GNN/6_GNN_Explanation.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F1op-CbyLuN4",
        "outputId": "ad391923-6515-4737-dec5-abb4b76778ea"
      },
      "source": [
        "# Install required packages.\n",
        "import os\n",
        "import torch\n",
        "os.environ['TORCH'] = torch.__version__\n",
        "print(torch.__version__)\n",
        "\n",
        "!pip install -q torch-scatter -f https://data.pyg.org/whl/torch-${TORCH}.html\n",
        "!pip install -q torch-sparse -f https://data.pyg.org/whl/torch-${TORCH}.html\n",
        "!pip install -q git+https://github.com/pyg-team/pytorch_geometric.git\n",
        "!pip install -q captum\n",
        "\n",
        "# Helper function for visualization.\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.11.0+cu113\n",
            "\u001b[K     |████████████████████████████████| 7.9 MB 7.8 MB/s \n",
            "\u001b[K     |████████████████████████████████| 3.5 MB 9.8 MB/s \n",
            "\u001b[?25h  Building wheel for torch-geometric (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "\u001b[K     |████████████████████████████████| 1.4 MB 10.2 MB/s \n",
            "\u001b[?25h"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nMTL0kk0seBw"
      },
      "source": [
        "# Explaining GNN Model Predictions using Captum\n",
        "\n",
        "In this tutorial we demonstrate how to apply feature attribution methods to graphs. Specifically, we try to find the most important edges for each instance prediction.  \n",
        "\n",
        "We use the Mutagenicity dataset from [TUDatasets](https://chrsmrrs.github.io/datasets/). This dataset consists of 4337 molecule graphs where the task is to predict the molecule mutagenicity."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mJtgD2A1uJAa"
      },
      "source": [
        "## Loading the dataset\n",
        "\n",
        "We load the dataset and use 10% of the data as the test split."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SE2iREv4q2dL",
        "outputId": "25b13669-9aa3-44d1-cd9a-62d357b466ee"
      },
      "source": [
        "from torch_geometric.loader import DataLoader\n",
        "from torch_geometric.datasets import TUDataset\n",
        "\n",
        "path = '.'\n",
        "dataset = TUDataset(path, name='Mutagenicity').shuffle()\n",
        "test_dataset = dataset[:len(dataset) // 10]\n",
        "train_dataset = dataset[len(dataset) // 10:]\n",
        "test_loader = DataLoader(test_dataset, batch_size=128)\n",
        "train_loader = DataLoader(train_dataset, batch_size=128)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Downloading https://www.chrsmrrs.com/graphkerneldatasets/Mutagenicity.zip\n",
            "Extracting ./Mutagenicity/Mutagenicity.zip\n",
            "Processing...\n",
            "Done!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g35SSQ3oukNM"
      },
      "source": [
        "## Visualizing the data\n",
        "\n",
        "We define some utility functions for visualizing the molecules and draw a random molecule."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9Hh3YNASuYxm"
      },
      "source": [
        "import networkx as nx\n",
        "import numpy as np\n",
        "\n",
        "from torch_geometric.utils import to_networkx\n",
        "\n",
        "\n",
        "def draw_molecule(g, edge_mask=None, draw_edge_labels=False):\n",
        "    g = g.copy().to_undirected()\n",
        "    node_labels = {}\n",
        "    for u, data in g.nodes(data=True):\n",
        "        node_labels[u] = data['name']\n",
        "    pos = nx.planar_layout(g)\n",
        "    pos = nx.spring_layout(g, pos=pos)\n",
        "    if edge_mask is None:\n",
        "        edge_color = 'black'\n",
        "        widths = None\n",
        "    else:\n",
        "        edge_color = [edge_mask[(u, v)] for u, v in g.edges()]\n",
        "        widths = [x * 10 for x in edge_color]\n",
        "    nx.draw(g, pos=pos, labels=node_labels, width=widths,\n",
        "            edge_color=edge_color, edge_cmap=plt.cm.Blues,\n",
        "            node_color='azure')\n",
        "\n",
        "    if draw_edge_labels and edge_mask is not None:\n",
        "        edge_labels = {k: ('%.2f' % v) for k, v in edge_mask.items()}\n",
        "        nx.draw_networkx_edge_labels(g, pos, edge_labels=edge_labels,\n",
        "                                    font_color='red')\n",
        "    plt.show()\n",
        "\n",
        "\n",
        "def to_molecule(data):\n",
        "    ATOM_MAP = ['C', 'O', 'Cl', 'H', 'N', 'F',\n",
        "                'Br', 'S', 'P', 'I', 'Na', 'K', 'Li', 'Ca']\n",
        "    g = to_networkx(data, node_attrs=['x'])\n",
        "    for u, data in g.nodes(data=True):\n",
        "        data['name'] = ATOM_MAP[data['x'].index(1.0)]\n",
        "        del data['x']\n",
        "    return g\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cJ3JuTH1vV1V"
      },
      "source": [
        "## Sample visualization\n",
        "\n",
        "We sample a single molecule from train_dataset and visualize it"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "id": "4Z2uE7zVuhXU",
