Spelled-Out-Intro-to-GCN.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "!pip install -q git+https://github.com/pyg-team/pytorch_geometric.git"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kvIt1ZurIXDu",
        "outputId": "0308d10d-d565-42a7-9a3b-82a79214d17e"
      },
      "id": "kvIt1ZurIXDu",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  Installing build dependencies ... \u001b[?25l\u001b[?25hdone\n",
            "  Getting requirements to build wheel ... \u001b[?25l\u001b[?25hdone\n",
            "  Preparing metadata (pyproject.toml) ... \u001b[?25l\u001b[?25hdone\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "021e8900-0521-477b-93d3-82c00204a3dc",
      "metadata": {
        "id": "021e8900-0521-477b-93d3-82c00204a3dc"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import random\n",
        "import os\n",
        "import math\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "import matplotlib.pyplot as plt\n",
        "from torch_geometric.datasets.karate import KarateClub\n",
        "from torch_geometric.datasets import Planetoid\n",
        "from torch_geometric.utils import to_dense_adj\n",
        "import torch.nn.functional as F\n",
        "\n",
        "import networkx as nx\n",
        "from torch_geometric.utils import to_networkx\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6ac18c57-9e61-4267-bb6c-ef55daeba8b7",
      "metadata": {
        "id": "6ac18c57-9e61-4267-bb6c-ef55daeba8b7"
      },
      "source": [
        "## Formulation of the GCN and it's intuition"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "3d6cc303-0192-4960-b103-43c57dfb8523",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 529
        },
        "id": "3d6cc303-0192-4960-b103-43c57dfb8523",
        "outputId": "6e440f53-df79-4bbd-9581-5899c013b876"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Number of nodes in the graph 6\n",
            "Number of edges in the graph 9\n",
            "\n",
            "Adjacency Matrix shape (6, 6)\n",
            "[[0 1 0 1 0 1]\n",
            " [1 0 1 1 1 0]\n",
            " [0 1 0 1 0 0]\n",
            " [1 1 1 0 0 1]\n",
            " [0 1 0 0 0 1]\n",
            " [1 0 0 1 1 0]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 300x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# create a new sample graph\n",
        "adj = np.array([[0,1,0,1,0,1], [1,0,1,1,1,0], [0,1,0,1,0,0], [1,1,1,0,0,1], [0,1,0,0,0,1], [1,0,0,1,1,0]])\n",
        "G = nx.from_numpy_array(adj)\n",
        "num_nodes = G.number_of_nodes()\n",
        "num_edges = G.number_of_edges()\n",
        "print(f\"Number of nodes in the graph {num_nodes}\")\n",
        "print(f\"Number of edges in the graph {num_edges}\")\n",
        "print()\n",
        "\n",
        "print(f\"Adjacency Matrix shape {adj.shape}\")\n",
        "print(adj)\n",
        "\n",
        "# draw the graph using networkx\n",
        "pos = nx.circular_layout(G)\n",
        "plt.figure(figsize=(3, 3))\n",
        "nx.draw(G, pos, with_labels=True, node_size=300, font_size=15, font_color='black')\n",
        "plt.title(\"Normal Graph\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# create random features for each node having 3 dimensions\n",
        "x = np.round(np.random.randn(num_nodes, 3), 2)\n",
