DeepFool_latest.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tah3TtonGh7r"
      },
      "source": [
        "# DeepFool Demo\n",
        "\n",
        "- Team member: Zihan Wang, Songlin Liu, Bingzhao Shan\n",
        "\n",
        "- Date: Feb 09\n",
        "\n",
        "Replication Summary:\n",
        "\n",
        "- Experiment done on a two-layer fully connected neural network on MNIST [Section2]\n",
        "\n",
        "- Generated adversarial samples using DeepFool and FGSM for visual comparison [Section3]\n",
        "\n",
        "- Quantative evaluation between DeepFool and FGSM [Section4]\n",
        "\n",
        "- Fine-tuning experiment and over-perpurbed experiment [Section5]\n",
        "\n"
      ],
      "id": "tah3TtonGh7r"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WmqPVPKSGoOs"
      },
      "source": [
        "## 1.Setup"
      ],
      "id": "WmqPVPKSGoOs"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "opB1fdJO6gIW"
      },
      "source": [
        "!pip install adversarial-robustness-toolbox"
      ],
      "id": "opB1fdJO6gIW",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "black-malta"
      },
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import torch.optim as optim\n",
        "import numpy as np\n",
        "import time \n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "from torchvision import datasets, transforms\n",
        "from torch.utils.data import DataLoader\n",
        "\n",
        "from art.attacks.evasion import FastGradientMethod, DeepFool\n",
        "from art.estimators.classification import PyTorchClassifier\n",
        "from art.utils import load_mnist"
      ],
      "id": "black-malta",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D0d6RXUYGszk"
      },
      "source": [
        "## 2.Initialize an NN and get the accuracy on the original test set"
      ],
      "id": "D0d6RXUYGszk"
    },
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        "id": "scenic-receiver",
        "outputId": "52d2d591-ba8f-4c1a-94a4-98661f96905d"
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      "source": [
        "# Step 0: Define the neural network model, return logits instead of activation in forward method\n",
        "\n",
        "class Net(nn.Module):\n",
        "  def __init__(self):\n",
        "    super(Net, self).__init__()\n",
        "    self.fc1 = nn.Linear(784,500)\n",
        "    self.fc2 = nn.Linear(500,150)\n",
        "    self.fc3 = nn.Linear(in_features=150, out_features=10)\n",
        "  \n",
        "  def forward(self, x):\n",
        "    x = x.view(-1,784)\n",
        "    x = self.fc1(x)\n",
        "    x = F.relu(x)\n",
        "    x = self.fc2(x)\n",
        "    x = F.relu(x)\n",
        "    x = self.fc3(x)\n",
        "    return x\n",
        "\n",
        "\n",
        "# Step 1: Load the MNIST dataset\n",
        "(x_train, y_train), (x_test, y_test), min_pixel_value, max_pixel_value = load_mnist()\n",
        "\n",
        "# Transform to normalized Tensors \n",
        "transform = transforms.Compose([transforms.ToTensor(),])\n",
        "                                # transforms.Normalize((0.1307,), (0.3081,))])\n",
        "\n",
        "train_dataset = datasets.MNIST('./MNIST/', train=True, transform=transform, download=True)\n",
        "test_dataset = datasets.MNIST('./MNIST/', train=False, transform=transform, download=True)\n",
        "\n",
        "\n",
        "train_loader = DataLoader(train_dataset, batch_size=len(train_dataset))\n",
        "test_loader = DataLoader(test_dataset, batch_size=len(test_dataset))\n",
        "# Convert to numpy array \n",
        "x_train = next(iter(train_loader))[0].numpy()\n",
        "x_test = next(iter(test_loader))[0].numpy()\n",
        "y_train = next(iter(train_loader))[1].numpy()\n",
        "y_test = next(iter(test_loader))[1].numpy()\n",
        "\n",
        "def convert_1hot(data):\n",
        "  rows = len(data)\n",
        "  cols = 10\n",
        "  new_data = np.zeros((rows,cols))\n",
        "  for idx, i in enumerate(data):\n",
        "    new_data[idx,i] = 1\n",
        "  return new_data\n",
        "y_train = convert_1hot(y_train)\n",
        "y_test = convert_1hot(y_test)\n",
        "\n",
        "# Step 2: Create the model\n",
        "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
