 'k--')\n", "plt.plot([0, 0], [-0.2, 1.2], 'k-')\n", "plt.plot([-5, 5], [-3/4, 7/4], 'g--')\n", "plt.plot(z, logit(z), \"b-\", linewidth=2)\n", "props = dict(facecolor='black', shrink=0.1)\n", "plt.annotate('Saturating', xytext=(3.5, 0.7), xy=(5, 1), arrowprops=props, fontsize=14, ha=\"center\")\n", "plt.annotate('Saturating', xytext=(-3.5, 0.3), xy=(-5, 0), arrowprops=props, fontsize=14, ha=\"center\")\n", "plt.annotate('Linear', xytext=(2, 0.2), xy=(0, 0.5), arrowprops=props, fontsize=14, ha=\"center\")\n", "plt.grid(True)\n", "plt.title(\"Sigmoid activation function\", fontsize=14)\n", "plt.axis([-5, 5, -0.2, 1.2]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Variance of outputs grows at each layer. Final layers essentially saturate. Gradients on final layers then very small and when propagate gradients back with back-propagation then get vanishing gradients." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Weight initialisation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To avoid this problem need signals and gradents to *not* decay as propagating through network.\n", "\n", "Avoid decaying signals/gradients by promoting equal variance at outputs and inputs of layer." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Can be promoted by random initialisation of weights to follow Gaussian with standard deviation:\n", "\n", "\\begin{eqnarray}\n", "\\text{Sigmoid activation:} \\quad\\quad & \\sigma = \\sqrt{\\frac{2}{n_{\\rm inputs}+n_{\\rm outputs}}} \\\\\n", "\\text{Hyperbolic tangent activation:} \\quad\\quad & \\sigma = 4\\sqrt{\\frac{2}{n_{\\rm inputs}+n_{\\rm outputs}}} \\\\\n", "\\text{ReLU activation:} \\quad\\quad & \\sigma = \\sqrt{2}\\sqrt{\\frac{2}{n_{\\rm inputs}+n_{\\rm outputs}}} \\\\\n", "\\end{eqnarray}\n", "\n", "where $n_{\\rm inputs}$ and $n_{\\rm outputs}$ are the number of input and output nodes, respectively, for the layer." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are a lot of different weight initialisation strategies." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Weight initialisation in TensorFlow" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:56.603200Z", "iopub.status.busy": "2024-01-10T00:22:56.602586Z", "iopub.status.idle": "2024-01-10T00:22:58.735681Z", "shell.execute_reply": "2024-01-10T00:22:58.734962Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2024-01-10 00:22:56.772636: I tensorflow/tsl/cuda/cudart_stub.cc:28] Could not find cuda drivers on your machine, GPU will not be used.\n", "2024-01-10 00:22:56.822106: I tensorflow/tsl/cuda/cudart_stub.cc:28] Could not find cuda drivers on your machine, GPU will not be used.\n", "2024-01-10 00:22:56.823186: I tensorflow/core/platform/cpu_feature_guard.cc:182] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.\n", "To enable the following instructions: AVX2 AVX512F FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "2024-01-10 00:22:57.633927: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT\n" ] } ], "source": [ "import tensorflow as tf\n", "from tensorflow import keras" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:58.739586Z", "iopub.status.busy": "2024-01-10T00:22:58.738814Z", "iopub.status.idle": "2024-01-10T00:22:58.757156Z", "shell.execute_reply": "2024-01-10T00:22:58.756535Z" } }, "outputs": [ { "data": { "text/plain": [ "['Constant',\n", " 'GlorotNormal',\n", " 'GlorotUniform',\n", " 'HeNormal',\n", " 'HeUniform',\n", " 'Identity',\n", " 'Initializer',\n", " 'LecunNormal',\n", " 'LecunUniform',\n", " 'Ones',\n", " 'Orthogonal',\n", " 'RandomNormal',\n", " 'RandomUniform',\n", " 'TruncatedNormal',\n", " 'VarianceScaling',\n", " 'Zeros',\n", " 'constant',\n", " 'deserialize',\n", " 'get',\n", " 'glorot_normal',\n", " 'glorot_uniform',\n", " 'he_normal',\n", " 'he_uniform',\n", " 'identity',\n", " 'lecun_normal',\n", " 'lecun_uniform',\n", " 'ones',\n", " 'orthogonal',\n", " 'random_normal',\n", " 'random_uniform',\n", " 'serialize',\n", " 'truncated_normal',\n", " 'variance_scaling',\n", " 'zeros']" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[name for name in dir(keras.initializers) if not name.startswith(\"_\")]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Can often simply set initialiser when defining layer." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:58.760271Z", "iopub.status.busy": "2024-01-10T00:22:58.759695Z", "iopub.status.idle": "2024-01-10T00:22:58.772055Z", "shell.execute_reply": "2024-01-10T00:22:58.771514Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reset_state()\n", "\n", "keras.layers.Dense(10, activation=\"relu\", kernel_initializer=\"he_normal\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or can set up a `VarianceScaling` object directly." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:58.775092Z", "iopub.status.busy": "2024-01-10T00:22:58.774709Z", "iopub.status.idle": "2024-01-10T00:22:58.780920Z", "shell.execute_reply": "2024-01-10T00:22:58.780386Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "he_avg_init = keras.initializers.VarianceScaling(scale=2., mode='fan_avg', distribution='uniform')\n", "keras.layers.Dense(10, activation=\"sigmoid\", kernel_initializer=he_avg_init)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Non-saturating activation functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ReLU activation behaves much better than the sigmoid in deep networks since it does not saturate for positive values (and it is fast to compute)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "However, the ReLU does suffer from the *dying neuron* problem.\n", "\n", "In this senario neurons effectively die and only output zero. The neuron is unlikely to come back to life since the gradient of the ReLU activation function is zero for negative inputs." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Leaky ReLU\n", "\n", "The *leaky ReLU* avoids this problem and is defined by\n", "\n", "$$\n", "\\text{LeakyReLU}_\\alpha(z) = \\max(\\alpha z, z),\n", "$$\n", "\n", "where the hyperparameter $\\alpha$ defines how much the leaky ReLU leaks (typically $\\alpha=0.01$)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's plot the Leaky ReLU activation function for $\\alpha=0.05$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:58.784177Z", "iopub.status.busy": "2024-01-10T00:22:58.783818Z", "iopub.status.idle": "2024-01-10T00:22:58.786852Z", "shell.execute_reply": "2024-01-10T00:22:58.786289Z" } }, "outputs": [], "source": [ "def leaky_relu(z, alpha=0.01):\n", " return np.maximum(alpha*z, z)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:58.789638Z", "iopub.status.busy": "2024-01-10T00:22:58.789267Z", "iopub.status.idle": "2024-01-10T00:22:58.987976Z", "shell.execute_reply": "2024-01-10T00:22:58.987228Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "z = np.linspace(-5, 5, 200)\n", "\n", "plt.figure(figsize=(8,4))\n", "plt.plot(z, leaky_relu(z, 0.05), \"b-\", linewidth=2)\n", "plt.plot([-5, 5], [0, 0], 'k-')\n", "plt.plot([0, 0], [-0.5, 4.2], 'k-')\n", "plt.grid(True)\n", "props = dict(facecolor='black', shrink=0.1)\n", "plt.annotate('Leak', xytext=(-3.5, 0.5), xy=(-5, -0.2), arrowprops=props, fontsize=14, ha=\"center\")\n", "plt.title(\"Leaky ReLU activation function\", fontsize=14)\n", "plt.axis([-5, 5, -0.5, 4.2]);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### ELU\n", "\n", "Another alternative is the *exponental linear unit* (ELU)." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:58.991306Z", "iopub.status.busy": "2024-01-10T00:22:58.990702Z", "iopub.status.idle": "2024-01-10T00:22:58.994461Z", "shell.execute_reply": "2024-01-10T00:22:58.993777Z" } }, "outputs": [], "source": [ "def elu(z, alpha=1):\n", " return np.where(z < 0, alpha * (np.exp(z) - 1), z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot the ELU activation function for $\\alpha=1$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:58.997558Z", "iopub.status.busy": "2024-01-10T00:22:58.997119Z", "iopub.status.idle": "2024-01-10T00:22:59.226483Z", "shell.execute_reply": "2024-01-10T00:22:59.225800Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8,4))\n", "plt.plot(z, elu(z), \"b-\", linewidth=2)\n", "plt.plot([-5, 5], [0, 0], 'k-')\n", "plt.plot([-5, 5], [-1, -1], 'k--')\n", "plt.plot([0, 0], [-2.2, 3.2], 'k-')\n", "plt.grid(True)\n", "plt.title(r\"ELU activation function ($\\alpha=1$)\", fontsize=14)\n", "plt.axis([-5, 5, -2.2, 3.2]);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Properties:\n", "- Non-zero gradient for $z<0$ to avoid dying neuron issue.\n", "- Smooth so gradients well defined.\n", "- But is slower to compute." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Activations functions in TensorFlow" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "TensorFlow supports a lot of activation functions." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:59.229844Z", "iopub.status.busy": "2024-01-10T00:22:59.229364Z", "iopub.status.idle": "2024-01-10T00:22:59.235862Z", "shell.execute_reply": "2024-01-10T00:22:59.235200Z" } }, "outputs": [ { "data": { "text/plain": [ "['deserialize',\n", " 'elu',\n", " 'exponential',\n", " 'gelu',\n", " 'get',\n", " 'hard_sigmoid',\n", " 'linear',\n", " 'mish',\n", " 'relu',\n", " 'selu',\n", " 'serialize',\n", " 'sigmoid',\n", " 'softmax',\n", " 'softplus',\n", " 'softsign',\n", " 'swish',\n", " 'tanh']" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[m for m in dir(keras.activations) if not m.startswith(\"_\")]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Can again simply set when definiting layer or can construct directly." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:59.239248Z", "iopub.status.busy": "2024-01-10T00:22:59.238501Z", "iopub.status.idle": "2024-01-10T00:22:59.247878Z", "shell.execute_reply": "2024-01-10T00:22:59.247198Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reset_state()\n", "keras.layers.Dense(10, activation=\"elu\", name=\"hidden1\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:59.250824Z", "iopub.status.busy": "2024-01-10T00:22:59.250376Z", "iopub.status.idle": "2024-01-10T00:22:59.259860Z", "shell.execute_reply": "2024-01-10T00:22:59.259199Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reset_state()\n", "keras.layers.Dense(10, activation=keras.layers.Activation(\"elu\"), name=\"hidden1\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Batch normalisation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While weight normalisation can reduce gradient problems at the beginning of training, it does not guarantee that these problems won't resurface during training.\n", "\n", "*Batch normalisation* adds normalisation during training to address these issues." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Consists of zero-centering and normalising inputs just before the activation function, followed by shifting and scaling the result. The shift and scale are considered additional parameters that are learnt during training.\n", "\n", "This approach allows training to select the appropriate scale and shift (mean) for each layer." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The mean and standard deviation of the unnormalised inputs are computed for each mini-batch, hence the name *batch normalisation*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "When the trained network is applied to the test set there are no batches, so instead a running mean and standard deviation computed on the *training* set are used." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Batch normalisation in TensorFlow" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:59.263208Z", "iopub.status.busy": "2024-01-10T00:22:59.262658Z", "iopub.status.idle": "2024-01-10T00:22:59.400527Z", "shell.execute_reply": "2024-01-10T00:22:59.399918Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: \"sequential\"\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "_________________________________________________________________\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Layer (type) Output Shape Param # \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "=================================================================\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " flatten (Flatten) (None, 784) 0 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " batch_normalization (Batch (None, 784) 3136 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Normalization) \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense (Dense) (None, 300) 235500 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " batch_normalization_1 (Bat (None, 300) 1200 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " chNormalization) \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense_1 (Dense) (None, 100) 30100 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " batch_normalization_2 (Bat (None, 100) 400 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " chNormalization) \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense_2 (Dense) (None, 10) 1010 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "=================================================================\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Total params: 271346 (1.04 MB)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Trainable params: 268978 (1.03 MB)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Non-trainable params: 2368 (9.25 KB)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "_________________________________________________________________\n" ] } ], "source": [ "reset_state()\n", "\n", "import tensorflow as tf\n", "\n", "n_inputs = 28 * 28\n", "n_hidden1 = 300\n", "n_hidden2 = 100\n", "n_outputs = 10\n", "\n", "model = keras.models.Sequential([\n", "keras.layers.Flatten(input_shape=[28, 28]), keras.layers.BatchNormalization(),\n", "keras.layers.Dense(n_hidden1, activation=\"elu\", kernel_initializer=\"he_normal\"), keras.layers.BatchNormalization(),\n", "keras.layers.Dense(n_hidden2, activation=\"elu\", kernel_initializer=\"he_normal\"), keras.layers.BatchNormalization(),\n", "keras.layers.Dense(n_outputs, activation=\"softmax\")\n", "])\n", "\n", "model.summary()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:59.410248Z", "iopub.status.busy": "2024-01-10T00:22:59.410005Z", "iopub.status.idle": "2024-01-10T00:22:59.417708Z", "shell.execute_reply": "2024-01-10T00:22:59.417114Z" } }, "outputs": [ { "data": { "text/plain": [ "[('batch_normalization/gamma:0', True),\n", " ('batch_normalization/beta:0', True),\n", " ('batch_normalization/moving_mean:0', False),\n", " ('batch_normalization/moving_variance:0', False)]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[(var.name, var.trainable) for var in model.layers[1].variables]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "tags": [ "exercise_pointer" ] }, "source": [ "**Exercises:** *You can now complete Exercise 1 in the exercises associated with this lecture.*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Pretraining and transfer learning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A deep network trained for one task can often be adapted for a similar task." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Reuse lower layers of network trained for another task.\n", "\n", "\n", "\n", "[Credit: Geron]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "For transfer learning to be successful the data must have similar low-level features." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Reusing a Keras model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's work through a transfer learning example." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Split the fashion MNIST training set into two:\n", "* `X_train_A`: all images of all items, except sandals and shirts (classes 5 and 6).\n", "* `X_train_B`: first 200 images of sandals or shirts.\n", "\n", "The validation set and the test set are split similarly, but without restricting the number of images." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Dataset B corresponds to a simple problem (binary classification) but we only have a small number of training instances. \n", "\n", "Dataset A corresponds to a more difficult problem (classification between 8 classes) but we have much more data.\n", "\n", "We will attempt to transfer knowledge from setting A to B, since classes in set A (sneakers, ankle boots, coats, t-shirts, etc.) are somewhat similar to classes in set B (sandals and shirts). " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Aside: Note that only patterns that occur in the same location can be reused since we are using `Dense` layers (CNNs will be much more effective in tranferring information detected anywhere in the image due to their translational equivariance properties, as we'll see in the CNN lecture)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Set up data" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:22:59.421321Z", "iopub.status.busy": "2024-01-10T00:22:59.421081Z", "iopub.status.idle": "2024-01-10T00:23:00.131437Z", "shell.execute_reply": "2024-01-10T00:23:00.130720Z" }, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "(X_train_full, y_train_full), (X_test, y_test) = keras.datasets.fashion_mnist.load_data()\n", "X_train_full = X_train_full / 255.0\n", "X_test = X_test / 255.0\n", "X_valid, X_train = X_train_full[:5000], X_train_full[5000:]\n", "y_valid, y_train = y_train_full[:5000], y_train_full[5000:]\n", "\n", "def split_dataset(X, y):\n", " y_5_or_6 = (y == 5) | (y == 6) # sandals or shirts\n", " y_A = y[~y_5_or_6]\n", " y_A[y_A > 6] -= 2 # class indices 7, 8, 9 should be moved to 5, 6, 7\n", " y_B = (y[y_5_or_6] == 6).astype(np.float32) # binary classification task: is it a shirt (class 6)?\n", " return ((X[~y_5_or_6], y_A),\n", " (X[y_5_or_6], y_B))\n", "\n", "(X_train_A, y_train_A), (X_train_B, y_train_B) = split_dataset(X_train, y_train)\n", "(X_valid_A, y_valid_A), (X_valid_B, y_valid_B) = split_dataset(X_valid, y_valid)\n", "(X_test_A, y_test_A), (X_test_B, y_test_B) = split_dataset(X_test, y_test)\n", "X_train_B = X_train_B[:200]\n", "y_train_B = y_train_B[:200]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:00.135205Z", "iopub.status.busy": "2024-01-10T00:23:00.134695Z", "iopub.status.idle": "2024-01-10T00:23:00.141530Z", "shell.execute_reply": "2024-01-10T00:23:00.140918Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "((43986, 28, 28), (200, 28, 28))" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_train_A.shape, X_train_B.shape" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:00.144646Z", "iopub.status.busy": "2024-01-10T00:23:00.144207Z", "iopub.status.idle": "2024-01-10T00:23:00.151271Z", "shell.execute_reply": "2024-01-10T00:23:00.150672Z" } }, "outputs": [ { "data": { "text/plain": [ "array([4, 0, 5, 7, 7, 7, 4, 4, 3, 4, 0, 1, 6, 3, 4, 3, 2, 6, 5, 3, 4, 