        "outputId": "14795a19-032e-4836-b07d-b5fe6b594e7f"
      },
      "source": [
        "import random\n",
        "\n",
        "data = random.choice([t for t in train_dataset])\n",
        "mol = to_molecule(data)\n",
        "plt.figure(figsize=(10, 5))\n",
        "draw_molecule(mol)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6kZo9g1hwCGG"
      },
      "source": [
        "## Training the model\n",
        "\n",
        "In the next section, we train a GNN model with 5 convolution layers. We use GraphConv which supports `edge_weight` as a parameter. Many convolution layers in Pytorch Geometric supoort this argument."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GBVIOfMCCHAb"
      },
      "source": [
        "### Define the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iI1qpFUhrA2p"
      },
      "source": [
        "import torch\n",
        "from torch.nn import Linear\n",
        "import torch.nn.functional as F\n",
        "\n",
        "from torch_geometric.nn import GraphConv, global_add_pool\n",
        "\n",
        "class Net(torch.nn.Module):\n",
        "    def __init__(self, dim):\n",
        "        super(Net, self).__init__()\n",
        "\n",
        "        num_features = dataset.num_features\n",
        "        self.dim = dim\n",
        "\n",
        "        self.conv1 = GraphConv(num_features, dim)\n",
        "        self.conv2 = GraphConv(dim, dim)\n",
        "        self.conv3 = GraphConv(dim, dim)\n",
        "        self.conv4 = GraphConv(dim, dim)\n",
        "        self.conv5 = GraphConv(dim, dim)\n",
        "\n",
        "        self.lin1 = Linear(dim, dim)\n",
        "        self.lin2 = Linear(dim, dataset.num_classes)\n",
        "\n",
        "    def forward(self, x, edge_index, batch, edge_weight=None):\n",
        "        x = self.conv1(x, edge_index, edge_weight).relu()\n",
        "        x = self.conv2(x, edge_index, edge_weight).relu()\n",
        "        x = self.conv3(x, edge_index, edge_weight).relu()\n",
        "        x = self.conv4(x, edge_index, edge_weight).relu()\n",
        "        x = self.conv5(x, edge_index, edge_weight).relu()\n",
        "        x = global_add_pool(x, batch)\n",
        "        x = self.lin1(x).relu()\n",
        "        x = F.dropout(x, p=0.5, training=self.training)\n",
        "        x = self.lin2(x)\n",
        "        return F.log_softmax(x, dim=-1)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L3WOZ40OCKO5"
      },
      "source": [
        "### Define train and test functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ExNsODp3rKjN"
      },
      "source": [
        "def train(epoch):\n",
        "    model.train()\n",
        "\n",
        "    if epoch == 51:\n",
        "        for param_group in optimizer.param_groups:\n",
        "            param_group['lr'] = 0.5 * param_group['lr']\n",
        "\n",
        "    loss_all = 0\n",
        "    for data in train_loader:\n",
        "        data = data.to(device)\n",
        "        optimizer.zero_grad()\n",
        "        output = model(data.x, data.edge_index, data.batch)\n",
        "        loss = F.nll_loss(output, data.y)\n",
        "        loss.backward()\n",
        "        loss_all += loss.item() * data.num_graphs\n",
        "        optimizer.step()\n",
        "    return loss_all / len(train_dataset)\n",
        "\n",
        "\n",
        "def test(loader):\n",
        "    model.eval()\n",
        "\n",
        "    correct = 0\n",
        "    for data in loader:\n",
        "        data = data.to(device)\n",
        "        output = model(data.x, data.edge_index, data.batch)\n",
        "        pred = output.max(dim=1)[1]\n",
        "        correct += pred.eq(data.y).sum().item()\n",
        "    return correct / len(loader.dataset)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rsv9CQ6hCNMI"
      },
      "source": [
        "### Train the model for 100 epochs\n",
        "\n",
        "The accuracy should be around 80% in the end"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4imSoTlMrQdN",
        "outputId": "410f11c4-8fac-4086-80a1-46bd4c0a8709"
      },
      "source": [
        "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
        "model = Net(dim=32).to(device)\n",
        "optimizer = torch.optim.Adam(model.parameters(), lr=0.001)\n",
        "\n",
        "for epoch in range(1, 101):\n",
        "    loss = train(epoch)\n",
        "    train_acc = test(train_loader)\n",
        "    test_acc = test(test_loader)\n",
        "    print(f'Epoch: {epoch:03d}, Loss: {loss:.4f}, '\n",
        "          f'Train Acc: {train_acc:.4f}, Test Acc: {test_acc:.4f}')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch: 001, Loss: 0.7441, Train Acc: 0.5904, Test Acc: 0.5473\n",
            "Epoch: 002, Loss: 0.6459, Train Acc: 0.6550, Test Acc: 0.6328\n",
            "Epoch: 003, Loss: 0.6112, Train Acc: 0.7018, Test Acc: 0.6975\n",
            "Epoch: 004, Loss: 0.5862, Train Acc: 0.7152, Test Acc: 0.7136\n",
            "Epoch: 005, Loss: 0.5750, Train Acc: 0.7318, Test Acc: 0.7206\n",