        "model = Net().to(device)\n",
        "\n",
        "# Step 2a: Define the loss function and the optimizer\n",
        "criterion = nn.CrossEntropyLoss()\n",
        "# optimizer = optim.Adam(model.parameters(), lr=0.01)\n",
        "optimizer = optim.SGD(model.parameters(), lr=0.03)\n",
        "\n",
        "# Step 3: Create the ART classifier\n",
        "classifier = PyTorchClassifier(\n",
        "    model=model,\n",
        "    clip_values=(min_pixel_value, max_pixel_value),\n",
        "    loss=criterion,\n",
        "    optimizer=optimizer,\n",
        "    input_shape=(1, 28, 28),\n",
        "    nb_classes=10,\n",
        ")\n",
        "\n",
        "# Step 4: Train the ART classifier\n",
        "classifier.fit(x_train, y_train, batch_size=64, nb_epochs=3)\n",
        "\n",
        "# Step 5: Evaluate the ART classifier on benign test examples\n",
        "predictions = classifier.predict(x_test)\n",
        "accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\n",
        "print(\"Accuracy on benign test examples: {}%\".format(accuracy * 100))\n",
        "\n",
        "# add the original accuracy on the test dataset\n",
        "df_accuracy_on_original_test_set = [accuracy * 100]\n",
        "fg_accuracy_on_original_test_set = [accuracy * 100]\n",
        "df_accuracy_on_original_test_set_alpha2 = [accuracy * 100]\n",
        "df_accuracy_on_original_test_set_alpha3 = [accuracy * 100]"
      ],
      "id": "scenic-receiver",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ./MNIST/MNIST/raw/train-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "d966c4e693804b128f15b24a82069b5e",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ./MNIST/MNIST/raw/train-images-idx3-ubyte.gz to ./MNIST/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ./MNIST/MNIST/raw/train-labels-idx1-ubyte.gz\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "a422e8c275ec4b059ee3cff25cd884fc",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ./MNIST/MNIST/raw/train-labels-idx1-ubyte.gz to ./MNIST/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ./MNIST/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "1aa4b404694b4f928d7e92a7d998d166",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ./MNIST/MNIST/raw/t10k-images-idx3-ubyte.gz to ./MNIST/MNIST/raw\n",
            "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ./MNIST/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "3c4829330f934b9ea2572899afe94a0a",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Extracting ./MNIST/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./MNIST/MNIST/raw\n",
            "Processing...\n",
            "Done!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/torchvision/datasets/mnist.py:480: UserWarning: The given NumPy array is not writeable, and PyTorch does not support non-writeable tensors. This means you can write to the underlying (supposedly non-writeable) NumPy array using the tensor. You may want to copy the array to protect its data or make it writeable before converting it to a tensor. This type of warning will be suppressed for the rest of this program. (Triggered internally at  /pytorch/torch/csrc/utils/tensor_numpy.cpp:141.)\n",
            "  return torch.from_numpy(parsed.astype(m[2], copy=False)).view(*s)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "\n",
            "\n",
            "Accuracy on benign test examples: 93.39%\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vonY8n9eG18c"
      },
      "source": [
        "## 3. Visual Demo (DeepFool v.s. FGSM)"
      ],
      "id": "vonY8n9eG18c"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uyJYbdRY6r6l"
      },
      "source": [
        "def render_frame(image, logits, ground_truth):\n",
        "    # actually draw the figure\n",
        "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 8))\n",
        "\n",
        "    # image\n",
        "    ax1.imshow(image[0], cmap='gray')\n",
        "    fig.sca(ax1)\n",
        "    plt.xticks([])\n",
        "    plt.yticks([])\n",
        "    \n",
        "    # classification\n",
        "    probs = np.exp(logits) / sum(np.exp(logits))\n",
        "    topk = probs.argsort()[::-1]\n",
        "    topprobs = probs[topk]\n",
        "    barlist = ax2.bar(range(10), topprobs)\n",
        "    for i, v in enumerate(topk):\n",