5,\n", " 1, 3, 4, 2, 0, 6, 7, 1], dtype=uint8)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y_train_A[:30]" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:00.154309Z", "iopub.status.busy": "2024-01-10T00:23:00.153858Z", "iopub.status.idle": "2024-01-10T00:23:00.160738Z", "shell.execute_reply": "2024-01-10T00:23:00.160192Z" } }, "outputs": [ { "data": { "text/plain": [ "array([1., 1., 0., 0., 0., 0., 1., 1., 1., 0., 0., 1., 1., 0., 0., 0., 0.,\n", " 0., 0., 1., 1., 0., 0., 1., 1., 0., 1., 1., 1., 1.], dtype=float32)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y_train_B[:30]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Define, compile, fit and save model on dataset A" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:00.163573Z", "iopub.status.busy": "2024-01-10T00:23:00.163211Z", "iopub.status.idle": "2024-01-10T00:23:00.242899Z", "shell.execute_reply": "2024-01-10T00:23:00.242202Z" } }, "outputs": [], "source": [ "reset_state()\n", "model_A = keras.models.Sequential()\n", "model_A.add(keras.layers.Flatten(input_shape=[28, 28]))\n", "for n_hidden in (300, 100, 50, 50, 50):\n", " model_A.add(keras.layers.Dense(n_hidden, activation=\"selu\"))\n", "model_A.add(keras.layers.Dense(8, activation=\"softmax\"))" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:00.246777Z", "iopub.status.busy": "2024-01-10T00:23:00.246306Z", "iopub.status.idle": "2024-01-10T00:23:00.260897Z", "shell.execute_reply": "2024-01-10T00:23:00.260316Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: \"sequential\"\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "_________________________________________________________________\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " Layer (type) Output Shape Param # \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "=================================================================\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " flatten (Flatten) (None, 784) 0 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense (Dense) (None, 300) 235500 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense_1 (Dense) (None, 100) 30100 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense_2 (Dense) (None, 50) 5050 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense_3 (Dense) (None, 50) 2550 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense_4 (Dense) (None, 50) 2550 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " dense_5 (Dense) (None, 8) 408 \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " \n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "=================================================================\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Total params: 276158 (1.05 MB)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Trainable params: 276158 (1.05 MB)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Non-trainable params: 0 (0.00 Byte)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "_________________________________________________________________\n" ] } ], "source": [ "model_A.summary()" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:00.270442Z", "iopub.status.busy": "2024-01-10T00:23:00.270062Z", "iopub.status.idle": "2024-01-10T00:23:00.282166Z", "shell.execute_reply": "2024-01-10T00:23:00.281544Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "model_A.compile(loss=\"sparse_categorical_crossentropy\",\n", " optimizer=keras.optimizers.legacy.SGD(learning_rate=1e-3),\n", " metrics=[\"accuracy\"])" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:00.285085Z", "iopub.status.busy": "2024-01-10T00:23:00.284855Z", "iopub.status.idle": "2024-01-10T00:23:57.929063Z", "shell.execute_reply": "2024-01-10T00:23:57.928392Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch 1/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 8:50 - loss: 2.8891 - accuracy: 0.0938" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"output_type": "stream", "text": [ "Epoch 2/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 4s - loss: 0.4284 - accuracy: 0.8750" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 29/1375 [..............................] - ETA: 2s - loss: 0.3657 - accuracy: 0.8825" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 54/1375 [>.............................] - ETA: 2s - loss: 0.3820 - accuracy: 0.8681" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1371/1375 [============================>.] - ETA: 0s - loss: 0.3519 - accuracy: 0.8785" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.3519 - accuracy: 0.8784 - val_loss: 0.3242 - val_accuracy: 0.8889\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 3/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 3s - loss: 0.3832 - accuracy: 0.9375" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2939 - accuracy: 0.8995 - val_loss: 0.2830 - val_accuracy: 0.9053\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 5/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 4s - loss: 0.4527 - accuracy: 0.8125" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 29/1375 [..............................] - ETA: 2s - loss: 0.2789 - accuracy: 0.9095" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1355/1375 [============================>.] - ETA: 0s - loss: 0.2813 - accuracy: 0.9042" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2811 - accuracy: 0.9043 - val_loss: 0.2721 - val_accuracy: 0.9083\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 6/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 3s - loss: 0.2328 - accuracy: 0.9062" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"output_type": "stream", "text": [ "Epoch 7/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 6s - loss: 0.5773 - accuracy: 0.8750" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 27/1375 [..............................] - ETA: 2s - loss: 0.2829 - accuracy: 0.9097" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 53/1375 [>.............................] - ETA: 2s - loss: 0.2677 - accuracy: 0.9098" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1362/1375 [============================>.] - ETA: 0s - loss: 0.2568 - accuracy: 0.9137" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2572 - accuracy: 0.9136 - val_loss: 0.2570 - val_accuracy: 