        "print(f\"Feature Matrix shape {x.shape}\")\n",
        "print(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qtNsdYkTYB8z",
        "outputId": "b02f215a-3b47-4870-d096-759d83ddde0f"
      },
      "id": "qtNsdYkTYB8z",
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Feature Matrix shape (6, 3)\n",
            "[[ 1.06 -0.19 -0.26]\n",
            " [ 1.15 -2.07  0.67]\n",
            " [-0.14 -0.77 -0.59]\n",
            " [-0.37  0.91  1.15]\n",
            " [ 0.58  0.37 -0.61]\n",
            " [ 0.06  1.21  0.62]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We will implement and understand the following equation proposed by Kipf et.al. in the paper titled [\"Semi-Supervised Classification with Graph Convolutional Networks\"](https://arxiv.org/pdf/1609.02907.pdf). The equation for one layer of Graph Convolution Nwtwork (GCN) is defined as :\n",
        "\n",
        "$H^{(l+1)} = \\sigma(\\tilde{D}^{\\frac{-1}{2}}\\tilde{A}\\tilde{D}^{\\frac{-1}{2}}H^{(l)}W^{(l)})$\n",
        "\n",
        "where $\\tilde{A} \\in \\mathbb{R}^{N \\times N} = A + I_N$ (Graph with self loops), $N$ is the number of nodes.\n",
        "\n",
        "$\\tilde{D}_{ii} \\in \\mathbb{R}^{N \\times N} = \\sum_j\\tilde{A}_{ij}$ (Degree matrix)\n",
        "\n",
        "$W^{(𝑙)} \\in \\mathbb{R}^{D \\times W} $ is $l^{th}$ layer trainable weight matrix.\n",
        "\n",
        "$\\sigma({\\cdot})$ denotes an activation function such as ReLU.\n",
        "\n",
        "$H^{(𝑙)}$ is the matrix of activations in the $l^{th}$ layer; $H^{(0)} = X \\in \\mathbb{R}^{N \\times D}$ (Input feature matrix).\n",
        "\n"
      ],
      "metadata": {
        "id": "z8Z_QlH4lfah"
      },
      "id": "z8Z_QlH4lfah"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's start with the very first part of the equation -\n",
        "$AH^{(0)}$. Here we are first starting with unnormalized adjacency matrix and later we will build the intuition of normalization."
      ],
      "metadata": {
        "id": "ztqdPHAkBa6J"
      },
      "id": "ztqdPHAkBa6J"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "3d93caf9-cafc-4d55-a1aa-3fc3eefce21a",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3d93caf9-cafc-4d55-a1aa-3fc3eefce21a",
        "outputId": "c05a0cd4-6b4f-498f-9bc6-4766478c8261"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "AX =\n",
            "[[ 0.84  0.05  2.44]\n",
            " [ 1.13  0.32 -0.31]\n",
            " [ 0.78 -1.16  1.82]\n",
            " [ 2.13 -1.82  0.44]\n",
            " [ 1.21 -0.86  1.29]\n",
            " [ 1.27  1.09  0.28]]\n",
            "\n",
            "Node 0 is connected to Node 1 [ 1.15 -2.07  0.67], Node 3 [-0.37  0.91  1.15], Node 5 [0.06 1.21 0.62], \n",
            "Sum of connected neighbors [0.84 0.05 2.44]\n",
            "\n",
            "Node 1 is connected to Node 0 [ 1.06 -0.19 -0.26], Node 2 [-0.14 -0.77 -0.59], Node 3 [-0.37  0.91  1.15], Node 4 [ 0.58  0.37 -0.61], \n",
            "Sum of connected neighbors [ 1.13  0.32 -0.31]\n",
            "\n",
            "Node 2 is connected to Node 1 [ 1.15 -2.07  0.67], Node 3 [-0.37  0.91  1.15], \n",
            "Sum of connected neighbors [ 0.78 -1.16  1.82]\n",
            "\n",