        "        if i == 0:\n",
        "            barlist[i].set_color('r')\n",
        "        if v == ground_truth:\n",
        "            barlist[i].set_color('g')\n",
        "        \n",
        "    plt.sca(ax2)\n",
        "    plt.ylim([0, 1.1])\n",
        "    plt.xticks(range(10), [i for i in topk])\n",
        "    fig.subplots_adjust(bottom=0.1)\n",
        "\n",
        "    # save the plot\n",
        "    # path = os.path.join('./adv-examples', f'gt-{ground_truth}.png')\n",
        "    # if os.path.exists(path):\n",
        "    #     os.remove(path)\n",
        "    # plt.savefig(path)\n",
        "\n",
        "\n",
        "\n",
        "def render_frame_compare(image, df_adv, fgs_adv, df_logits, fgs_logits, ground_truth):\n",
        "\n",
        "\n",
        "    # actually draw the figure\n",
        "    fig, (ax1, ax2, ax3, ax4, ax5, ax6, ax7) = plt.subplots(1, 7, figsize=(16, 3))\n",
        "\n",
        "    # the raw image\n",
        "    ax1.imshow(image[0], cmap='gray')\n",
        "    fig.sca(ax1)\n",
        "    plt.xticks([])\n",
        "    plt.yticks([])\n",
        "\n",
        "    # show the difference\n",
        "    ax2.imshow(df_adv[0] - image[0], cmap='gray')\n",
        "    fig.sca(ax2)\n",
        "    plt.xticks([])\n",
        "    plt.yticks([])\n",
        "\n",
        "    # df_adv\n",
        "    ax3.imshow(df_adv[0], cmap='gray')\n",
        "    fig.sca(ax3)\n",
        "    plt.xticks([])\n",
        "    plt.yticks([])\n",
        "    \n",
        "    # df classification\n",
        "    probs = np.exp(df_logits) / sum(np.exp(df_logits))\n",
        "    topk = probs.argsort()[::-1]\n",
        "    topprobs = probs[topk]\n",
        "    barlist = ax4.bar(range(10), topprobs)\n",
        "    for i, v in enumerate(topk):\n",
        "        if i == 0:\n",
        "            barlist[i].set_color('r')\n",
        "        if v == ground_truth:\n",
        "            barlist[i].set_color('g')\n",
        "        \n",
        "    plt.sca(ax4)\n",
        "    plt.ylim([0, 1.1])\n",
        "    plt.xticks(range(10), [i for i in topk])\n",
        "\n",
        "\n",
        "    # fg_adv diff\n",
        "    ax5.imshow(fgs_adv[0] - image[0], cmap='gray')\n",
        "    fig.sca(ax5)\n",
        "    plt.xticks([])\n",
        "    plt.yticks([])\n",
        "\n",
        "    # fg_adv diff\n",
        "    ax6.imshow(fgs_adv[0], cmap='gray')\n",
        "    fig.sca(ax6)\n",
        "    plt.xticks([])\n",
        "    plt.yticks([])\n",
        "\n",
        "\n",
        "    # df classification\n",
        "    probs = np.exp(fgs_logits) / sum(np.exp(fgs_logits))\n",
        "    topk = probs.argsort()[::-1]\n",
        "    topprobs = probs[topk]\n",
        "    barlist = ax7.bar(range(10), topprobs)\n",
        "    for i, v in enumerate(topk):\n",
        "        if i == 0:\n",
        "            barlist[i].set_color('r')\n",
        "        if v == ground_truth:\n",
        "            barlist[i].set_color('g')\n",
        "        \n",
        "    plt.sca(ax7)\n",
        "    plt.ylim([0, 1.1])\n",
        "    plt.xticks(range(10), [i for i in topk])\n",
        "    \n",
        "    # fgsm classification\n",
        "    # probs = np.exp(fgs_adv) / sum(np.exp(fgs_logits))\n",
        "    # topk = probs.argsort()[::-1]\n",
        "    # topprobs = probs[topk]\n",
        "    # barlist = ax5.bar(range(10), topprobs)\n",
        "    # for i, v in enumerate(topk):\n",
        "    #     if i == 0:\n",
        "    #         barlist[i].set_color('r')\n",
        "    #     if v == ground_truth:\n",
        "    #         barlist[i].set_color('g')\n",
        "        \n",
        "    # plt.sca(ax5)\n",
        "    # plt.ylim([0, 1.1])\n",
        "    # plt.xticks(range(10), [i for i in topk])\n",
        "    # fig.subplots_adjust(bottom=0.1)\n",
        "\n",
        "\n",
        "    \n"
      ],
      "id": "uyJYbdRY6r6l",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 66,
          "referenced_widgets": [
            "44918757dc7b419e8c05a4b9946f5fb0",
            "c0dbcf500ae64537b9f68c1ab6ad3df8",
            "0cd58e1541be4fea8c7b3430a63b6d98",
            "cc749ff6b1ff4ec99748cfcb7dcb9abd",
            "3b7b1339ce984a12b95196f005bb11df",
            "109f20bc8c7f4fc3a86dd2ae66205f9c",