0.9126\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 9/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 4s - loss: 0.1835 - accuracy: 0.9062" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - ETA: 0s - loss: 0.2517 - accuracy: 0.9144" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2517 - accuracy: 0.9144 - val_loss: 0.2537 - val_accuracy: 0.9126\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 10/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 4s - loss: 0.3150 - accuracy: 0.9375" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"output_type": "stream", "text": [ "Epoch 11/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 3s - loss: 0.5573 - accuracy: 0.7812" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 29/1375 [..............................] - ETA: 2s - loss: 0.2315 - accuracy: 0.9246" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 55/1375 [>.............................] - ETA: 2s - loss: 0.2344 - accuracy: 0.9239" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1311/1375 [===========================>..] - ETA: 0s - loss: 0.2430 - accuracy: 0.9167" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1338/1375 [============================>.] - ETA: 0s - loss: 0.2425 - accuracy: 0.9170" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1365/1375 [============================>.] - ETA: 0s - loss: 0.2429 - accuracy: 0.9168" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2429 - accuracy: 0.9168 - val_loss: 0.2460 - val_accuracy: 0.9158\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 12/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 4s - loss: 0.1553 - accuracy: 0.9375" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 31/1375 [..............................] - ETA: 2s - loss: 0.2504 - accuracy: 0.9153" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"output_type": "stream", "text": [ "Epoch 13/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 3s - loss: 0.2853 - accuracy: 0.9375" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 28/1375 [..............................] - ETA: 2s - loss: 0.2405 - accuracy: 0.9163" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 55/1375 [>.............................] - ETA: 2s - loss: 0.2244 - accuracy: 0.9222" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1360/1375 [============================>.] - ETA: 0s - loss: 0.2354 - accuracy: 0.9210" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2357 - accuracy: 0.9208 - val_loss: 0.2431 - val_accuracy: 0.9155\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 14/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 4s - loss: 0.1433 - accuracy: 0.9688" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"output_type": "stream", "text": [ "Epoch 15/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 4s - loss: 0.2259 - accuracy: 0.9375" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 29/1375 [..............................] - ETA: 2s - loss: 0.2009 - accuracy: 0.9332" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 55/1375 [>.............................] - ETA: 2s - loss: 0.2099 - accuracy: 0.9335" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2295 - accuracy: 0.9226 - val_loss: 0.2464 - val_accuracy: 0.9106\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 16/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 3s - loss: 0.2003 - accuracy: 0.9062" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 30/1375 [..............................] - ETA: 2s - loss: 0.2021 - accuracy: 0.9271" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"output_type": "stream", "text": [ "Epoch 17/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 4s - loss: 0.1594 - accuracy: 0.9375" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 30/1375 [..............................] - ETA: 2s - loss: 0.2122 - accuracy: 0.9250" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 57/1375 [>.............................] - ETA: 2s - loss: 0.2099 - accuracy: 0.9309" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1368/1375 [============================>.] - ETA: 0s - loss: 0.2239 - accuracy: 0.9238" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2240 - accuracy: 0.9237 - val_loss: 0.2420 - val_accuracy: 0.9141\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 18/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 3s - loss: 0.1302 - accuracy: 0.9688" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2212 - accuracy: 0.9247 - val_loss: 0.2449 - val_accuracy: 0.9108\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 19/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 3s - loss: 0.2694 - accuracy: 0.9062" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 31/1375 [..............................] - ETA: 2s - loss: 0.2491 - accuracy: 0.9083" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"output_type": "stream", "text": [ "Epoch 20/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", " 1/1375 [..............................] - ETA: 3s - loss: 0.3790 - accuracy: 0.8750" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 28/1375 [..............................] - ETA: 2s - loss: 0.2060 - accuracy: 0.9342" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", " 55/1375 [>.............................] - ETA: 2s - loss: 0.1890 - accuracy: 0.9341" ] }, { "name": "stdout", "output_type": "stream", "text": [ 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"\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "1375/1375 [==============================] - 3s 2ms/step - loss: 0.2167 - accuracy: 0.9269 - val_loss: 0.2360 - val_accuracy: 0.9168\n" ] } ], "source": [ "history = model_A.fit(X_train_A, y_train_A, epochs=20,\n", " validation_data=(X_valid_A, y_valid_A))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We achieve an accuracy ~92%, which is reasonable." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:57.932232Z", "iopub.status.busy": "2024-01-10T00:23:57.931988Z", "iopub.status.idle": "2024-01-10T00:23:57.956644Z", "shell.execute_reply": "2024-01-10T00:23:57.956100Z" }, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/keras/src/engine/training.py:3000: UserWarning: You are saving your model as an HDF5 file via `model.save()`. This file format is considered legacy. We recommend using instead the native Keras format, e.g. `model.save('my_model.keras')`.