            "Node 3 is connected to Node 0 [ 1.06 -0.19 -0.26], Node 1 [ 1.15 -2.07  0.67], Node 2 [-0.14 -0.77 -0.59], Node 5 [0.06 1.21 0.62], \n",
            "Sum of connected neighbors [ 2.13 -1.82  0.44]\n",
            "\n",
            "Node 4 is connected to Node 1 [ 1.15 -2.07  0.67], Node 5 [0.06 1.21 0.62], \n",
            "Sum of connected neighbors [ 1.21 -0.86  1.29]\n",
            "\n",
            "Node 5 is connected to Node 0 [ 1.06 -0.19 -0.26], Node 3 [-0.37  0.91  1.15], Node 4 [ 0.58  0.37 -0.61], \n",
            "Sum of connected neighbors [1.27 1.09 0.28]\n",
            "\n",
            "That's what we call message passing!\n"
          ]
        }
      ],
      "source": [
        "# First and important part of the equation - AX\n",
        "print(\"AX =\")\n",
        "print(adj @ x) # (6 x 6) @ (6 x 3) -> 6 x 3\n",
        "print()\n",
        "\n",
        "# Lets understand what this multiplication is doing.\n",
        "for i in range(num_nodes):\n",
        "    res = 0.\n",
        "    print(f\"Node {i} is connected to\", end=' ')\n",
        "    for n in G[i].keys():\n",
        "        res += x[n]\n",
        "        print(f\"Node {n} {x[n]},\", end=' ')\n",
        "\n",
        "    print()\n",
        "    print(f\"Sum of connected neighbors {res}\")\n",
        "    print()\n",
        "print(f\"That's what we call message passing!\")\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9e97ed66-f0aa-477d-8a4c-b7f83afd7963",
      "metadata": {
        "id": "9e97ed66-f0aa-477d-8a4c-b7f83afd7963"
      },
      "source": [
        "### But there are **two problems**:\n",
        "- While updating the node features, the node is **not taking it's own feature** into account.\n",
        "- Aggregated features are **not normalized**."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "id": "97e2251a-c4b9-4c5b-9d7d-23919b0c9389",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 478
        },
        "id": "97e2251a-c4b9-4c5b-9d7d-23919b0c9389",
        "outputId": "42b2991e-2cb5-4312-9429-0d03cd5fdac7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Adjacency matrix with self loops\n",
            "[[1. 1. 0. 1. 0. 1.]\n",
            " [1. 1. 1. 1. 1. 0.]\n",
            " [0. 1. 1. 1. 0. 0.]\n",
            " [1. 1. 1. 1. 0. 1.]\n",
            " [0. 1. 0. 0. 1. 1.]\n",
            " [1. 0. 0. 1. 1. 1.]]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 300x300 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# add self loop for all the nodes\n",
        "adj_loop = adj + np.eye(adj.shape[0]) # A_tilde = A + I\n",
        "# There are papers which also suggested doing A + 2I which will give more important to its own features while aggregating\n",
        "print(\"Adjacency matrix with self loops\")\n",
        "print(adj_loop)\n",
        "\n",
        "# Plot the graph with self loops\n",
        "G_loop = nx.from_numpy_array(adj_loop)\n",
        "pos = nx.circular_layout(G_loop)\n",
        "plt.figure(figsize=(3, 3))\n",
        "nx.draw(G_loop, pos, with_labels=True, node_size=300, font_size=15, font_color='black')\n",
        "plt.title(\"Graph with self loop\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Incorporating self-loops into the graph ensures that our own node features are included during the aggregation process."