            "7d40d1175c3144189be8f94f79552ce9",
            "99bce5f769ab4a899fec0287b7a22ab9"
          ]
        },
        "id": "FACrVCIj2WUg",
        "outputId": "723584c9-7c2e-4a8a-9450-ea825c57da20"
      },
      "source": [
        "# attack the test dataset using deep fool\n",
        "attack = DeepFool(classifier=classifier,max_iter=50,batch_size=64,epsilon=0.02)\n",
        "visual_demo_test_df = attack.generate(x=x_test)\n",
        "\n",
        "# attack the test dataset using fgsm\n",
        "attack2 = FastGradientMethod(estimator=classifier, eps=0.25, eps_step=1e-2, targeted=False, batch_size=64, minimal=True)\n",
        "visual_demo_test_fgs = attack2.generate(x=x_test)"
      ],
      "id": "FACrVCIj2WUg",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "44918757dc7b419e8c05a4b9946f5fb0",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, description='DeepFool', max=157.0, style=ProgressStyle(description_wid…"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "tKH1K56x2490",
        "outputId": "64dcd326-d39e-472c-ca2d-804977c8f5c5"
      },
      "source": [
        "# visual_demo_test_df.shape\n",
        "# plt.figure(figsize = (20,2))\n",
        "# plt.imshow(visual_demo_test_df[100, 0, :], cmap='gray')\n",
        "\n",
        "# predictions = np.argmax(classifier.predict(visual_demo_test_df), axis=1)\n",
        "# y_true = np.argmax(y_test, axis=1)\n",
        "\n",
        "# render_frame(visual_demo_test_df[10, :], predictions[10], y_true[10])  \n",
        "\n",
        "\n",
        "df_predictions = classifier.predict(visual_demo_test_df)\n",
        "fgs_predictions = classifier.predict(visual_demo_test_fgs)\n",
        "y_true = np.argmax(y_test, axis=1)\n",
        "visited = []\n",
        "\n",
        "for i in range(visual_demo_test_df.shape[0]):\n",
        "    if len(visited) == 10:\n",
        "        break\n",
        "    \n",
        "    y = np.argmax(y_test[i])\n",
        "    if y in visited:\n",
        "        continue\n",
        "\n",
        "    pred = np.argmax(df_predictions[i])\n",
        "    if y == pred:\n",
        "        continue\n",
        "    \n",
        "    pred = np.argmax(fgs_predictions[i])\n",
        "    if y == pred:\n",
        "        continue\n",
        "    \n",
        "    visited.append(y)\n",
        "    render_frame_compare(x_test[i], visual_demo_test_df[i], visual_demo_test_fgs[i], df_predictions[i], fgs_predictions[i], y)   \n",
        "\n",
        "\n",
        "\n",
        "# From left to right:\n",
        "# Raw image   --->  deepfool - raw image ---> deepfool ---> deepfool confidence ---> fgsm - raw image ---> fgsm ---> fgsm confidence"
      ],
      "id": "tKH1K56x2490",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x216 with 7 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nDeOvT-oHMjW"
      },
      "source": [
        "## 4. Attack using DeepFool and FGSM"
      ],
      "id": "nDeOvT-oHMjW"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "abWZlSehlnXL"
      },
      "source": [
        "# raw_image_tensor: N x H x W x C\n",
        "# perturbed_tensor: N x H x W x C\n",
        "# Note: they must be of the same order\n",
        "# Note: perturbed tensor is the tensor generated by DeepFool, prediction label should be different\n",
        "\n",
        "def robustness(image_tensor, perturbed_tensor):\n",
        "\n",
        "    # get the data size\n",
        "    assert image_tensor.shape == perturbed_tensor.shape\n",
        "    N = image_tensor.shape[0]\n",
        "\n",
        "    # get the perturbation\n",
        "    r = image_tensor - perturbed_tensor\n",
        "\n",
        "    rval = 0\n",
        "    for i in range(N):\n",
        "\n",
        "        # l2 norm on r\n",
        "        norm_r = np.sqrt(np.sum(r[i, :]**2))\n",
        "\n",
        "        # l2 norm on x\n",
        "        norm_x = np.sqrt(np.sum(image_tensor[i, :]**2))\n",
        "\n",
        "        # accumulate\n",
        "        rval += norm_r / norm_x\n",
        "\n",
        "    return rval / N\n",
        "\n",
        "\n",
        "# image_tensor = np.ones((2, 2, 2, 1))\n",
        "# perturbed_tensor = np.ones((2, 2, 2, 1))\n",
        "# perturbed_tensor[:, 0, 0, :] = 0\n",
        "# print(robustness(image_tensor, perturbed_tensor))\n"
      ],