\n", " saving_api.save_model(\n" ] } ], "source": [ "model_A.save(\"my_model_A.h5\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Repeat on dataset B" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:57.959952Z", "iopub.status.busy": "2024-01-10T00:23:57.959374Z", "iopub.status.idle": "2024-01-10T00:23:58.021468Z", "shell.execute_reply": "2024-01-10T00:23:58.020785Z" } }, "outputs": [], "source": [ "model_B = keras.models.Sequential()\n", "model_B.add(keras.layers.Flatten(input_shape=[28, 28]))\n", "for n_hidden in (300, 100, 50, 50, 50):\n", " model_B.add(keras.layers.Dense(n_hidden, activation=\"selu\"))\n", "model_B.add(keras.layers.Dense(1, activation=\"sigmoid\"))" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:58.024937Z", "iopub.status.busy": "2024-01-10T00:23:58.024352Z", "iopub.status.idle": "2024-01-10T00:23:58.031911Z", "shell.execute_reply": "2024-01-10T00:23:58.031293Z" } }, "outputs": [], "source": [ "model_B.compile(loss=\"binary_crossentropy\",\n", " optimizer=keras.optimizers.legacy.SGD(learning_rate=1e-3),\n", " metrics=[\"accuracy\"])" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:23:58.034840Z", "iopub.status.busy": "2024-01-10T00:23:58.034370Z", "iopub.status.idle": "2024-01-10T00:24:01.010070Z", "shell.execute_reply": "2024-01-10T00:24:01.009366Z" }, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch 1/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 2s - loss: 0.8455 - accuracy: 0.3750" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 1s 34ms/step - loss: 0.7139 - accuracy: 0.5350 - val_loss: 0.5838 - val_accuracy: 0.7211\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 2/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.5860 - accuracy: 0.6875" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 12ms/step - loss: 0.5292 - accuracy: 0.7400 - val_loss: 0.4795 - val_accuracy: 0.8063\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 3/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.4263 - accuracy: 0.8750" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 15ms/step - loss: 0.4344 - accuracy: 0.8200 - val_loss: 0.4068 - val_accuracy: 0.8570\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 4/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.2972 - accuracy: 0.9062" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 11ms/step - loss: 0.3672 - accuracy: 0.8650 - val_loss: 0.3518 - val_accuracy: 0.8905\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 5/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - 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ETA: 0s - loss: 0.1790 - accuracy: 0.9375" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 15ms/step - loss: 0.1986 - accuracy: 0.9700 - val_loss: 0.2123 - val_accuracy: 0.9554\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 10/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.1974 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 11ms/step - loss: 0.1803 - accuracy: 0.9900 - val_loss: 0.1971 - val_accuracy: 0.9584\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 11/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - 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ETA: 0s - loss: 0.1179 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 11ms/step - loss: 0.1414 - accuracy: 0.9900 - val_loss: 0.1630 - val_accuracy: 0.9675\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 14/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.1178 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 15ms/step - loss: 0.1319 - accuracy: 0.9900 - val_loss: 0.1547 - val_accuracy: 0.9696\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 15/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.1295 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 11ms/step - loss: 0.1238 - accuracy: 0.9900 - val_loss: 0.1470 - val_accuracy: 0.9706\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 16/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.0947 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 12ms/step - loss: 0.1165 - accuracy: 0.9900 - val_loss: 0.1405 - val_accuracy: 0.9767\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 17/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.1075 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 15ms/step - loss: 0.1101 - accuracy: 0.9900 - val_loss: 0.1347 - val_accuracy: 0.9777\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 18/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.0942 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 12ms/step - loss: 0.1045 - accuracy: 0.9900 - val_loss: 0.1294 - val_accuracy: 0.9787\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 19/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.0712 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 15ms/step - loss: 0.0991 - accuracy: 0.9900 - val_loss: 0.1243 - val_accuracy: 0.9787\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 20/20\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.0666 - accuracy: 1.0000" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 11ms/step - loss: 0.0941 - accuracy: 0.9900 - val_loss: 0.1202 - val_accuracy: 0.9787\n" ] } ], "source": [ "history = model_B.fit(X_train_B, y_train_B, epochs=20,\n", " validation_data=(X_valid_B, y_valid_B))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We achieve an accuracy ~97% since this is an easier problem (binary classification).\n", "\n", "However, we could do better by transferring information from setting A." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Freezing lower layers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The lower layers of the first network have already learnt low-level features for the first task, so they can be reused as they are. \n", "\n", "That is, we freeze their weights so that they are not altered during subsequent training of the new network.\n", "\n", "We will take all layers from model A and then add a final output layer for our binary classification problem." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:24:01.014025Z", "iopub.status.busy": "2024-01-10T00:24:01.013593Z", "iopub.status.idle": "2024-01-10T00:24:01.136711Z", "shell.execute_reply": "2024-01-10T00:24:01.136018Z" } }, "outputs": [], "source": [ "model_A = keras.models.load_model(\"my_model_A.h5\")\n", "model_B_on_A = keras.models.Sequential(model_A.layers[:-1]) # Reuse all layers except output.\n", "model_B_on_A.add(keras.layers.Dense(1, activation=\"sigmoid\"))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Note that `model_B_on_A` and `model_A` now share layers. When you train on `model_B_on_A` that will also impact `model_A`.\n", "\n", "To avoid this you can clone a model." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's freeze all layers except the final dense output layer." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:24:01.140756Z", "iopub.status.busy": "2024-01-10T00:24:01.140151Z", "iopub.status.idle": "2024-01-10T00:24:01.149291Z", "shell.execute_reply": "2024-01-10T00:24:01.148631Z" } }, "outputs": [], "source": [ "for layer in model_B_on_A.layers[:-1]:\n", " layer.trainable = False\n", "\n", "model_B_on_A.compile(loss=\"binary_crossentropy\",\n", " optimizer=keras.optimizers.legacy.SGD(learning_rate=1e-3),\n", " metrics=[\"accuracy\"])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:24:01.152616Z", "iopub.status.busy": "2024-01-10T00:24:01.152021Z", "iopub.status.idle": "2024-01-10T00:24:02.154705Z", "shell.execute_reply": "2024-01-10T00:24:02.153966Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch 1/4\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 1s - loss: 0.8270 - accuracy: 0.4062" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 1s 37ms/step - loss: 0.7710 - accuracy: 0.4450 - val_loss: 0.7481 - val_accuracy: 0.4706\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 2/4\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.6625 - accuracy: 0.4688" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 11ms/step - loss: 0.7053 - accuracy: 0.4800 - val_loss: 0.6830 - val_accuracy: 0.5132\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 3/4\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.6738 - accuracy: 0.5312" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 11ms/step - loss: 0.6409 - accuracy: 0.5500 - val_loss: 0.6285 - val_accuracy: 0.5588\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 4/4\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.6079 - accuracy: 0.6250" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 11ms/step - loss: 0.5871 - accuracy: 0.6050 - val_loss: 0.5807 - val_accuracy: 0.6055\n" ] } ], "source": [ "history = model_B_on_A.fit(X_train_B, y_train_B, epochs=4,\n", " validation_data=(X_valid_B, y_valid_B))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even with just one trained layer and a few epochs, our model is starting to learn the new problem." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now let's unfreeze the lower layers and train the full model to fine-tune it." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:24:02.158195Z", "iopub.status.busy": "2024-01-10T00:24:02.157585Z", "iopub.status.idle": "2024-01-10T00:24:02.166504Z", "shell.execute_reply": "2024-01-10T00:24:02.165827Z" } }, "outputs": [], "source": [ "for layer in model_B_on_A.layers[:-1]:\n", " layer.trainable = True\n", "\n", "model_B_on_A.compile(loss=\"binary_crossentropy\",\n", " optimizer=keras.optimizers.legacy.SGD(learning_rate=1e-3),\n", " metrics=[\"accuracy\"])" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "execution": { "iopub.execute_input": "2024-01-10T00:24:02.169499Z", "iopub.status.busy": "2024-01-10T00:24:02.169102Z", "iopub.status.idle": "2024-01-10T00:24:05.143309Z", "shell.execute_reply": "2024-01-10T00:24:05.142593Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Epoch 1/16\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 2s - loss: 0.5912 - accuracy: 0.5312" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 1s 37ms/step - loss: 0.4916 - accuracy: 0.7150 - val_loss: 0.4261 - val_accuracy: 0.8012\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 2/16\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - ETA: 0s - loss: 0.3601 - accuracy: 0.9062" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", "7/7 [==============================] - 0s 15ms/step - loss: 0.3612 - accuracy: 0.8700 - val_loss: 0.3239 - val_accuracy: 0.9057\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Epoch 3/16\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\r", "1/7 [===>..........................] - 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\\eta \\nabla_\\theta J(\\theta)$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Momentum optimization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Momentum optimization uses the gradients to modify a momentum vector and uses the momentum to update the weights:\n", "\n", "1. $m \\leftarrow \\beta m + \\eta \\nabla_\\theta J(\\theta)$\n", "2. $\\theta \\leftarrow \\theta - m$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Gradient is used as an acceleration rather than speed. Can help to traverse plateaus and to avoid local minima.\n", "\n", "The additional hyperparameter $\\beta$ is introduced as a friction term to avoid the momentum growing too large (typically $\\beta \\sim 0.9$)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Nesterov accelerated gradient" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nesterov accelerated gradient is a variant of momentum optimization where the gradient is computed further ahead in the direction of the momentum:\n", "\n", "1. $m \\leftarrow \\beta m + \\eta \\nabla_\\theta J(\\theta + \\beta m)$\n", "2. $\\theta \\leftarrow \\theta - m$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "In general the momentum will be pointing toward the optimum and so Nesterov modification typically provides an improvement over standard momentum optimization." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### AdaGrad" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "AdaGrad scales down the gradient vector along the steepest direction by incorporating a gradient squared term:\n", "\n", "1. $s \\leftarrow s + \\nabla_\\theta J(\\theta) \\otimes \\nabla_\\theta J(\\theta)$\n", "2. $\\theta \\leftarrow \\theta - \\eta \\nabla_\\theta J(\\theta) \\oslash \\sqrt{s+\\epsilon}$\n", "\n", "Note that $\\otimes$ and $\\oslash$ are elementwise multiplication and division, respectively.