      ],
      "metadata": {
        "id": "hEmUTX_HEXpd"
      },
      "id": "hEmUTX_HEXpd"
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "id": "24dc417f-8a57-4e6f-832d-79229e0fb228",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "24dc417f-8a57-4e6f-832d-79229e0fb228",
        "outputId": "1973554f-1d14-4c90-8b7a-cd1351edb15e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "A_tilde X =\n",
            "[[ 1.9  -0.14  2.18]\n",
            " [ 2.28 -1.75  0.36]\n",
            " [ 0.64 -1.93  1.23]\n",
            " [ 1.76 -0.91  1.59]\n",
            " [ 1.79 -0.49  0.68]\n",
            " [ 1.33  2.3   0.9 ]]\n",
            "\n",
            "Node 0 is connected to Node 0 [ 1.06 -0.19 -0.26], Node 1 [ 1.15 -2.07  0.67], Node 3 [-0.37  0.91  1.15], Node 5 [0.06 1.21 0.62], \n",
            "Sum of connected neighbors [ 1.9  -0.14  2.18]\n",
            "\n",
            "Node 1 is connected to Node 0 [ 1.06 -0.19 -0.26], Node 1 [ 1.15 -2.07  0.67], Node 2 [-0.14 -0.77 -0.59], Node 3 [-0.37  0.91  1.15], Node 4 [ 0.58  0.37 -0.61], \n",
            "Sum of connected neighbors [ 2.28 -1.75  0.36]\n",
            "\n",
            "Node 2 is connected to Node 1 [ 1.15 -2.07  0.67], Node 2 [-0.14 -0.77 -0.59], Node 3 [-0.37  0.91  1.15], \n",
            "Sum of connected neighbors [ 0.64 -1.93  1.23]\n",
            "\n",
            "Node 3 is connected to Node 0 [ 1.06 -0.19 -0.26], Node 1 [ 1.15 -2.07  0.67], Node 2 [-0.14 -0.77 -0.59], Node 3 [-0.37  0.91  1.15], Node 5 [0.06 1.21 0.62], \n",
            "Sum of connected neighbors [ 1.76 -0.91  1.59]\n",
            "\n",
            "Node 4 is connected to Node 1 [ 1.15 -2.07  0.67], Node 4 [ 0.58  0.37 -0.61], Node 5 [0.06 1.21 0.62], \n",
            "Sum of connected neighbors [ 1.79 -0.49  0.68]\n",
            "\n",
            "Node 5 is connected to Node 0 [ 1.06 -0.19 -0.26], Node 3 [-0.37  0.91  1.15], Node 4 [ 0.58  0.37 -0.61], Node 5 [0.06 1.21 0.62], \n",
            "Sum of connected neighbors [1.33 2.3  0.9 ]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "print(\"A_tilde X =\")\n",
        "print(adj_loop @ x)\n",
        "print()\n",
        "\n",
        "for i in range(num_nodes):\n",
        "    res = 0.\n",
        "    print(f\"Node {i} is connected to\", end=' ')\n",
        "    for n in G_loop[i].keys():\n",
        "        res += x[n]\n",
        "        print(f\"Node {n} {x[n]},\", end=' ')\n",
        "\n",
        "    print()\n",
        "    print(f\"Sum of connected neighbors {res}\")\n",
        "    print()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now, lets take the second problem into the account. The aggregated features are not normalized. Here I would love to quote the lines written by [Matthew M. Bernstein](https://mbernste.github.io/) on his blog post explaining [GCN](https://mbernste.github.io/posts/gcn/):\n",
        "\n",
        "> We see that this aggregation step simply adds together all of the feature vectors of i’s adjacent nodes with its own feature vector. A problem becomes apparent: for nodes that have many neighbors, this sum will be large and we will get vectors with large magnitudes. Conversely, for nodes with few neighbors, this sum will result in vectors with small magnitudes. This is not a desirable property! When attempting to train our neural network, each node’s vector will be highly dependent on the number of neighbors that surround it and it will be challenging to optimize weights that look for signals in the neighboring nodes that are independent of the number of neighbors. Another problem is that if we have multiple layers, the vector associated with a given node may blow up in magnitude the deeper into the layers they go, which can lead to numerical stability issues. Thus, we need a way to perform this aggregation step so that the aggregated vector for each node is of similar magnitude and is not dependent on each node’s number of neighbors.\n",
        "\n",
        "> One idea to mitigate this issue would be to take the mean of the neighboring vectors rather than the sum.\n",
        "\n",
        "To calculate the mean of the feature vectors, we can generate the degree matrix $D$, which is essentially the sum of each row in the adjacency matrix. This matrix is *diagonal*, with each entry representing the degree of the corresponding node.\n",
        "\n",
        "$D_{ii} \\in \\mathbb{R}^{N \\times N} = \\sum_j\\tilde{A}_{ij}$\n",
        "\n",
        "Once we calculate the degree matrix $D$, we can do the following:\n",
        "\n",
        "$D^{-1}\\tilde{A}$\n",
        "\n",
        "where $D^{-1}$ is the element wise inverse of the non-zero elements of the $D$ matrix. This equation makes sure that updated features are normalized."