            "Epoch: 006, Loss: 0.5557, Train Acc: 0.7392, Test Acc: 0.7390\n",
            "Epoch: 007, Loss: 0.5473, Train Acc: 0.7464, Test Acc: 0.7367\n",
            "Epoch: 008, Loss: 0.5433, Train Acc: 0.7403, Test Acc: 0.7321\n",
            "Epoch: 009, Loss: 0.5469, Train Acc: 0.7551, Test Acc: 0.7483\n",
            "Epoch: 010, Loss: 0.5243, Train Acc: 0.7779, Test Acc: 0.7483\n",
            "Epoch: 011, Loss: 0.5178, Train Acc: 0.7772, Test Acc: 0.7529\n",
            "Epoch: 012, Loss: 0.4972, Train Acc: 0.7787, Test Acc: 0.7575\n",
            "Epoch: 013, Loss: 0.4926, Train Acc: 0.7797, Test Acc: 0.7529\n",
            "Epoch: 014, Loss: 0.4908, Train Acc: 0.7900, Test Acc: 0.7852\n",
            "Epoch: 015, Loss: 0.4843, Train Acc: 0.7971, Test Acc: 0.7552\n",
            "Epoch: 016, Loss: 0.4906, Train Acc: 0.7825, Test Acc: 0.7483\n",
            "Epoch: 017, Loss: 0.4744, Train Acc: 0.8048, Test Acc: 0.7737\n",
            "Epoch: 018, Loss: 0.4581, Train Acc: 0.8069, Test Acc: 0.7691\n",
            "Epoch: 019, Loss: 0.4522, Train Acc: 0.8110, Test Acc: 0.7737\n",
            "Epoch: 020, Loss: 0.4546, Train Acc: 0.8071, Test Acc: 0.7968\n",
            "Epoch: 021, Loss: 0.4520, Train Acc: 0.8110, Test Acc: 0.7598\n",
            "Epoch: 022, Loss: 0.4441, Train Acc: 0.8148, Test Acc: 0.7829\n",
            "Epoch: 023, Loss: 0.4572, Train Acc: 0.8015, Test Acc: 0.7783\n",
            "Epoch: 024, Loss: 0.4407, Train Acc: 0.8215, Test Acc: 0.7783\n",
            "Epoch: 025, Loss: 0.4382, Train Acc: 0.8153, Test Acc: 0.7806\n",
            "Epoch: 026, Loss: 0.4296, Train Acc: 0.8240, Test Acc: 0.7829\n",
            "Epoch: 027, Loss: 0.4234, Train Acc: 0.8158, Test Acc: 0.7829\n",
            "Epoch: 028, Loss: 0.4233, Train Acc: 0.8163, Test Acc: 0.7829\n",
            "Epoch: 029, Loss: 0.4221, Train Acc: 0.8112, Test Acc: 0.7829\n",
            "Epoch: 030, Loss: 0.4138, Train Acc: 0.8227, Test Acc: 0.7829\n",
            "Epoch: 031, Loss: 0.4158, Train Acc: 0.8199, Test Acc: 0.7737\n",
            "Epoch: 032, Loss: 0.4070, Train Acc: 0.8289, Test Acc: 0.7852\n",
            "Epoch: 033, Loss: 0.4043, Train Acc: 0.8202, Test Acc: 0.7852\n",
            "Epoch: 034, Loss: 0.4047, Train Acc: 0.8263, Test Acc: 0.7945\n",
            "Epoch: 035, Loss: 0.4024, Train Acc: 0.8181, Test Acc: 0.7875\n",
            "Epoch: 036, Loss: 0.4050, Train Acc: 0.8376, Test Acc: 0.7945\n",
            "Epoch: 037, Loss: 0.3865, Train Acc: 0.8363, Test Acc: 0.7945\n",
            "Epoch: 038, Loss: 0.3889, Train Acc: 0.8274, Test Acc: 0.7945\n",
            "Epoch: 039, Loss: 0.3964, Train Acc: 0.8176, Test Acc: 0.7991\n",
            "Epoch: 040, Loss: 0.3856, Train Acc: 0.8407, Test Acc: 0.8199\n",
            "Epoch: 041, Loss: 0.3877, Train Acc: 0.8391, Test Acc: 0.8037\n",
            "Epoch: 042, Loss: 0.3901, Train Acc: 0.8448, Test Acc: 0.7991\n",
            "Epoch: 043, Loss: 0.3802, Train Acc: 0.8448, Test Acc: 0.7991\n",
            "Epoch: 044, Loss: 0.3781, Train Acc: 0.8363, Test Acc: 0.8037\n",
            "Epoch: 045, Loss: 0.3817, Train Acc: 0.8543, Test Acc: 0.8176\n",
            "Epoch: 046, Loss: 0.3673, Train Acc: 0.8491, Test Acc: 0.8152\n",
            "Epoch: 047, Loss: 0.3666, Train Acc: 0.8409, Test Acc: 0.8152\n",
            "Epoch: 048, Loss: 0.3729, Train Acc: 0.8430, Test Acc: 0.8060\n",
            "Epoch: 049, Loss: 0.3651, Train Acc: 0.8484, Test Acc: 0.8176\n",
            "Epoch: 050, Loss: 0.3740, Train Acc: 0.8522, Test Acc: 0.8129\n",
            "Epoch: 051, Loss: 0.3615, Train Acc: 0.8578, Test Acc: 0.8014\n",
            "Epoch: 052, Loss: 0.3554, Train Acc: 0.8632, Test Acc: 0.8060\n",
            "Epoch: 053, Loss: 0.3490, Train Acc: 0.8607, Test Acc: 0.7921\n",
            "Epoch: 054, Loss: 0.3427, Train Acc: 0.8642, Test Acc: 0.8083\n",
            "Epoch: 055, Loss: 0.3324, Train Acc: 0.8635, Test Acc: 0.7898\n",
            "Epoch: 056, Loss: 0.3350, Train Acc: 0.8681, Test Acc: 0.8106\n",
            "Epoch: 057, Loss: 0.3296, Train Acc: 0.8704, Test Acc: 0.8152\n",
            "Epoch: 058, Loss: 0.3381, Train Acc: 0.8642, Test Acc: 0.8245\n",
            "Epoch: 059, Loss: 0.3298, Train Acc: 0.8683, Test Acc: 0.8152\n",
            "Epoch: 060, Loss: 0.3284, Train Acc: 0.8712, Test Acc: 0.8152\n",
            "Epoch: 061, Loss: 0.3288, Train Acc: 0.8660, Test Acc: 0.8014\n",
            "Epoch: 062, Loss: 0.3295, Train Acc: 0.8701, Test Acc: 0.8014\n",
            "Epoch: 063, Loss: 0.3274, Train Acc: 0.8637, Test Acc: 0.7921\n",
            "Epoch: 064, Loss: 0.3284, Train Acc: 0.8681, Test Acc: 0.8014\n",
            "Epoch: 065, Loss: 0.3278, Train Acc: 0.8632, Test Acc: 0.7945\n",
            "Epoch: 066, Loss: 0.3222, Train Acc: 0.8645, Test Acc: 0.7968\n",
            "Epoch: 067, Loss: 0.3249, Train Acc: 0.8730, Test Acc: 0.7991\n",
            "Epoch: 068, Loss: 0.3107, Train Acc: 0.8717, Test Acc: 0.8014\n",
            "Epoch: 069, Loss: 0.3219, Train Acc: 0.8760, Test Acc: 0.7968\n",
            "Epoch: 070, Loss: 0.3127, Train Acc: 0.8763, Test Acc: 0.8060\n",
            "Epoch: 071, Loss: 0.3111, Train Acc: 0.8799, Test Acc: 0.8060\n",