      "id": "abWZlSehlnXL",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "improving-student",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 183,
          "referenced_widgets": [
            "6a753c401cf14ab49a7534e7ba92ff03",
            "a125e069c62e4d5390aab86d4ccd4011",
            "47b46e5bd54345329b3b33feb7f59bd8",
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            "aa2e8e2e95a149869fb7235e6175ba63",
            "16f554844f974bc9986f93f59ea941b8",
            "6ba95f42c70a4fc7b87455faddfb51fb",
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            "67de9965fb1e49ad82e9592bdcbfccae",
            "8a90d9dac89d41f8ab4582df25bd9e72"
          ]
        },
        "outputId": "c1d9c551-74ba-400c-9a75-1fe356293c5b"
      },
      "source": [
        "t0 = time.time()\n",
        "# Step 6: Generate (untargeted) adversarial test examples\n",
        "attack = DeepFool(classifier=classifier,max_iter=50,batch_size=64,epsilon=0.02)\n",
        "x_train_adv_dp = attack.generate(x=x_train)\n",
        "old_x_test_adv_dp = attack.generate(x=x_test)\n",
        "print(\"DeepFool time: {} s\".format(time.time()-t0))\n",
        "\n",
        "# Step 7: Evaluate the ART classifier on adversarial test examples\n",
        "predictions = classifier.predict(old_x_test_adv_dp)\n",
        "accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\n",
        "all_rob_dp = []\n",
        "all_rob_dp.append(robustness(x_test, old_x_test_adv_dp))\n",
        "all_rob_fg = []\n",
        "\n",
        "# for over-perpurtabation\n",
        "all_rob_dp2 = []\n",
        "all_rob_dp3 = []\n",
        "all_rob_dp2.append(robustness(x_test, old_x_test_adv_dp))\n",
        "all_rob_dp3.append(robustness(x_test, old_x_test_adv_dp))\n",
        "\n",
        "# evaluation of robustness is done using deepfool\n",
        "all_rob_fg.append(robustness(x_test, old_x_test_adv_dp))\n",
        "print(\"DeepFool: Accuracy on adversarial test examples: {}%\".format(accuracy * 100))\n",
        "\n",
        "\n",
        "t0 = time.time()\n",
        "# fg_attack = FastGradientMethod(estimator=classifier, eps=0.2, targeted=False)\n",
        "attack = FastGradientMethod(estimator=classifier, eps=0.25, eps_step=1e-2, targeted=False, batch_size=64, minimal=True)\n",
        "x_train_adv_fg = attack.generate(x=x_train)\n",
        "old_x_test_adv_fg = attack.generate(x=x_test)\n",
        "print(\"FGSM time: {} s\".format(time.time()-t0))\n",
        "\n",
        "# Step 7: Evaluate the ART classifier on adversarial test examples\n",
        "predictions = classifier.predict(old_x_test_adv_fg)\n",
        "accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\n",
        "\n",
        "print(\"FGSM: Accuracy on adversarial test examples: {}%\".format(accuracy * 100))\n"
      ],
      "id": "improving-student",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "6a753c401cf14ab49a7534e7ba92ff03",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, description='DeepFool', max=938.0, style=ProgressStyle(description_wid…"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "aa2e8e2e95a149869fb7235e6175ba63",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(FloatProgress(value=0.0, description='DeepFool', max=157.0, style=ProgressStyle(description_wid…"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool time: 730.7994379997253 s\n",
            "DeepFool: Accuracy on adversarial test examples: 3.95%\n",
            "FGSM time: 26.078370332717896 s\n",
            "FGSM: Accuracy on adversarial test examples: 4.02%\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dqs8ysfFHbH3"
      },
      "source": [
        "## 5. Fine-tune & over-perpurtabed experiment"
      ],
      "id": "dqs8ysfFHbH3"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
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        },
        "id": "02ACXmex9dno",
        "outputId": "65f8ad17-2d6d-485a-adfa-e943dd96572c"
      },
      "source": [
        "\r\n",
        "# make a copy of the model\r\n",
        "import copy\r\n",
        "model_copy = copy.deepcopy(model)\r\n",
        "classifier_copy = copy.deepcopy(classifier)\r\n",
        "\r\n",
        "\r\n",
        "# Step 8: Fine-tunning with adversial examples \r\n",
        "\r\n",
        "\r\n",
        "# DeepFool alpha = 3\r\n",
