notebooks/adversarial_training_mnist.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table style=\"border: none\" align=\"center\">\n",
    "   <tr style=\"border: none\">\n",
    "      <th style=\"border: none\"><font face=\"verdana\" size=\"4\" color=\"black\"><b>  Demonstrate adversarial training using ART  </b></font></font></th>\n",
    "   </tr> \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we demonstrate adversarial training using ART on the MNIST dataset.\n",
    "\n",
    "\n",
    "## Contents\n",
    "\n",
    "1.\t[Load prereqs and data](#prereqs)\n",
    "2.  [Train and evaluate a baseline classifier](#classifier)\n",
    "3.  [Adversarially train a robust classifier](#adv_training)\n",
    "4.\t[Evaluate the robust classifier](#evaluation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"prereqs\"></a>\n",
    "## 1. Load prereqs and data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "from keras.models import load_model\n",
    "\n",
    "from art import config\n",
    "from art.utils import load_dataset, get_file\n",
    "from art.estimators.classification import KerasClassifier\n",
    "from art.attacks.evasion import FastGradientMethod\n",
    "from art.attacks.evasion import BasicIterativeMethod\n",
    "from art.defences.trainer import AdversarialTrainer\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, y_train), (x_test, y_test), min_, max_ = load_dataset('mnist')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"classifier\"></a>\n",
    "## 2. Train and evaluate a baseline classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the classifier model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = get_file('mnist_cnn_original.h5', extract=False, path=config.ART_DATA_PATH,\n",
    "                url='https://www.dropbox.com/s/p2nyzne9chcerid/mnist_cnn_original.h5?dl=1')\n",
    "classifier_model = load_model(path)\n",
    "classifier = KerasClassifier(clip_values=(min_, max_), model=classifier_model, use_logits=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_1\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_1 (Conv2D)            (None, 26, 26, 32)        320       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2 (None, 13, 13, 32)        0         \n",
      "_________________________________________________________________\n",
      "conv2d_2 (Conv2D)            (None, 11, 11, 64)        18496     \n",
      "_________________________________________________________________\n",
      "max_pooling2d_2 (MaxPooling2 (None, 5, 5, 64)          0         \n",
      "_________________________________________________________________\n",
      "flatten_1 (Flatten)          (None, 1600)              0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 128)               204928    \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 10)                1290      \n",
      "=================================================================\n",
      "Total params: 225,034\n",
      "Trainable params: 225,034\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "classifier_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluate the classifier performance on the first 100 original test samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original test data (first 100 images):\n",
      "Correctly classified: 100\n",
      "Incorrectly classified: 0\n"
     ]
    }
   ],
   "source": [
    "x_test_pred = np.argmax(classifier.predict(x_test[:100]), axis=1)\n",
    "nb_correct_pred = np.sum(x_test_pred == np.argmax(y_test[:100], axis=1))\n",
    "\n",
    "print(\"Original test data (first 100 images):\")\n",
    "print(\"Correctly classified: {}\".format(nb_correct_pred))\n",
    "print(\"Incorrectly classified: {}\".format(100-nb_correct_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate some adversarial samples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "attacker = FastGradientMethod(classifier, eps=0.5)\n",
    "x_test_adv = attacker.generate(x_test[:100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And evaluate performance on those:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adversarial test data (first 100 images):\n",
      "Correctly classified: 21\n",
      "Incorrectly classified: 79\n"
     ]
    }
   ],
   "source": [
    "x_test_adv_pred = np.argmax(classifier.predict(x_test_adv), axis=1)\n",
    "nb_correct_adv_pred = np.sum(x_test_adv_pred == np.argmax(y_test[:100], axis=1))\n",
    "\n",
    "print(\"Adversarial test data (first 100 images):\")\n",
    "print(\"Correctly classified: {}\".format(nb_correct_adv_pred))\n",
    "print(\"Incorrectly classified: {}\".format(100-nb_correct_adv_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"adv_training\"></a>\n",
    "## 3. Adversarially train a robust classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = get_file('mnist_cnn_robust.h5', extract=False, path=config.ART_DATA_PATH,\n",
    "                url='https://www.dropbox.com/s/yutsncaniiy5uy8/mnist_cnn_robust.h5?dl=1')\n",
    "robust_classifier_model = load_model(path)\n",
    "robust_classifier = KerasClassifier(clip_values=(min_, max_), model=robust_classifier_model, use_logits=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: the robust classifier has the same architecture as above, except the first dense layer has **1024** instead of **128** units. (This was recommend by Madry et al. (2017), *Towards Deep Learning Models Resistant to Adversarial Attacks*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_2\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_3 (Conv2D)            (None, 26, 26, 32)        320       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_3 (MaxPooling2 (None, 13, 13, 32)        0         \n",