            "Epoch: 072, Loss: 0.3119, Train Acc: 0.8599, Test Acc: 0.8060\n",
            "Epoch: 073, Loss: 0.3134, Train Acc: 0.8696, Test Acc: 0.7921\n",
            "Epoch: 074, Loss: 0.3067, Train Acc: 0.8770, Test Acc: 0.7991\n",
            "Epoch: 075, Loss: 0.3108, Train Acc: 0.8768, Test Acc: 0.7968\n",
            "Epoch: 076, Loss: 0.3090, Train Acc: 0.8809, Test Acc: 0.7991\n",
            "Epoch: 077, Loss: 0.3002, Train Acc: 0.8791, Test Acc: 0.8014\n",
            "Epoch: 078, Loss: 0.3116, Train Acc: 0.8699, Test Acc: 0.7875\n",
            "Epoch: 079, Loss: 0.3068, Train Acc: 0.8753, Test Acc: 0.7921\n",
            "Epoch: 080, Loss: 0.3019, Train Acc: 0.8760, Test Acc: 0.7991\n",
            "Epoch: 081, Loss: 0.3026, Train Acc: 0.8691, Test Acc: 0.7829\n",
            "Epoch: 082, Loss: 0.2940, Train Acc: 0.8768, Test Acc: 0.7968\n",
            "Epoch: 083, Loss: 0.2946, Train Acc: 0.8783, Test Acc: 0.8152\n",
            "Epoch: 084, Loss: 0.2936, Train Acc: 0.8827, Test Acc: 0.8060\n",
            "Epoch: 085, Loss: 0.2945, Train Acc: 0.8747, Test Acc: 0.8014\n",
            "Epoch: 086, Loss: 0.2948, Train Acc: 0.8735, Test Acc: 0.7875\n",
            "Epoch: 087, Loss: 0.2940, Train Acc: 0.8801, Test Acc: 0.8060\n",
            "Epoch: 088, Loss: 0.2905, Train Acc: 0.8842, Test Acc: 0.8060\n",
            "Epoch: 089, Loss: 0.3051, Train Acc: 0.8614, Test Acc: 0.8222\n",
            "Epoch: 090, Loss: 0.3221, Train Acc: 0.8699, Test Acc: 0.7968\n",
            "Epoch: 091, Loss: 0.2995, Train Acc: 0.8809, Test Acc: 0.8037\n",
            "Epoch: 092, Loss: 0.2845, Train Acc: 0.8886, Test Acc: 0.8176\n",
            "Epoch: 093, Loss: 0.2907, Train Acc: 0.8899, Test Acc: 0.8152\n",
            "Epoch: 094, Loss: 0.2846, Train Acc: 0.8837, Test Acc: 0.7991\n",
            "Epoch: 095, Loss: 0.2774, Train Acc: 0.8878, Test Acc: 0.8060\n",
            "Epoch: 096, Loss: 0.2893, Train Acc: 0.8824, Test Acc: 0.7921\n",
            "Epoch: 097, Loss: 0.2769, Train Acc: 0.8870, Test Acc: 0.7991\n",
            "Epoch: 098, Loss: 0.2789, Train Acc: 0.8919, Test Acc: 0.8060\n",
            "Epoch: 099, Loss: 0.2794, Train Acc: 0.8901, Test Acc: 0.8037\n",
            "Epoch: 100, Loss: 0.2770, Train Acc: 0.8852, Test Acc: 0.7945\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PzX9xwFxCTff"
      },
      "source": [
        "## Explaining the predictions\n",
        "\n",
        "Now we look at two popular attribution methods. First, we calculate the gradient of the output with respect to the edge weights $w_{e_i}$. Edge weights are initially one for all edges.\n",
        "For the saliency method, we use the absolute value of the gradient as the attribution value for each edge:\n",
        "\n",
        "$$\n",
        "Attribution_{e_i} = |\\frac{\\partial F(x)}{\\partial w_{e_i}}|\n",
        "$$\n",
        "\n",
        "Where $x$ is the input and $F(x)$ is the output of the GNN model on input $x$.\n",
        "\n",
        "For Integrated Gradients method, we interpolate between the current input and a baseline input where the weight of all edges is zero and accumulate the gradient values for each edge:\n",
        "\n",
        "$$\n",
        "Attribution_{e_i} = \\int_{\\alpha =0}^1 \\frac{\\partial F(x_{\\alpha)}}{\\partial w_{e_i}} d\\alpha\n",
        "$$\n",
        "\n",
        "Where $x_{\\alpha}$ is the same as the original input graph but the weight of all edges is set to $\\alpha$. Integrated Gradients complete formulation is more complicated but since our initial edge weights are equal to one and the baseline is zero, it can be simplified to the formulation above. You can read more about this method [here](https://arxiv.org/abs/1703.01365). Of course, this can not be calculated directly and is approximated by a discrete sum.\n",
        "\n",
        "We use the [captum](https://captum.ai/) library for calculating the attribution values. We define the `model_forward` function which calculates the `batch` argument assuming that we are only explaining a single graph at a time.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wz6B1NgorzAX"
      },
      "source": [
        "from captum.attr import Saliency, IntegratedGradients\n",
        "\n",
        "def model_forward(edge_mask, data):\n",
        "    batch = torch.zeros(data.x.shape[0], dtype=int).to(device)\n",
        "    out = model(data.x, data.edge_index, batch, edge_mask)\n",
        "    return out\n",
        "\n",
        "\n",
        "def explain(method, data, target=0):\n",
        "    input_mask = torch.ones(data.edge_index.shape[1]).requires_grad_(True).to(device)\n",
        "    if method == 'ig':\n",
        "        ig = IntegratedGradients(model_forward)\n",
        "        mask = ig.attribute(input_mask, target=target,\n",
        "                            additional_forward_args=(data,),\n",
        "                            internal_batch_size=data.edge_index.shape[1])\n",
        "    elif method == 'saliency':\n",
        "        saliency = Saliency(model_forward)\n",
        "        mask = saliency.attribute(input_mask, target=target,\n",