        "# optimizer = optim.Adam(classifier.model.parameters(), lr=0.005)\r\n",
        "classifier = copy.deepcopy(classifier_copy)\r\n",
        "optimizer = optim.SGD(classifier.model.parameters(), lr=0.015)\r\n",
        "classifier.optimizer = optimizer\r\n",
        "for i in range(5):\r\n",
        "  print(\"DeepFool Current epoch alpha=2:\" + str(i+1))\r\n",
        "\r\n",
        "  \r\n",
        "  # over purterbed alpha=2\r\n",
        "  classifier.fit((x_train_adv_dp - x_train)*3 + x_train, y_train, batch_size=64, nb_epochs=1)\r\n",
        "\r\n",
        "  # evaluation is based on deepfool\r\n",
        "  attack = DeepFool(classifier=classifier, max_iter=50, batch_size=64, epsilon=0.02)\r\n",
        "  x_test_adv_dp = attack.generate(x=x_test)\r\n",
        "  rob = robustness(x_test, x_test_adv_dp)\r\n",
        "  all_rob_dp3.append(rob)\r\n",
        "\r\n",
        "  # accuracy on the first perturbed dataset\r\n",
        "  predictions = classifier.predict(old_x_test_adv_dp)\r\n",
        "  accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\r\n",
        "  print(\"DeepFool Accuracy on adversarial test examples alpha=3: {}%\".format(accuracy * 100))\r\n",
        "\r\n",
        "  # accuracy on the original dataset\r\n",
        "  predictions = classifier.predict(x_test)\r\n",
        "  accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\r\n",
        "  df_accuracy_on_original_test_set_alpha3.append(accuracy * 100)\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "# DeepFool alpha = 2\r\n",
        "# optimizer = optim.Adam(classifier.model.parameters(), lr=0.005)\r\n",
        "classifier = copy.deepcopy(classifier_copy)\r\n",
        "optimizer = optim.SGD(classifier.model.parameters(), lr=0.015)\r\n",
        "classifier.optimizer = optimizer\r\n",
        "for i in range(5):\r\n",
        "  print(\"DeepFool Current epoch alpha=2:\" + str(i+1))\r\n",
        "\r\n",
        "  \r\n",
        "  # over purterbed alpha=2\r\n",
        "  classifier.fit((x_train_adv_dp - x_train)*2 + x_train, y_train, batch_size=64, nb_epochs=1)\r\n",
        "\r\n",
        "  # evaluation is based on deepfool\r\n",
        "  attack = DeepFool(classifier=classifier, max_iter=50, batch_size=64, epsilon=0.02)\r\n",
        "  x_test_adv_dp = attack.generate(x=x_test)\r\n",
        "  rob = robustness(x_test, x_test_adv_dp)\r\n",
        "  all_rob_dp2.append(rob)\r\n",
        "\r\n",
        "  # accuracy on the first perturbed dataset\r\n",
        "  predictions = classifier.predict(old_x_test_adv_dp)\r\n",
        "  accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\r\n",
        "  print(\"DeepFool Accuracy on adversarial test examples alpha=2: {}%\".format(accuracy * 100))\r\n",
        "\r\n",
        "  # accuracy on the original dataset\r\n",
        "  predictions = classifier.predict(x_test)\r\n",
        "  accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\r\n",
        "  df_accuracy_on_original_test_set_alpha2.append(accuracy * 100)\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "# DeepFool alpha = 1\r\n",
        "classifier = copy.deepcopy(classifier_copy)\r\n",
        "# optimizer = optim.Adam(classifier.model.parameters(), lr=0.005)\r\n",
        "optimizer = optim.SGD(classifier.model.parameters(), lr=0.015)\r\n",
        "classifier.optimizer = optimizer\r\n",
        "for i in range(5):\r\n",
        "  print(\"DeepFool Current epoch:\" + str(i+1))\r\n",
        "  classifier.fit(x_train_adv_dp, y_train, batch_size=64, nb_epochs=1)\r\n",
        "\r\n",
        "  # evaluation is based on deepfool\r\n",
        "  attack = DeepFool(classifier=classifier, max_iter=50, batch_size=64, epsilon=0.02)\r\n",
        "  x_test_adv_dp = attack.generate(x=x_test)\r\n",
        "  rob = robustness(x_test, x_test_adv_dp)\r\n",
        "  all_rob_dp.append(rob)\r\n",
        "\r\n",
        "  # accuracy on the first perturbed dataset\r\n",
        "  predictions = classifier.predict(old_x_test_adv_dp)\r\n",
        "  accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\r\n",
        "  print(\"DeepFool Accuracy on adversarial test examples: {}%\".format(accuracy * 100))\r\n",
        "\r\n",
        "  # accuracy on the original dataset\r\n",
        "  predictions = classifier.predict(x_test)\r\n",
        "  accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\r\n",