      ],
      "metadata": {
        "id": "dz83saSzFQP1"
      },
      "id": "dz83saSzFQP1"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "id": "9aa592e2-fc8c-4255-88cf-58615aad01d8",
      "metadata": {
        "id": "9aa592e2-fc8c-4255-88cf-58615aad01d8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b974bbfc-d467-4850-b537-1dfa467ad9f3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Adjacency matrix before\n",
            "[[1. 1. 0. 1. 0. 1.]\n",
            " [1. 1. 1. 1. 1. 0.]\n",
            " [0. 1. 1. 1. 0. 0.]\n",
            " [1. 1. 1. 1. 0. 1.]\n",
            " [0. 1. 0. 0. 1. 1.]\n",
            " [1. 0. 0. 1. 1. 1.]]\n",
            "Adjacency matrix after\n",
            "[[0.25       0.25       0.         0.25       0.         0.25      ]\n",
            " [0.2        0.2        0.2        0.2        0.2        0.        ]\n",
            " [0.         0.33333333 0.33333333 0.33333333 0.         0.        ]\n",
            " [0.2        0.2        0.2        0.2        0.         0.2       ]\n",
            " [0.         0.33333333 0.         0.         0.33333333 0.33333333]\n",
            " [0.25       0.         0.         0.25       0.25       0.25      ]]\n"
          ]
        }
      ],
      "source": [
        "# compute the degree of each node, which is nothing but the sum of rows of adajcency matrix\n",
        "D = np.sum(adj_loop, axis=1)\n",
        "print(\"Adjacency matrix before\")\n",
        "print(adj_loop)\n",
        "\n",
        "# Normalization of the adjacency matrix based on the number of neighbors (D_inv A_tilde)\n",
        "norm = np.diag(D ** -1) @ adj_loop # (N x N) @ (N x N) -> N x N\n",
        "print(\"Adjacency matrix after\")\n",
        "print(norm)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We observe that after the normalization of adjacency matrix, **all the neighboring nodes with respect to one node has equal importance**."
      ],
      "metadata": {
        "id": "hiUS8k-_QT_s"
      },
      "id": "hiUS8k-_QT_s"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "id": "bcd71701-1af0-4137-9b78-af59b40c7bdb",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 467
        },
        "id": "bcd71701-1af0-4137-9b78-af59b40c7bdb",
        "outputId": "427f041c-f62f-4c36-e9e8-e4d728f34ef0"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# helper code to draw the graph showing node importance\n",
        "\n",
        "# pick the node\n",
        "node = 1\n",
        "\n",
        "# get the normalized values as color\n",
        "color_map = norm[node]\n",
        "\n",
        "# set color to the edges\n",
        "color_edges = []\n",
        "for idx, i in enumerate(norm[node]):\n",
        "    if i > 0.0:\n",
        "        G_loop.edges[(node, idx)]['weight'] = i * 10\n",
        "for k in G_loop.edges.keys():\n",
        "    color_edges.append(G_loop.edges[k]['weight'])\n",
        "\n",
        "# draw the graph\n",
        "pos = nx.circular_layout(G_loop)\n",
        "vmin = min(color_map)\n",
        "vmax = max(color_map)\n",
        "plt.figure(figsize=(6, 4))\n",
        "nx.draw(G_loop, pos, node_color=color_map, width=2,\n",
        "           with_labels=True, vmin=vmin, vmax=vmax, edge_color=color_edges)\n",
        "sm = plt.cm.ScalarMappable(norm=plt.Normalize(vmin = vmin, vmax=vmax))\n",
        "sm._A = []\n",
        "plt.colorbar(sm, ax=plt.gca())\n",
        "plt.title(f\"Graph showing importance of nodes wrt node {node}\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8a10db79-1196-46a6-8022-c08f201e7706",
      "metadata": {
        "id": "8a10db79-1196-46a6-8022-c08f201e7706"
      },