\n", "\n", "The parameter $\\epsilon$ is introduced for numerical stability (typically $\\epsilon\\sim 10^{-10}$).\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Basically, AdaGrad correspondings to an *adaptive learning rate* where the learning rate is decayed faster for steep directions.\n", "\n", "Consequently, it requires much less tuning of the learning rate $\\eta$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "\n", "[Credit: Geron]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### RMSProp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "RMSProp extends AdaGrad by introducing an exponential decay in the accumulated squared gradient:\n", "\n", "1. $s \\leftarrow \\beta s + (1-\\beta) \\nabla_\\theta J(\\theta) \\otimes \\nabla_\\theta J(\\theta)$\n", "2. $\\theta \\leftarrow \\theta - \\eta \\nabla_\\theta J(\\theta) \\oslash \\sqrt{s+\\epsilon}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "(Typically $\\beta\\sim 0.9$.)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Avoids the problem where AdaGrad slows down too fast and so doesn't converge to the global optimum." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Adam optimization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Adam optimization combines momentum and RMSProp:\n", "\n", "1. $m \\leftarrow \\beta_1 m + (1-\\beta_1) \\nabla_\\theta J(\\theta)$\n", "2. $s \\leftarrow \\beta_2 s + (1-\\beta_2) \\nabla_\\theta J(\\theta)\\otimes\\nabla_\\theta J(\\theta)$\n", "3. $m \\leftarrow \\frac{m}{1-\\beta_1^{t}}$, where $t$ is the iteration number \n", "4. $s \\leftarrow \\frac{s}{1-\\beta_2^{t}}$, where $t$ is the iteration number\n", "5. $\\theta \\leftarrow \\theta - \\eta m \\oslash \\sqrt{s+\\epsilon}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Steps 3 and 4 are introduced to boost $m$ and $s$ at the beginnning of training (since they are initialised to 0 they can otherwise be low at the beginning).\n", "\n", "(Typically $\\beta_1 \\sim 0.9$, $\\beta_2 \\sim 0.999$.)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Regularization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deep networks have many parameters (sometimes millions) and so are prone to overfitting.\n", "\n", "Regularization therefore becomes increasingly important." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Early stopping" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A simple regularization strategy is to end training early, e.g. when performance on validation set starts to degrade.\n", "\n", "Although early stopping works well, other regularisation techniques can lead to better performance." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### $\\ell_2$ and $\\ell_1$ regularization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Tikhonov* regularization adopts $\\ell_2$ regularising term (also called *Ridge regression*):\n", "\n", "\n", "$$ R(\\theta) = \\frac{1}{2} \\sum_{j=1}^n \\theta_j^2 = \\frac{1}{2} \\theta^{\\rm T}\\theta.$$\n", "\n", "\n", "*Lasso* regularization adopts $\\ell_1$ regularising term:\n", "\n", "$$ R(\\theta) =\\sum_{j=1}^n \\left\\vert \\theta_j \\right\\vert .$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "*Elastic net* regularization provides a mix of Tikhonov and Lasso regularization, controlled by mix ratio $r$:\n", "\n", "$$ R(\\theta) = r\\sum_{j=1}^n \\left\\vert \\theta_j \\right\\vert + \\frac{1-r}{2} \\sum_{j=1}^n \\theta_j^2.$$\n", "\n", "- For $r=0$, corresponds to Tikhonov regularization.\n", "- For $r=1$, corresponds to Lasso regularization." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Dropout" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dropout is a very popular and effective regularlisation technique developed by [Geoff Hinton in 2012](http://www.jmlr.org/papers/volume15/srivastava14a.old/srivastava14a.pdf)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Dropout involves simply dropping each neuron for a given training set with probability $p$.\n", "\n", "\n", "\n", "[Credit: Geron]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "Dropout encourages each neuron to be as effective as possible individually and not to rely heavily on a few nearby neurons but to consider all input neurons carefully." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The probability $p$ is called the *dropout rate* (typically $p \\sim 0.5$).\n", "\n", "After training the neurons don't get dropped." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The number of inputs of active neurons is lower when dropout is applied during training, than when the network is applied during testing. \n", "\n", "For example, if $p=0.5$, on average there are half as many input neurons during training than when testing. During testing each neuron will get an input signal (approximately) twice as large as during training.\n", "\n", "It is important to account for this difference.\n", "\n", "To compensate, after training each neurons input weights are multiplied by the keep probability $1-p$ before applying the network to test data." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Data augmentation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Data augmentation can be applied both as a regularization technique and to increase the volume of the training set.\n", "\n", "Essentially, new training instances are created from the original training set." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "For example, for images, data augmentation can be performed by rotating, shifting, scaling, flipping, changing the contrast, ..., of the original images in the training data-set.\n", "\n", "\n", "\n", "[Credit: Geron]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Appropriate data augmentation strategies depend on the type of data under consideration." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Typically training instances are generated on the fly to avoid additional storage requirements. \n", "\n", "Tensor Flow has built in functionality for many transformations for image data, making data augmentation for image data straightforward." ] } ], "metadata": { "celltoolbar": "Slideshow", "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": "3.11.11" } }, "nbformat": 4, "nbformat_minor": 4 }