        "                                  additional_forward_args=(data,))\n",
        "    else:\n",
        "        raise Exception('Unknown explanation method')\n",
        "\n",
        "    edge_mask = np.abs(mask.cpu().detach().numpy())\n",
        "    if edge_mask.max() > 0:  # avoid division by zero\n",
        "        edge_mask = edge_mask / edge_mask.max()\n",
        "    return edge_mask"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0FPGLRtSFacR"
      },
      "source": [
        "Finally we take a random sample from the test dataset and run the explanation methods. For a simpler visualization, we make the graph undirected and merge the explanations of each edge in both directions.\n",
        "\n",
        "It is known that NO2 substructure makes the molecules mutagenic in many cases and you can verify this by the model explanations.\n",
        "\n",
        "Mutagenic molecules have label 0 in this dataset and we only sample from those molecules but you can change the code and see the explanations for the other class as well.\n",
        "\n",
        "In this visualization, edge colors and thickness represent the importance. You can also see the numeric value by passing `draw_edge_labels` to `draw_molecule` function.\n",
        "\n",
        "As you can see Integrated Gradients tend to create more accurate explanations."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 621
        },
        "id": "Z1mJVbKorh5y",
        "outputId": "771555b4-e2b0-4701-984c-88537723f10c"
      },
      "source": [
        "import random\n",
        "from collections import defaultdict\n",
        "\n",
        "def aggregate_edge_directions(edge_mask, data):\n",
        "    edge_mask_dict = defaultdict(float)\n",
        "    for val, u, v in list(zip(edge_mask, *data.edge_index)):\n",
        "        u, v = u.item(), v.item()\n",
        "        if u > v:\n",
        "            u, v = v, u\n",
        "        edge_mask_dict[(u, v)] += val\n",
        "    return edge_mask_dict\n",
        "\n",
        "\n",
        "data = random.choice([t for t in test_dataset if not t.y.item()])\n",
        "mol = to_molecule(data)\n",
        "\n",
        "for title, method in [('Integrated Gradients', 'ig'), ('Saliency', 'saliency')]:\n",
        "    edge_mask = explain(method, data, target=0)\n",
        "    edge_mask_dict = aggregate_edge_directions(edge_mask, data)\n",
        "    plt.figure(figsize=(10, 5))\n",
        "    plt.title(title)\n",
        "    draw_molecule(mol, edge_mask_dict)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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I5Sql7k3SHB5GPOQSDHgGyKfDsnYsNvDM6x/gt3uODeVpEVGFSKl7k2HWQDnr3jDDQ27EpEQaPgAKrFUX6eb0RHSrvODbBzvxwlsfYn9rHwI+BXNOaYTfy8l/RG6nRh8mgB5DABIgKxIkWHeZXpT3blNOiHg4jZPcggFPBokdViT657tHe/BhVwgHj4ew+3/a0B3uD4e6wwa27zmKT09tLs8JE5HtyABkA/Aow7fkPBcSMzzkQgx4BhEr1AUAAQnYsOtAxmN/+eej+OTHRiHg438rEVlMIZLmzNgB6/CQG3EOTx4mjarB9Al1Gb/fp5l47u2jw3hGRGR3pgBkm/W0SXN4uAEguYTN3ob2d/W07ENWL7xzDO192jCdDRHZnRD223KGGR5yIwY8eTqxvhozJo7I+P2wbmLbW0eG8YyIyK5iE4Il2w1p9f+dc3jILRjwFODqac3I1n+9+NcWtPREhu+EiMiW7DicBQyctMyIh9zBhm/F4pkAQgB6YZV6741+Xaqh6rF1VfjER+ozfl83Bba++WGJ/jUiqlSmABSbZXcAK+MUy/Iww0Nu4aiAJ7aXTResGjpa9Dkt+nUXit8vK+bTU5ugyJk7spfea8WRrnT7JxORW5imQJZuoqxi83hYh4fcwjEBTxi5BTOxoKjYUGR00IeLP9qQ8fuGAH72J2Z5iNzMFLBtwBNLPHGVFrmFIwKeMKwhq3yEUHzQs3DKGHiy9Gav/K0NB9vzPTMicgprDo89I55YhodzeMgtKj7g0ZE+2Nm0YQNmTpmCZr8fpzQ14bavfhXt7e1Jx4RQ3PBWfY0Xl3ysMeP3hQCe+dPhIv4FIqpkhp2HtKK9P+fwkFtUfMCTLkuzdvVq3HfHHVj58MM40NGBF197De/v34+Fl1yCSCQy6Ovz8akzxsCnZv5vfG1fO/a19Rb5rxBRJbLzkBYzPOQ2FR3wmEjN0HR2duLBFSvw0Nq1mHPZZfB4PDhx4kSs37IFB/btw082bkw6Xkdxq7fqqj2Ye+qorMc880dmeYjcxq41eGK4SovcpqIDnnSVbv7r1VcRCoUwf9GipOcDgQAuufxy7HzxxaTnhRCIFHmHM+/00fB7Mu+S/vsPOvHesZ6i/g0iqiwCyFqvq9z6V2lxpRa5Q0UHPOkyM60tLWhobISqpm7g2dTcjNaWlqTnJEnC7v3tWLdrP17Z21bQthABn4p5p4/OeswWZnmIXMU07TucBbDaMrlPRW/rne492tDYiNaWFui6nhL0fHj4MBoaUycZK4qEl/e24eW9bQCAE0ZWYUpzLc4cG8SpYwLwZpmjEzP3tFHYvucousJG2u+/dbgLf/6wC6c3BQf/wYio4lnzd+wZ8ZgAfNUKGqoUyLKEPlgfBl5U+F0wURYVHfCk60rOnTEDPp8Pzz37LBYuXhx/vru7Gzu2b8e9DzyQ8preSHKQcuB4CAeOh/CrvxyFR5YweUwNzhxbiynNQZxYX522E6v2KLjyjDHY9PtDKd8LVqmYcXI9Og2BbiEgSxJksHMhcjJTCNttK6HDWqihA/BWq/BF+zIj+gjD+lDwocI/HIjSqOhrOl1fUldXhztWrMDym29GsLYWF82ejUMHD+L2pUsxdvx4XHPddUnHR3QTB49nrpWjmQJvH+7G24e7AQC1VSrOaA7izOYgpowNoqHGGz/20o+NwvN/OYrjfdZU6hMb/Jg7ZQzOGFcLAcCryvGOBWDnQuRkpgAUGwU8A+uVZZpMrUcfVbD6JiKnkEQFz1YzYW0Xkc6Pf/hDPPHII/j73r0I1tbiigULcN+DD2LEyJFJx2m6iW/+9M/oDhdWkWdsnS+e/Tm9KYD/2NuG9b/7AJ84pQFXnTsOHlnOqfAYOxciZ+kOmfB5JHiU8g9rFVKcFWC/RM5S0QEPUNzeWKYp8Mb7HXhy599Lci6KBEwaVYMJDX5ceXYzfGrmlVvpsHMhco7OPgMBX243PEMptp3OQJs2bMDjq1fHbwrnLVyIe7/zHYwYMSLpuBowA03OYKOEa2GKCRA008QLb5VuvytDACFDpAQ7UyZOxKTRo9HT09/t/Pipp3DFrFlJry+28jMR2Ycp7LEsvdzFWYnsouIDHhVWZqQQsm7i0lMacf6JIxDw5ZeNyWTulDHwpJmpaBgGvv+97w36enYuRJXPLkUH7VCclcguKj7gAawsT75BTxWAxioPZp/SiFtnnYT/u3gK/s8Vk3HNWc04rSkApYA0dLBKxRnjatOmsL/+jW9g7apVKft5DcTOhajyCZtsKVGK4qyZ2iGqNI4ZmvUBUNC/5DKTTKuiZFnCyY1+nNzox8IzmxDSDOw50o03D3XhrcNd+CCHXc9nnFyftjYQAJw1fTounDULj61ahW/df3/WdiIoPGtFROVn2KQGTyHFWd/4/e9zaoeo0jgm4AGsH0aF9eaMRP8UsOr15Fv3psqj4KzxdThrfB0AoK0ngrcOW8HPW4e60BFKDavGjazOWqTwrpUrcdkFF+Art9yS9d9m50JU2exSg