      "source": [
        "### But there is another problem.\n",
        "It's a simple mean of the neighboring nodes and the resultant adjacency matrix is not symmetric in nature. So, here is the **renormalization trick** proposed by Kipf et. al. The equation is as follows:\n",
        "\n",
        "$\\tilde{D}^{\\frac{-1}{2}}\\tilde{A}\\tilde{D}^{\\frac{-1}{2}}$\n",
        "\n",
        "This *renormalization* trick is different and better than the previous one, let's see how. Again, I would love to quote Matthew here:\n",
        "> However, ths begs the question, **why use this alternative normalization approach rather than the more straightforward mean normalization?** It turns out that this alternative normalization approach **<u>normalizes for something beyond how many neighbors each node has, it also normalizes for how many neighbors each neighbor has.</u>**\n",
        "\n",
        ">Let us say we have some node, Node i, with two neighbors: Neighbor 1 and Neighbor 2. Neighbor 1’s only neighbor is i. In contrast, Neighbor 2 is neighbors with many nodes in the graph (including i). Intuitively, because Neighbor 2 has so many neighbors, it has the opportunity to pass its message to more nodes in the graph. In contrast, Neighbor 1 can only pass its message to Node i and thus, its influence on the rest of the graph is dictated by how Node i is passing along its message. We see that Neighbor 1 is sort of “disempowered” relative to Neighbor 2 just based on its location in the graph. Is there some way to compensate for this imbalance? It turns out that the alternative normalization approach (i.e., $\\tilde{D}^{\\frac{-1}{2}}\\tilde{A}\\tilde{D}^{\\frac{-1}{2}}$), does just that!\n",
        "\n",
        "> Recall that the i,j element of $\\tilde{D}^{\\frac{-1}{2}}\\tilde{A}\\tilde{D}^{\\frac{-1}{2}}$ is given by $\\frac{1}{\\sqrt{d_{ii}d_{jj}}}$. **We see that this value will not only be lower if node i has many neighbors, it will also be lower if node j, its neighbor, has many neighbors!** This helps to boost the signal propogated by nodes with few neighbors relative to nodes with many neighbors."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "id": "cec9610d-166c-4ee6-b6b1-010c1279cd99",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cec9610d-166c-4ee6-b6b1-010c1279cd99",
        "outputId": "2e52789c-8f6d-45c7-89b0-a5a0e5b4ea31"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Symmetric Normalization using Renormalization trick\n",
            "[[0.25       0.2236068  0.         0.2236068  0.         0.25      ]\n",
            " [0.2236068  0.2        0.25819889 0.2        0.25819889 0.        ]\n",
            " [0.         0.25819889 0.33333333 0.25819889 0.         0.        ]\n",
            " [0.2236068  0.2        0.25819889 0.2        0.         0.2236068 ]\n",
            " [0.         0.25819889 0.         0.         0.33333333 0.28867513]\n",
            " [0.25       0.         0.         0.2236068  0.28867513 0.25      ]]\n",
            "\n",
            "Mean Normalization\n",
            "[[0.25       0.25       0.         0.25       0.         0.25      ]\n",
            " [0.2        0.2        0.2        0.2        0.2        0.        ]\n",
            " [0.         0.33333333 0.33333333 0.33333333 0.         0.        ]\n",
            " [0.2        0.2        0.2        0.2        0.         0.2       ]\n",
            " [0.         0.33333333 0.         0.         0.33333333 0.33333333]\n",
            " [0.25       0.         0.         0.25       0.25       0.25      ]]\n"
          ]
        }
      ],
      "source": [
        "# renormalization trick from the paper\n",