        "  df_accuracy_on_original_test_set.append(accuracy * 100)\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "\r\n",
        "# FGSM\r\n",
        "classifier2 = copy.deepcopy(classifier_copy)\r\n",
        "# optimizer2 = optim.Adam(classifier2.model.parameters(), lr=0.005)\r\n",
        "optimizer2 = optim.SGD(classifier2.model.parameters(), lr=0.015)\r\n",
        "classifier2.optimizer = optimizer2\r\n",
        "for i in range(5):\r\n",
        "  print(\"FGSM Current epoch:\" + str(i+1))\r\n",
        "  classifier2.fit(x_train_adv_fg, y_train, batch_size=64, nb_epochs=1)\r\n",
        "\r\n",
        "  # evaluation on deepfool\r\n",
        "  attack = DeepFool(classifier=classifier2,max_iter=50,batch_size=64,epsilon=0.02)\r\n",
        "  x_test_adv_fg = attack.generate(x=x_test)\r\n",
        "  rob = robustness(x_test, x_test_adv_fg)\r\n",
        "  all_rob_fg.append(rob)\r\n",
        "\r\n",
        "  # accuracy on the first perturbed dataset\r\n",
        "  predictions = classifier2.predict(old_x_test_adv_fg)\r\n",
        "  accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\r\n",
        "  print(\"FGSM Accuracy on adversarial test examples: {}%\".format(accuracy * 100))\r\n",
        "\r\n",
        "  # accuracy on the original test dataset\r\n",
        "  predictions = classifier2.predict(x_test)\r\n",
        "  accuracy = np.sum(np.argmax(predictions, axis=1) == np.argmax(y_test, axis=1)) / len(y_test)\r\n",
        "  fg_accuracy_on_original_test_set.append(accuracy * 100)\r\n",
        "\r\n"
      ],
      "id": "02ACXmex9dno",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "DeepFool Current epoch alpha=2:1\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=3: 86.53%\n",
            "DeepFool Current epoch alpha=2:2\n"
          ],
          "name": "stdout"
        },
        {
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          "data": {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=3: 92.77%\n",
            "DeepFool Current epoch alpha=2:3\n"
          ],
          "name": "stdout"
        },
        {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=3: 95.46%\n",
            "DeepFool Current epoch alpha=2:4\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=3: 95.78%\n",
            "DeepFool Current epoch alpha=2:5\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=3: 96.2%\n",
            "DeepFool Current epoch alpha=2:1\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=2: 90.11%\n",
            "DeepFool Current epoch alpha=2:2\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
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        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=2: 94.85%\n",
            "DeepFool Current epoch alpha=2:3\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=2: 96.11%\n",
            "DeepFool Current epoch alpha=2:4\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=2: 96.56%\n",
            "DeepFool Current epoch alpha=2:5\n"
          ],
          "name": "stdout"
        },
        {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples alpha=2: 96.76%\n",
            "DeepFool Current epoch:1\n"
          ],
          "name": "stdout"
        },
        {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples: 91.91%\n",
            "DeepFool Current epoch:2\n"
          ],
          "name": "stdout"
        },
        {
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        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples: 94.69999999999999%\n",
            "DeepFool Current epoch:3\n"
          ],
          "name": "stdout"
        },
        {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples: 96.21%\n",
            "DeepFool Current epoch:4\n"
          ],
          "name": "stdout"
        },
        {
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        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples: 96.6%\n",
            "DeepFool Current epoch:5\n"
          ],
          "name": "stdout"
        },
        {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "DeepFool Accuracy on adversarial test examples: 96.53%\n",
            "FGSM Current epoch:1\n"
          ],
          "name": "stdout"
        },
        {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "FGSM Accuracy on adversarial test examples: 93.8%\n",
