adversialexample.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "import torchvision\n",
    "import matplotlib.pyplot as plt\n",
    "from time import time\n",
    "from torchvision import datasets, transforms\n",
    "from torch import nn, optim\n",
    "import torch.nn.functional as F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data\n",
    "\n",
    "Load MNIST data on which we try to conduct adversial attacks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "transform = transforms.Compose([transforms.ToTensor(),\n",
    "                              transforms.Normalize((0.5,), (0.5,)),\n",
    "                              ])\n",
    "\n",
    "# Prep the datasets\n",
    "trainset = datasets.MNIST('MnistData', download=True, train=True, transform=transform)\n",
    "valset = datasets.MNIST('MnistData', download=True, train=False, transform=transform)\n",
    "\n",
    "# Feeding for a NN\n",
    "trainloader = torch.utils.data.DataLoader(trainset, batch_size=64, shuffle=True)\n",
    "valloader = torch.utils.data.DataLoader(valset, batch_size=64, shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model\n",
    "\n",
    "For the model we train a basic 3-layer CNN "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class mnistnet(nn.Module):\n",
    "    \n",
    "    def __init__(self, input_size, hidden1, hidden2, output_size):\n",
    "        super(mnistnet, self).__init__()\n",
    "        # Define the layers\n",
    "        self.conv1 = nn.Conv2d(1, 3, 5)\n",
    "        self.pool = nn.MaxPool2d(2, 2)\n",
    "        self.conv2 = nn.Conv2d(3, 9, 5)\n",
    "        self.fl1 = nn.Linear(input_size, hidden1)\n",
    "        self.fl2 = nn.Linear(hidden1, hidden2)\n",
    "        self.fl3 = nn.Linear(hidden2, output_size)\n",
    "        self.out = nn.LogSoftmax(dim=1)\n",
    "        \n",
    "    # Forward pass\n",
    "    def forward(self, x):\n",
    "        x = self.pool(F.relu(self.conv1(x)))\n",
    "        x = self.pool(F.relu(self.conv2(x)))\n",
    "        x = x.view(-1, 9 * 4 * 4)\n",
    "        x = F.relu(self.fl1(x))\n",
    "        x = F.relu(self.fl2(x))\n",
    "        x = self.fl3(x)\n",
    "        return self.out(x)\n",
    "    \n",
    "my_network = mnistnet(9 * 4 * 4, 64, 32, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 10 loss 44.38596995547414"
     ]
    }
   ],
   "source": [
    "optimizer = optim.SGD(my_network.parameters(), lr=0.003, momentum=0.9)\n",
    "criterion = nn.NLLLoss()\n",
    "\n",
    "losses = []\n",
    "for epoch in range(10):\n",
    "    running_loss = 0\n",
    "    for images, labels in trainloader:\n",
    "        optimizer.zero_grad()\n",
    "        \n",
    "        output = my_network.forward(images)\n",
    "        loss = criterion(output, labels)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        \n",
    "        running_loss += loss.item()\n",
    "        \n",
    "    losses.append(running_loss)\n",
    "    print(\"\\rEpoch {} loss {}\".format(epoch+1,running_loss), end=\"\")\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.plot(losses)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adversial attack\n",
    "\n",
    "A simple adversial attack can be done with \n",
    "\n",
    "$augmented\\_img= img + \\epsilon * sign(f(img))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon 0.1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon 0.2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon 0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Try different epsilon values to see if there is a boundary\n",
    "for epsilon in [0, 0.1, 0.2, 0.5]:\n",
    "    print(\"Epsilon {}\".format(epsilon))\n",
    "    for i in range(2):\n",
    "        test_input = images[i]\n",
    "        test_input.requires_grad = True\n",
    "\n",
    "        # Find gradient for the test image\n",
    "        output = my_network(test_input.reshape(1,1,28,28))\n",
    "        my_network.zero_grad()\n",
    "        loss = criterion(output, labels[i].view(1))\n",
    "        loss.backward()\n",
    "\n",
    "        # Construct attack image\n",
    "        sign = test_input.grad.data.sign()\n",
    "        attack_mask = epsilon * sign\n",
    "        augmented_image = images[i] + attack_mask\n",
    "        adversial_out = my_network(augmented_image.reshape(1,1,28,28))\n",
    "        \n",
    "        # Visualize results\n",
    "        plt.figure()\n",
    "        plt.subplot(1,3,1)\n",
    "        plt.axis('off')\n",
    "        plt.title(\"Original, \\npredicted as {}\".format(output.max(1)[1].item()))\n",
    "        plt.imshow(images[i].reshape(28,28))\n",
    "        plt.subplot(1,3,2)\n",
    "        plt.axis('off')\n",
    "        plt.title(\"Adversial, \\npredicted as {}\".format(adversial_out.max(1)[1].item()))\n",
    "        plt.imshow(augmented_image.reshape(28,28))\n",
    "        plt.subplot(1,3,3)\n",
    "        plt.axis('off')\n",
    "        plt.title(\"Gradient mask\")\n",
    "        plt.imshow(attack_mask.reshape(28,28))\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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}