6dUxVkremULUZQN3pKlJ8PKkPhhrTDwR78u5oetr/HiokkN+NrHJ+KJxWfgu/MnY8k5YzGlORhfdur3Zp8HdNoZZ+CT8+bhkQcfzHrc8S7urk5UyeyyS/pgxVkTxYqzXjR7dk7tEFUaR2V4hossSTix3o8T6/2Yf8YYRAwTfz3SDdk3+H/nnf/8z7jo7LNx07JlGY/5993v4PzJ4/DRE8eU8rSJaAglZpZ1WYIsWSsvy1lRvRTFWTO1Q1RpeB2XgFeRMWVsLU5u8A967EcmTcLCa67Bk48+mvb7fX0R/PHP+zF/6TocPtZR6lMlohKL1bnpgjWHUAMgFAmGLCEcfb6YemHF8GZ4/pbly3HPAw/gnttvx4TaWsw57zyMmzABv/jtb+HzpRb7yNQOUSWp+MKDdpKp8vOUiROx9qmnMGvOHADAB++/j3M++lFMP/98/GrnzqRjQ2EN58y9B63Hu3HmKePwm6duRV2wesjPnYjyl28F43IUFy022FJhTQ0gqnQMeEqsmM7FMExsf+lNfPEbT8Wf+8T0j2LbY0tR5fOU5PyIqDQqZbuGTJWWc8VKy+QUHNIqsWI6snBEw9r1v0l67uX/fg9fuPtHMAyu3SKyCx3pg51nNm/GrOnTMS4QwOTmZlw1dy5279qVdMxwV1QvpjhrFRjskHMw4CmxQjuX3r4w7lvzc/zpLwdSvrf1t2/gfz+4BUzGEdlDuoroj61ZgztvvRW33XUX3j1yBG8fOIAbly7F89u25fT6oRQvzipEzv0I9/Yjp+GQ1hDJNd1tGCbCEQ33rfk5fvzTXVmPvecrV+Cuf5pbkvMjosKkm6vX0dGB08aNw+Pr12PB1Vfn1E4Qw3/H2R0xEAageuSMG31lKs5KVOl4TQ+RgZWfhSkgJRTm6OuLQJIl7Hjlz1i7/jdpMzsDffv7v8LohiC+eNWFQ3XaRDSIdNssvL57N0KhEOYtXJhXO8NZUV0Igd6wCVkCgl6l6OKsRJWGAc8QSqr8LEto7+7D7978O462dWHPe4ew5bnfofV4d15t3vKdn6BxZAALZk8bilMmokGkm03X1tqacbuGfNoZShFDQDMEGmrUeHFWIjdhMD8MYp1LU6Aa4+tqcOcDP8ETP/5t3sEOAJimwA13bcAr//1eyc+TiAaXbg5AfUNDfLuGYtoZSj1hE4oM+FTWTSZ3YsAzzM45/UT8ZM2X4FGzb0ORTTii46r//STe/OsHJTwzIspFtu0afrV1a1HtDBXDFOjTTAR8CiQbbGpKVA4MeMpg9vmn4gcrU8u356OzO4RPfW0d9h1sKdFZEVEuMm3XcOfKlbj9ppvwy61b0dvbC03T8OL27bh3+fKc2xkqPWEDEgC/l10+uRdXaZXRY5tfwjce/llRbUw6YRT+ff1tGFUfLNFZEVE2mSqqA8CWTZuw7pFH8O6ePQgEg5h2zjlYdvfdOG/mzJRjh2uVlhACH3ZqqPbIGOHntE1yLwY8ZXbPo9uwav2LRbVx9mkn4Nc/uAUBP6tmEA2HStquoSdioL3XwOigBx6Fw1nkXsxvltnKm6/E9Z86v6g2/vCXA7j29h8gopVje0Ii9/EBQBH3isN1ayKEQE/YhE+VGOyQ6zHgKTNJkvD4t67F5Z84o6h2dux+B19esRGmyS0oiIaaIgSMsJF/9XMhhnW7hthS9ICv8EUSRE7BgMcGVFXB0w/+I84786Si2vnJ9v/GHWt+zi0oiIaQEALHe3VEIia8Ob7XRHRLBz1s5PyaUuBSdKJ+DHhswl/txbOPfgUfO6mpqHYe2/QS1vxoR4nOiogSCSHQ3mcgogvU+1X4ZTmn3cRVAH1dGrq6dXSFjGE4Uy5FJxqIAY+N1NfV4BfrbsK4MSOKaudb39uGjb94rURnRUSAFex0hgyENBMja1R4Vav7jE1ADsKam+OJPueJfh0EEJAkNNaokCWgrUdHSBv6oWcuRSdKxneCzUxoGonnHr8JI2v9RbXzlZWbsf2Vt0t0VkTuJoRAV8hAb8TESL8Kn5radcYqqvthBUD+6NexIz2KjFFBDwDgaGcEujF0Q1tCCPRETPi9MmRmd4gAMOCxpVNPbsazj34F1VWegtswDBNLlv8Qv3vz7yU8MyJ36g6b6ImYGFGtoMpTeLdZ7VUw0q/CFMDRrgjMIZrP06eZMAVQw8nKRHEMeGzq/Kkfwcbv/iMUpfBfUV9Iw6KvP4F3/vZhCc+MyF16wga6wwbqqhVUe4sPIGqrFfi9MiK6QGu3VvJFBkIIdHMpOlEKBjw2dvknpuCJez9bVBttHb2Yf9Pj+ODI8RKdFZF79EYMdIYMBKsU+EsQ7ABWKYrGaBHAnrBZ8knMXIpOlB4DHpu77srz8e2vf6qoNj748DiuXPo42jp6SnRWRM7Xp5no6DMQ8MklDx5kScLoWs+QTGLmUnSi9BjwVIBlN8zB15b8Q1Ft7Pnbh7jq1ifR2xcp0VkROVdYM9Heq8PvLX2wEzMUk5jjS9G9XIpONBADngogSRK+e9tCLL7snKLa2f3G33D9N/8Vuj48dUCIKlFEN9HWq6PaI6O2amgDh1JPYo4vRfexaycaiO+KCiHLMn6w8jrMPv9jRbXzq5ffxtfu/3+sxkyUhmaYaOvRUeWRUVc9PFmSUk1i5lJ0ouwY8FQQr0fFv636Is4+7YSi2vnRtt247/HnSnRWRPZnAggB6IW103lv9OvEmTOaIdDWo8OrShgxTMEOULpJzFyKTpQdA54KE6ypws/XfhWTThhVVDsP/fA3eHzzzpKcE5Fd6bACnC4AYQBa9Dkt+nVX9PthU6CtR4MqSxjpV4d9/svAScx9kfyCHi5FJxocA54KNLo+iOfW3YSmxtqi2vnGqp9hywv/XaKzIrKXMKxgRh/kOF0I9EmA6pUxsmb4g52YxEnMx7q0vCYxa9Gl6MzuEGXGgKdCTRzXiG2PLUVtoKrgNoQQ+OI9T+PfX3unhGdGVH5hWENWMVMmTsTOHcmb6m7asAGXXXghIEmQJAmqT4FW5rkvSZOYO3OfxNwdXYpexaXoRBkx4KlgZ04ej58+8k/weQfbqzkzTTdwzbIf4A9/OVDCMyMqHx3JwU7OJAkhDJ4RGmq11QpqvDIiRm6TmLkUnSg3DHgq3MenfxQbHrihqI6uuzeMBV9bh//Zf7SEZ0ZUHuEyv75YkiShIcMk5nSTr7sNE5LEXdGJBsN3iAMsmD0N37tzcUGvbRwZwNLPz8aKZYvw1w+PozUUSVm9QlQpTBSfodFR/ut/4CTmHs3IOPlaqDL8tR70yVLZs1NEdlb4WAjZypeu/jiOtnXh/u8/n9Px0047AV+/8VJcfMHpEEKgusob/15YCIQlCSoAH3iRUOXIVkd8yYIFUNT+q1mLRDD17LMztlP47LjSiE1iPh42oakyJCGANJncWHZXjz6qYL1viSgZMzwOcteX5+JLV1046HHXX3Uhnn3qFnzyojNR5fMkBTsA4p1qbElvuVP8RLnKlpnZtHUrDrS3xx+r1q0rqJ3hJHsV1ASiK8ei78tnNm/GrOnTMS4QwOTmZlw1dy5279oVf00IfM8SpcOAx0EkScIj31yMT108NeMx1191Ie67bcrAhtsAACAASURBVCH81T4oivXrZwdKTlGq+uF2qEMen3ydkNV5bM0a3Hnrrbjtrrvw7pEjePvAAdy4dCme37Yt6bV2mHxNZDcMeBxGUWRseOAGfPycSSnfm3baCfFgJ4YdKDlJqdYo2WGt08CbjI6ODnzn3nux6vHHceWiRaipqYHH48Hc+fPx7YcfHvT1RG7HgMeBqnwePPPIP+HMU8YlPf/1Gy+Fz+uJf80OlJymVB1auTvGdJOvX9+9G6FQCPMWLsypDTtMviayk3K/r2mI1AWrsfWxpThxbAMAazXWxRecHh/GAtiBkvN4Mzz/1r59mDVnTtJzS264AS8kDN3m0s5wSTf5uq21FQ2NjVDV3JcRZJvETeQ2DHgcrHlUHX657iaMGhnA4ivPSylgxg6UnEZG8asKVZS/Y0x3Y1Hf0IDWlhboeu6Dy7xBIepX7vc1DbFJJ47Gz9d+FWd+bELKaix2oORExS7JtsOS7nSTps+dMQM+nw+/2rq1qHaI3IoBjwucc/qJmHXe5JTnC+lADZNdKNmbisJr6FTBHnWn0k2arqurw50rV+L2m27CL7duRW9vLzRNw4vbt+Pe5ctzbofIrezw3qZhMGpkENqA5xI7UEVVcfGll8Lj8WDnjh145aWXsPKhh1La+eMHHVAMgRkTR0Dmvj1kU7EsTT57atmpYF+mO9Gbly3DmKYmrLr/fnx5yRIEgkFMO+ccLLv77rzaIXIjSQy2Mx05QrZaOls2bcK6Rx7Bu3v2JHWg582cmXRcRDfx/Fsf4qV3WnDiyGp85qxmnDomMOTnTlQoHdZ1n23Q1o4VxU1Y20gUKwgGPUQxDHhcohQdqGaYWLFtD3rC/ZsZnjWuFtdMa0ZTrV3ujYlSmbAm3Juw5rVIsAIBL+wbEPSguNpXKoCaEp0LkRPY6aaGhlBs9UqhHahpCvz5UFdSsAMAfzzYiTcPdeIfPtqABWeMQcDHS4rsR0b598bKlw/FBTy8BSFKxgyPi8T2xipEWDex9rd78X5bX8Zj/B4F808fjTmnNMCj2PW+mahyhJHfPKQYO81HIrILBjwuU0gHGtZNbPvjIfzn/7TldPyogBdXT23CuRPq4js5E1Fh8n3PMtghSo8Bjwvl1YEKgb992I2nXj2Anogx+PEJJjX6ce1ZY3Fyoz/fUySiBLHJ15oQEAKQ5dQbCTtOviayEwY8LhXrQCNCQAgBRU4dgkrsQLvDOn7x56P47XutedfiOe+EOlw1tRmjAuUu2E9U2Q62h2FIgM+rIFCtVsTkayK7YMDjcm8e7kTIFAhWe6AqEgxTYOJIf8YO9EhXGFveOIzff9CZ17+jyhIundyIeaeNht+rlOTcidxmX0sfeiMmAlUKTqivtGnYROXFgMfl/nSwA+8e65/KrMgSFp3ZPOjr/nq0G//vj4fx9yyTmNMJ+hQsnNKEi06uh5ImLU9Emb13pBeaIVBfo6KpjjN1iPLBgMfl3jzUib8e7Y5/LUvAp6eOzem1phB4bV87fvrmh2jrHVjHObuxtT4sntaMqWODnNhMlAMhBPYc7gUAjK71ojHgKfMZEVUWDvu63MAkSz7hryxJmHnSSDx4xWR8+swmVKm5X06HOsP4l5f3YdVLf8eB4/lliYjcSE+YO+dVeJNAlC8GPC43sNsUsO4k8+FVZcw/fTS+O28yZp1cj3wSNn8+0o0VL7yHH/7ufbT35ZclInITTe9/X3oY8BDljQGPy6UbTip0jLOu2oMb/td4fPuyU3BGU+57bAkAr/ztOO745V+x7e0jCOtmgWdA5FyakRjwsOsmyhffNS6XLhtT7Kyu8SOqcPs/fATLZp2E8XW5ryQJ6yZ+/tYR3PHLd7Drb20wOb2MKE4zrBsBCQDjHaL8sUaVy8npMjwitr1icaY0B3HamABe+Vsbnn3zCDrDue0M1N6n46nffYAX323BZ84ayx3ZidCf4fEoEif6ExWAq7Rc7t2j3fjToeSaOgumNJU8Zd6nGXh+zzG88M6xpNR8Ls4aV4vF05rQXNufLarE3a+JinGgNYTusIEan4wTG6rLfTpEFYcZHpdLd6OYZyHlnFR7FHz6zCbMOrkeP33zQ+ze157za2M7ss+a1IBPnTkGilfNuIt0GCyxT84UG9Li/B2iwvCd43JpJy0PYdKvocaLf5pxAlZcOgmTR9Xk/DpDACEhEJZlaIOcX2xX+HBxp0pkG0IIRBKGtIgofwx4XC7dBTAcY5wnNfjxzdkfwc0fPxFjcthj64JJ9Vhw1lh4VTkepG3asAEzp0xBs9+PU5qacNtXv4r29v7MUQgMesgZDNG/mIABD1FhGPC43HBneAb+2+eMr8P/ufwUfPbssajJsMfWCfXV8WAnZu3q1bjvjjuw8uGHcaCjAy++9hre378fCy+5BJFIJH5cCMg4/EVUKWLDWQCHtIgKxXeOyw3XHJ5sVEXGpZMb8d15k/HJyY0pe2zNOW001ITnOjs78eCKFXho7VrMuewyeDwenDhxItZv2YID+/bhJxs3Jr2eWR6qdCw6SFQ8Bjwul67rLNe6vYBPxbVnj8UDl5+C6RPqos8pOG1sEHJCwPNfr76KUCiE+YsWJb8+EMAll1+OnS++mPS8Dms1F1GlSi46yICHqBBcyOJyaevwDMssnszGBH342oUn4q9He/De8d6UAKy1pQUNjY1Q1dTLt6m5GW/8/vcpz0cA5F4CkcheYkNaKmvwEBWMAY/LDUWl5VKZPLoG40f5oQ84yYbGRrS2tEDX9ZSg58PDh9HQ2JjSFjM8VMk0rtAiKhqHtFwuXfc53HN4skoTkZ07YwZ8Ph+ee/bZpOe7u7uxY/t2XDR7dspr7PQjEeWLAQ9R8RjwuFz6zUPtEx6k697r6upwx4oVWH7zzdjxwgvQNA379+3DFxYvxtjx43HNddfl1A5RpWDRQaLicUjL5WQbD2kBmSPyW5Yvx8iGBtxz++34+969CNbW4ooFC/CDTZvg8/lybofI7kxTILYq3csMD5WQ27bo4V5aLnekK4yX97YmPfcPkxrQGEgNGsrBBNBVgnaCcOYbmJwvrJnYe6wPAHBCvQ+BKt6nUnF0WOU6stUoc+IWPU76WagAdp/DI8O6SAsuHigEVKRfjUZUCVh0kEopDKsg62D06KMKVuDjBHz3uFzaVVrDfxpZFftm0yMmdDtFcUR5YA0eKpVcg51ETtqihwGPy6Wtw2OzUU4VhdfQqZIkBDwy+iImQpppu5+NaDCxgEeRkVSAkygfOlKDnSkTJ2Lnjh1Jz23asAGXXXhh0nNO2aKHQ1ouJ0nAiaNqEKz2QFUk6IaA4lFgwl7RcCzLk8/dSTwVK0sI+GSENIHusIkan8whLqoYXKFFpVBsliaMyg8YKv38qUCxSWtytQeTqlQocn9nKoRAF+w3ac0HQEFhk+0kSUK11wrousMmqjwyV7xQRYiwBg8VyUTxGZrYFj2VHHbb5bOMhlHiOK4kSVAGZDtitXnsOGlNjT4KXU6pKhICsozeiIBuCFR7WKqf7E1nwENFipSwnUreoocBj8sUOmkNsE/QA1hBTaFvPFmSUOO17py7wiZqvHLKDu1EdiCESKiyXMn31lRO2bbWWbJgAZSELXq0SARTzz4773YqAd9BLpJu0lrMM5s3Y9b06RgXCGByczOumjsXu3ftin/fKZPWYiRJgk+VUeOV0csJzWRTXKFFpZCtZ9u0dSsOtLfHH6vWrSuonUrAgMdFMk1ae2zNGtx566247a678O6RI3j7wAHcuHQpnt+2LafXVzIlOqHZFEBPxITJoIdshAEPlUKprpxKvwI5pOUSmSatdXR04Dv33ovH16/HlYsWxZ+fO38+5s6fn3SsEyatpSNJEvxeCVp0QnO1R+aHC9lCUtFB1WnvPBoupbpyKv0KrPTzpxxlmrT2+u7dCIVCmLdwYVHtOIFHsbI9Yd1Eb4RDXFR+sQyPJAGMwalQXqAkmyR6i26hvJjhcYlMk83aWlvR0NgIVc3tUqj0SWuDsSY0y4jonNBM5RcLeLwKVxNSYYQQME1ro2gTIqm8/lv79qUcv+SGG7DkhhtSnldR+RmSSj9/ylGm2L6+oQGtLS3Q9dymJLsh5yFJEnwea0JzT8REWGe2h8ojFvCoXKFFeRJCwDAFdBOQZaBaltLvJZQjO63SLRTfRS6R6TI/d8YM+Hw+/Grr1qLacSJFlhD0yTBMoCciOKGZhoUJa1VkL4DqgIqRI3zw+1XHZ1epdGKBjiRZQ/WyJBW3RQ+cMRzEgMclJFOkHcOtq6vDnStX4vabbsIvt25Fb28vNE3Di9u3497ly1OOd9sFY01oluFTJXSHzaRVM0SlpAPoAdAFa0WkBsDnU+H3q/BUKeiKft9J5SGotEzTqtskoT/QSeRD/kGPnQrPFksSzNU7lhACEUNYG2fqAlVBNeM8gC2bNmHdI4/g3T17EAgGMe2cc7Ds7rtx3syZSccF4b6gJ8YUAj1hE6osoYoVmqmE8i0I6qQPISqeKQSM6DydXOYcxrYWyneLnkrHgMeBDNMKcvo0E4YJ+FQJ1V4ZhipBL/BDWggB2RSodflcAiEEwrp1F+XnhGYqgUzBzjObN+PxNWvw3jvvIBAMYsq0aVh2992YEd3JmkFP5Sp0a5yBhIjO0ZGsR743YaU6j0rhpOCtYgzFRSaEQEQX6I2YCOsCigRUe2VUJ3wox/bGKtTxjghCqoyGgMe1H/SSZGV3VEWgJ2KiSpXgZX0UKlCm6uePrVmDf3nwQaz5/vcx+5OfhNfrxY4XXsDz27bFA54QrM102YlXjsEyK7EdyQfLrMQCHQmAKucf6MQUs0VPJWKGZxgNRRrRMK0gpy9iwhRAlcfK5mRaxlrIXloQAtBMtHZEIISVMh1d64Hfq+TbkqMIIdAbsd4+fi+HuCh/6ebkdHR04LRx4/D4+vVYcPXVWV+vAqgZqpOjkirFsKWIDl0BgFJEoONWDHiGSSnH6GPDKr0RExFdQJEBv1dGtUeGnEPmpdBz0QwTxzo19GnWO662WkFDjSenf9PJIrpASDfh98hQs1SHc1v6mLIzYU1QHmjHCy/gmnnzcCQUyqk+lpvn1VWKgm400d/3MtApDb5PhkGhO5QP3LtKNwS6+gwc69LR3mtAloD6GgWNARU1PiXnwMMH665wsK40dvcYC7w8iozmEV40BjyQAHT2GXi/LYy+iJH7D+ZAXlVCwCujT7PmTQ28h0i3+kaP/hmOPs/VN+6TqWp5vsVAnVz93AnSDVtOmTgRk0aPRk9PT/y5Hz/1FK6YNSvpuJAQCEeXmCsyoLIAZVEY8AyxgRf7lIkTsXPHjqRjNm3YgMui4/KJQgB0YU1Abu3W0dKtI6ybCPhkjK5VMcKvwqvKBb0BYsFMEFZA44k+54l+HUT6oEiSJNT5VYyv98GnytBNgUPtEbR0aa6uUyNHNyEFgO6wCdO0/i/CyC2YiQVFTtygldLLVFcn32KgrM9jb5ne04Zh4Pvf+96gr9eitXQY6BSPAc8QK+oDTAh06gKdfQZURUJDQEVj0AO/T0mpr1Co2KQ1P6wAxx/9erALw6vKGDfSi/oaKyTq6NPxQVsYIc293a8kSaj2WEOL3RETPYYoSWaPnCnT7UG+xUB106qoS/aTadNmAPj6N76BtatWob29PXMDkgRDkhjUlggDniGU7WLPiSRBUSU01Kqoq1Zst4O3JEkYWePB+HofvKq12/jB42G0dWuu3opBVST4fTL0NO+uZzZvxqzp0zEuEMDk5mZcNXcudu/alXRMCBzecjohkDHiybcYaEQzcbhDw+H2CFq6NXT2GQhpJoMgG8g23HjW9Om4cNYsPLZqVVHtUO64onEIleQilSTosPcvyqfKGD/Sh+O9Oo736Djeq6MnYmB0rRc+ly7ZDqfJwOWy1Dj+etj7d065EyI1tpFg7X6eKbC9edkyjGlqwqr778eXlyxJKgY6sPFqVUK1X0FEtwqNdmr9c+oU2dp41KPI8KoSvIrk+kUGQymim+gIaWjvsx71I6rRWJt54fddK1fisgsuwFduuSVru8zwlAZXaQ2hXlgTUxNNmTgRbS0tUBImJGqRCKaefTZeGHCnH+OBNdRUCcKaiSOdkfgWDPU11lwjN40/p1t9k89S4xiuvqlMmQKcgW+BTKu08jXwOhHCKowZMQS0aBCUuCWKFQRZAZBHYRBUiIhhoiMa1LSHNHT06Wjv09CrJS/gOG9SI5pGVKe8fsrEiVj71FOYNWcOvrRkCUY3NWHyqafiJxs34lc7d6Ycz/IDpcGbyCGUKZLctHUrZs2Z0//1hg14+qmn8m7HjnweGePrfTjeo6O9V0dbj46esJXtcUuBvnSZvdd370YoFMK8hQvzasdNRcEqVa4BzkAyrA64mOFLFalBsSRJVjYnVtQLyUFQJFopvK+vP2+gykjKAnnU1H2YhpNdSjhohpkQ1Gho79PRHtLQm+PKVE0fPDdz5z//My46+2zctGxZxmMYjpYGA54hVKqLtNIudlmS0BDwwO+VcaxLQ1gX+KAtjPqAB3XViuOzPem6uHyXGgPWZFRRQLl4GlqFBjjp+FBcwJPr1hKZgqCBWaCBQZBXleNZoOEIgkpViThfWixjE7KCmtjfe4osudHRp6HZNKHKmcO0j0yahIXXXIMnH30Up02ZkvYYd9wqDj0GPEOoVBdppV7s1V4F4+tltEYnUrZ2a9Fsjwceh+3JpRkmesMmesIG1GoFvqrkt1biUuNcg56usI6/t4bgVWX4