      "_________________________________________________________________\n",
      "conv2d_4 (Conv2D)            (None, 11, 11, 64)        18496     \n",
      "_________________________________________________________________\n",
      "max_pooling2d_4 (MaxPooling2 (None, 5, 5, 64)          0         \n",
      "_________________________________________________________________\n",
      "flatten_2 (Flatten)          (None, 1600)              0         \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 1024)              1639424   \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 10)                10250     \n",
      "=================================================================\n",
      "Total params: 1,668,490\n",
      "Trainable params: 1,668,490\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "robust_classifier_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also as recommended by Madry et al., we use BIM/PGD attacks during adversarial training:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "attacks = BasicIterativeMethod(robust_classifier, eps=0.3, eps_step=0.01, max_iter=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform adversarial training:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We had performed this before, starting with a randomly initialized model.\n",
    "# Adversarial training takes about 80 minutes on an NVIDIA V100.\n",
    "# The resulting model is the one loaded from mnist_cnn_robust.h5 above.\n",
    "\n",
    "# Here is the command we had used for the Adversarial Training\n",
    "\n",
    "# trainer = AdversarialTrainer(robust_classifier, attacks, ratio=1.0)\n",
    "# trainer.fit(x_train, y_train, nb_epochs=83, batch_size=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"evaluation\"></a>\n",
    "## 4. Evaluate the robust classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluate the robust classifier's performance on the original test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original test data (first 100 images):\n",
      "Correctly classified: 99\n",
      "Incorrectly classified: 1\n"
     ]
    }
   ],
   "source": [
    "x_test_robust_pred = np.argmax(robust_classifier.predict(x_test[:100]), axis=1)\n",
    "nb_correct_robust_pred = np.sum(x_test_robust_pred == np.argmax(y_test[:100], axis=1))\n",
    "\n",
    "print(\"Original test data (first 100 images):\")\n",
    "print(\"Correctly classified: {}\".format(nb_correct_robust_pred))\n",
    "print(\"Incorrectly classified: {}\".format(100-nb_correct_robust_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluate the robust classifier's performance on the adversarial test data (**white-box** setting):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "attacker_robust = FastGradientMethod(robust_classifier, eps=0.5)\n",
    "x_test_adv_robust = attacker_robust.generate(x_test[:100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adversarial test data (first 100 images):\n",
      "Correctly classified: 79\n",
      "Incorrectly classified: 21\n"
     ]
    }
   ],
   "source": [
    "x_test_adv_robust_pred = np.argmax(robust_classifier.predict(x_test_adv_robust), axis=1)\n",
    "nb_correct_adv_robust_pred = np.sum(x_test_adv_robust_pred == np.argmax(y_test[:100], axis=1))\n",
    "\n",
    "print(\"Adversarial test data (first 100 images):\")\n",
    "print(\"Correctly classified: {}\".format(nb_correct_adv_robust_pred))\n",
    "print(\"Incorrectly classified: {}\".format(100-nb_correct_adv_robust_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the performance of the original and the robust classifier over a range of `eps` values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps_range = [0.01, 0.02, 0.03, 0.04, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]\n",
    "nb_correct_original = []\n",
    "nb_correct_robust = []\n",
    "\n",
    "for eps in eps_range:\n",
    "    attacker.set_params(**{'eps': eps})\n",
    "    attacker_robust.set_params(**{'eps': eps})\n",
    "    x_test_adv = attacker.generate(x_test[:100])\n",
    "    x_test_adv_robust = attacker_robust.generate(x_test[:100])\n",
    "    \n",
    "    x_test_adv_pred = np.argmax(classifier.predict(x_test_adv), axis=1)\n",
    "    nb_correct_original += [np.sum(x_test_adv_pred == np.argmax(y_test[:100], axis=1))]\n",
    "    \n",
    "    x_test_adv_robust_pred = np.argmax(robust_classifier.predict(x_test_adv_robust), axis=1)\n",
    "    nb_correct_robust += [np.sum(x_test_adv_robust_pred == np.argmax(y_test[:100], axis=1))]\n",
    "\n",
    "eps_range = [0] + eps_range\n",
    "nb_correct_original = [nb_correct_pred] + nb_correct_original\n",
    "nb_correct_robust = [nb_correct_robust_pred] + nb_correct_robust"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(np.array(eps_range), np.array(nb_correct_original), 'b--', label='Original classifier')\n",
    "ax.plot(np.array(eps_range), np.array(nb_correct_robust), 'r--', label='Robust classifier')\n",
    "\n",
    "legend = ax.legend(loc='upper center', shadow=True, fontsize='large')\n",
    "legend.get_frame().set_facecolor('#00FFCC')\n",
    "\n",
    "plt.xlabel('Attack strength (eps)')\n",
    "plt.ylabel('Correct predictions')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}