            "FGSM Current epoch:2\n"
          ],
          "name": "stdout"
        },
        {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "FGSM Accuracy on adversarial test examples: 95.6%\n",
            "FGSM Current epoch:3\n"
          ],
          "name": "stdout"
        },
        {
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        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "FGSM Accuracy on adversarial test examples: 96.35000000000001%\n",
            "FGSM Current epoch:4\n"
          ],
          "name": "stdout"
        },
        {
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        {
          "output_type": "stream",
          "text": [
            "\n",
            "FGSM Accuracy on adversarial test examples: 96.67%\n",
            "FGSM Current epoch:5\n"
          ],
          "name": "stdout"
        },
        {
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        {
          "output_type": "stream",
          "text": [
            "\n",
            "FGSM Accuracy on adversarial test examples: 97.04%\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6bfPgCKUHsWy"
      },
      "source": [
        "### 5.1 DeepFool v.s. FGSM (avg robustness, fine-tuned model)"
      ],
      "id": "6bfPgCKUHsWy"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "english-large",
        "outputId": "0916923c-3979-43b8-c18a-c3124f739566"
      },
      "source": [
        "plt.plot(np.arange(6), all_rob_dp, label=\"DeepFool\")\n",
        "plt.plot(np.arange(6), all_rob_fg, label=\"FGSM\")\n",
        "plt.xlabel('Number of extra epochs')\n",
        "plt.ylabel('Avg robustness')\n",
        "plt.legend()"
      ],
      "id": "english-large",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f9b2d1ccda0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LcLJ211LH2bv"
      },
      "source": [
        "### 5.2 DeepFool v.s. FGSM (accuracy on the original test dataset, fine-tuned model)"
      ],
      "id": "LcLJ211LH2bv"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "pZXdYLzAWXrE",
        "outputId": "70443c0e-55a9-484b-8f8e-961c210abcc7"
      },
      "source": [
        "plt.plot(np.arange(6), df_accuracy_on_original_test_set, label=\"Fine-tuned with DeepFool\")\n",
        "plt.plot(np.arange(6), fg_accuracy_on_original_test_set, label=\"Fine-tuned with FGSM\")\n",
        "plt.xlabel('Number of extra epochs')\n",
        "plt.ylabel('Test accuracy on the original test dataset')\n",
        "plt.legend()"
      ],
      "id": "pZXdYLzAWXrE",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f9b2d87ba58>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Dzlx4LKICcn"
      },
      "source": [
        "### 5.3 DeepFool: over-perturbed samples and robustness"
      ],
      "id": "6Dzlx4LKICcn"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "lkTwX-CnBjMq",
        "outputId": "c2a84da6-b7b4-4d01-d6ba-992bb12dff2d"
      },
      "source": [
        "plt.plot(np.arange(6), all_rob_dp, label=\"alpha=1\")\n",
        "plt.plot(np.arange(6), all_rob_dp2, label=\"alpha=2\")\n",
        "plt.plot(np.arange(6), all_rob_dp3, label=\"alpha=3\")\n",
        "plt.xlabel('Number of extra epochs')\n",
        "plt.ylabel('Robustness: over-purtabed experiment')\n",
        "plt.legend()"
      ],
      "id": "lkTwX-CnBjMq",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f9b2d7f9390>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xIxZHKK9IJw3"
      },
      "source": [
        "### 5.4 DeepFool: over-purtabed samples and accuracy on the original test dataset"
      ],
      "id": "xIxZHKK9IJw3"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "WlaTidlUByZe",
        "outputId": "2f6ff604-ec95-4390-ded9-fc06be1d7ba8"
      },
      "source": [
        "plt.plot(np.arange(6), df_accuracy_on_original_test_set, label=\"alpha=1\")\n",
        "plt.plot(np.arange(6), df_accuracy_on_original_test_set_alpha2, label=\"alpha=2\")\n",
        "plt.plot(np.arange(6), df_accuracy_on_original_test_set_alpha3, label=\"alpha=3\")\n",
        "plt.xlabel('Number of extra epochs')\n",
        "plt.ylabel('Test accuracy on the original test dataset')\n",
        "plt.legend()"
      ],
      "id": "WlaTidlUByZe",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f9b2d7e4e48>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}