VBk+j4yqhL+7dXuP4VbKAGcgFVYWr9CidMV04JIkwadK8CU0YkYzQbEgKLZdTfx8Zal/KCz6Z6mCoFzrlcW2yClkLzHNiM2x0RMCnOIDm0zeb+3BqePqBj1u+b334idPP53+m0JAFeDNTwkw4BlCXpRmibG3BG2UiyxJGBX0osZn4FinhpBm4v22MBoDHgSrKjPbI6K1kXoiBnrCBnrDBsJ6/0fiKE9VSkecuNT4U1ddldO/Y5iAKYCQZlrL/fuSv6/KUjz4sT64rL97VbmswxH5sMvQRaKhDHDSiV0rdtgtXc4SBMWGwiK6id6EcdtYEBTLAmXa1iabdMHOYJunxo5P9/9gBTbJQU1Hn4buISySKklArU/FiGqP9ajyoK7aA1UCBv6rb+3bl/T1+AkTcCSU/gpQJQkyYntnCcgyKub9bTectDzEiq2g66TJaoYp0NqtoStkvf39Xhmjgl7bb8egGVbmpieawemNGMj2rqmr9WBknS9lIuja1avx6EMP4ZEnn8TFl14Kj8eDnTt24JWXXsLKhx5KOlYIgVCvjq7uCMKaCSPPd6lXkaKBkJwQFMm2KWA2FPvKFWK4g5ts7PJ/kgtTJGeBNMNE4nQVj9KfBfJG/57puosV3UyUaUXjqy+/jG8//HD/gUJAD+lo743Eg5r2YQxs6qo88QCn1qemnfyd7ufLR2IBWCEEDGFdt4XukJ6OHfrZ4cCAZ4iV8mJ3ip6wgWNdERim9YZtDHoQ8CVne8rV+Zux7E24P3sTySHaqPLIqPEpqPHKqPYp0Dxy2k/NLZs2Yd0jj+DdPXuSlhqfN3NmyrGx1TfWPjoCYd1EWLP27YroJsKaibBu5jWpXZKQEgTFHtkCz1Iq5b5y+bJTgJNJpX74mGb/XCBribwZ3/8JQNJcoMQgaOBNYT4rGk0h8OHxPrz+t9aS/zwSgNoqFXXRbE0ssAn61LyHk4vdSysdM7q/lgQUnPWppCC7FBjwDIOhuNgrnWEKtHRp6A5bd2I1Pivbo8jSsH0gxlauxIObiIHe8OABhCIjGtwo8PsU1PiUlA5wuDJ7sYmnseAnnBAIaXmmhRRZShoaSwyMhnuexkCF/47tH+A4WSwIsiZHm4gYIjkIUiX4AsllK/LdPNUwBX7z5iFEclgRlY4EIFilxoMaK8BRUVvlKek8uaHq1wrN+pTzxqNcnBC02Z6dxujtQpEljKnzoiak41iXhp6wib5ICA0jfBCe/O5js43lJzJNgd6INTTVG51/k0tQUB3N3sSCG586+LDQcK6+iQUpA5mxrNCAQCisJ995xximQG8keZJqjFeR4B0waTrfIbJ0myjG5DJfQ8HgHRYDHHuRZQlVsoQqD2D9Bq3rLJYFSleNPN8VjUIITGiowd4j2asaSQCCsaGoaFAzotpT8sAmEx+s/4FSZ1QkSYIaPX1T5DbXp9ANrYHK/lxiwDNMhupir3SBKhVVHgXHuiKImAKmKqUswx/swxBI/UAUwupQEycWp/sgH0iVpWhwEw1yvKnZm1yUc/VNjCxLqPYqqPYqKd/TDZE2EArrZtr5SdZduoHuAdMvk4bIBmSGBg6RZZrAn2sF6nTVpxngVB5FlqBEg6B0xVnzXdGoKjLqqj3xryUAgdjk4diQVHS+TblXNqrRx1ANW8qSBFnpz/oYpkjJ+qTb0DpWBDEmVhtuYDHcXG887KpSz7siDfXFXqlURUJTnRedpkj58Mp5OwYh0GMK9HVr8eXheg57Cfm9CdkbrwJvDtmbXNk5s6cqElTFylglig3zpQRCmpl2LpNIXEU2gCInBENeGb6AN+X/tqOjA9+59148vn49rly0KP783PnzMXf+/KRjdQCGSK1LxQCncqV7hxayorG+xosLT6qPZmzUrHVv7CC2afNQyZb1SbftTT4qedubSj3vijbUF3slEpIEKMnZnXw+DCFJMCXgSKcGM0Og41GkeNamxifD71WGvKR+pWX2+gvUyQgOuEhNIeKTpUPxQEhEh8hS/88NE+iNmOiNmKhVPPCK1MAkrwrUwsoGVDG4cYx0v8rEzVMVVR10RSMAjKj2wJ+Q5aF+iVkfXQA60rwR86DDulm3d0iZXrn7VyIApduOIVijoqNLgwTAHw1qaqJzb8q1JNspmT1ZklDlUVDlUTCwlFrSENmA7JAQgNeTPrjMa76GxE0UnSbTdZ/z5qmDtEP9JEmCUaLur1K3vWHAQ7ZQiu0YZFnCiIAHY2o8qPbar/iekzN7gw2R9WX4VeQ7X4NLSp0lW3HWxUuWYPGSJTm3Q4PLdMOwZMGCtBta59uO3TEwJltI90GW+GGYK180o2O3YMetrCEyOeNWIonzNXJqr5QnR2UX20C1GOk2UKX0sm1ofaC9Pf5YtW5dQe3YHa8TsoV0H2T5fhhmaofKL1NHkzhf45dbt6K3txeapuHF7dtx7/LlObdDlavYSfqVvEx6uLl1Q+sYDmmRLaT7ICtk8iI/EO0p29BFPvM1OHThPHYo4eAWbt/QmtcK2UKmD8R8Jy/yA9GeYkMXmQYnc5mvwaEL58qnhENsc4AqAD4OXefF7Rtac2sJsg1utOps3FeOBpPL3k6GZqCnR8fIahUBX2pRTcrOzf0s+w+yjeHajoHKg0MXNJhcSjiYiowuU+B4jwa/Rx7yWlpO4+Z+lhliso3YB2Ih+IFYGXzI/3fs9H3lKFWshIMfVjbBH/1ahrX9y8hqFYYA2vuK+eh2Jzf3swx4yFZiH4hCCOQ62soPxMriQ27DU7HUOX+3NFCwyiok2hkyCt4l3c3ceuPBgIdsRzYEert0SIPsZM4PxMoV+90FYf3+tLCBvj4dvb0afNHnOWeHMpEkCQ011lYSrT1azjdH1M+NNx7sT8h2ukIGhCkQjO62XcnbMVB2saGL9pCOlm5rS5BmP/dEosFVeWTU+GT0hE30RExOYC6AU7a9yRUDHrIV3RDojZgIVvVvDeHU7RioX+x3LWANZ5ZjzzOqPPV+D/oiYbT1aKj2yFA4gbkgTt72JpGTgjdygM6QAQlAkHdrrpIY32TY7J4ohSJLGOFXYXICM+WAAQ/ZRiy7E6jiUlO3Sfx1cz4G5SPoU+BVJHSFDIQ5gZmyYMBDttEVze5wLN59Ejd7ZYaH8sEJzJQrBjxkC7op0BMxUePjOLwbyUlDWvzAovz4PDICPgURXaA7bJT7dMimGPCQLXSFrE4qWMXsjhslDmEyw0OFGOlXIUvA8V4dBi8iSoMBD5WdYQr0hE0EmN1xLYkZHiqSIksYGZ3AfLyXE5gpFQMeKjtmdyhxDg/jHSpUwKfAq0roDvdPYDZh7d/WC2vjzN7o15ze7D4MeKisYtkdzt1xN5nL0qkEEicwH+/T0SMEumDtwK7B2jRTi37dheJ3DqfKwsKDVFbdIQMCzO64XdIqLUY8VASfKqO2RoXsUwYNZvTowwn7RNHgGPBQ2RimQHfYRI1Xhsrsjqsxw0OlEgag+JTkiWGDCEX/ZNDjbBzSorLpDjO7QxYpqQ4PIx4qjI5o8DIg2Nm0YQNmTpmCZr8fpzQ14bavfhXt7e1Jx4TA4S2nY8BDZWGaAt0hE36vDFVhdsftkistl+88qLKF0zy3dvVq3HfHHVj58MM40NGBF197De/v34+Fl1yCSCQy6OvJORjwUFl0h01mdyhOkiTEYh5meKgQJlIzNJ2dnXhwxQo8tHYt5lx2GTweD06cOBHrt2zBgX378JONG5OO18HVW07GgIeGnSkEusIGqr0yPMzuUFQsy8M5PFSISJrn/uvVVxEKhTB/0aKk5wOBAC65/HLsfPHFnNohZ2DAQ0MmU/2LrrAJIYBaZncogRSNeJjhoUKky8y0trSgobERqpq6PqepuRmtLS05tUPOwFVaVHI6rLHwtBMAhYDwyahRJUjM7lACZnioGOkum4bGRrS2tEDX9ZSg58PDh9HQ2JhTO+QMzPBQSYUxSDEvSYIkSZAVCT3gJEGymABq/B7Uj/TBH/CwGi7lLd3t07kzZsDn8+G5Z59Ner67uxs7tm/HRbNn59QOOQMzPFQyYfTXsxhUdNko61+4W2I2sCbgiS9P16LfD8PqpHxgZ0XZpbt7r6urwx0rVmD5zTcjWFuLi2bPxqGDB3H70qUYO348rrnuupzaIWfg75ZKIl7/IsGUiROxc8eOpOc2bdiAyy68TmCF9gAAAoJJREFUMOk51r9wp4HZQClDoTg9ehyzgZSNN8PztyxfjnseeAD33H47JtTWYs5552HchAn4xW9/C58v9VYrUztU+XjTRCVR7IdR7E6e3CGvbGAUs4GUjQyrD0l383T9jTfi+htvHLQNFcwCOBl/t1S0dPUv8sX6F+4xMBuYayYQYDaQsis2GGYw7WwMeKhopapbwfoX7lCKbCBROiqsjUALUQVmmZ2Ov18qWrbMzJIFC6AkLAfVIhFMPfvsvNshZyhlNpB3a5ROLEuTz5Apd0t3B/YZVLRsdSs2bd2KA+3t8ceqdesKaoecgdlAGg4+ADUY/I5ejR7HYMcdmOGhopWqbgXrXzhfpixePpnAbO0QxajRhwkrQDZh3VRJsO70veAdv9vw901FK9VFxIvR+TJl8fLJBGZrh2ggGdaQlR9WNscf/Zr9jfvwd05FK1XdCta/cD5mA4moXDikRUXLVP/irX37Uo5dcsMNWHLDDSnPs/6FOzAbSETlwn6DSoL1LygXzAYSUblIQggOh1NJFFI9F+CSULfJurlsDmIra4iI8sEMD5WMD/kX/WKw4z7MBhJROTDDQyWXuAN2JtwB292YDSSi4caAh4YM619QNvkGPQx2iKgYDHiIqGyYDSSi4cKAh4jKjtlAIhpqDHiIiIjI8XjzRERERI7HgIeIiIgcjwEPEREROR4DHiIiInI8BjxERETkeAx4iIiIyPEY8BAREZHjMeAhIiIix2PAQ0RERI7HgIeIiIgcjwEPEREROR4DHiIiInI8BjxERETkeAx4iIiIyPEY8BAREZHjMeAhIiIix2PAQ0RERI7HgIeIiIgcjwEPEREROR4DHiIiInK8/w+yugIyhmavxAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 720x360 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ]
    }
  ]
}