        "renorm = np.diag(D ** -0.5) @ adj_loop @ np.diag(D ** -0.5) # (N x N) @ (N x N) @ (N x N) -> N x N\n",
        "print(\"Symmetric Normalization using Renormalization trick\")\n",
        "print(renorm)\n",
        "print()\n",
        "print(\"Mean Normalization\")\n",
        "print(norm)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "node = 1\n",
        "print(f\"Graphs showing importance of node wrt node {node}\")\n",
        "plt.figure(figsize=(10, 4))\n",
        "plt.subplot(1, 2, 1)\n",
        "color_map = norm[node]\n",
        "color_edges = []\n",
        "for idx, i in enumerate(norm[node]):\n",
        "    if i > 0.0:\n",
        "        G_loop.edges[(node, idx)]['weight'] = i * 10\n",
        "for k in G_loop.edges.keys():\n",
        "    color_edges.append(G_loop.edges[k]['weight'])\n",
        "pos = nx.circular_layout(G_loop)\n",
        "vmin = min(color_map)\n",
        "vmax = max(color_map)\n",
        "nx.draw(G_loop, pos, node_color=color_map, width=2,\n",
        "           with_labels=True, vmin=vmin, vmax=vmax, edge_color=color_edges)\n",
        "sm = plt.cm.ScalarMappable(norm=plt.Normalize(vmin = vmin, vmax=vmax))\n",
        "sm._A = []\n",
        "plt.colorbar(sm, ax=plt.gca())\n",
        "plt.title(\"Mean Normalization\")\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "color_map = renorm[node]\n",
        "color_edges = []\n",
        "for idx, i in enumerate(renorm[node]):\n",
        "    if i > 0.0:\n",
        "        G_loop.edges[(node, idx)]['weight'] = i * 10\n",
        "for k in G_loop.edges.keys():\n",
        "    color_edges.append(G_loop.edges[k]['weight'])\n",
        "pos = nx.circular_layout(G_loop)\n",
        "vmin = min(color_map)\n",
        "vmax = max(color_map)\n",
        "nx.draw(G_loop, pos, node_color=color_map, width=2,\n",
        "           with_labels=True, vmin=vmin, vmax=vmax, edge_color=color_edges)\n",
        "sm = plt.cm.ScalarMappable(norm=plt.Normalize(vmin = vmin, vmax=vmax))\n",
        "sm._A = []\n",
        "plt.colorbar(sm, ax=plt.gca())\n",
        "plt.title(\"Renormalization Trick\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 392
        },
        "id": "70wCBBXYdV6n",
        "outputId": "65f81142-68dc-4eaa-91ba-46610d010f9f"
      },
      "id": "70wCBBXYdV6n",
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Graphs showing importance of node wrt node 1\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x400 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In mean normalization, we observe that the weights associated with Node 1 are identical for all its neighboring nodes. However, using the renormalization trick with respect to Node 1, Node 2 and Node 4 acquire the highest edge weights since they have only three neighbors (including themselves). Subsequently, Node 0 exhibits slightly lower edge weight as it has four neighbors. In contrast, Nodes 1 and 3 has the least edge weights due to having the highest number of neighboring nodes, each with five."
      ],
      "metadata": {
        "id": "ZE0KDaANV2ru"
      },
      "id": "ZE0KDaANV2ru"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "a2ef3657-52bb-4fc7-8bca-1130aa65d248",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a2ef3657-52bb-4fc7-8bca-1130aa65d248",
        "outputId": "203f5f7b-41da-47e0-b193-ebe3f2b7058c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Message passing using unnormalized adjacency matrix\n",
            "[[-0.81 -0.47 -2.18]\n",
            " [ 1.57 -2.5  -0.93]\n",
            " [-0.96 -0.11 -3.02]\n",
            " [ 2.51 -0.92 -0.69]\n",
            " [ 0.81 -0.23 -0.88]\n",
            " [ 0.37 -1.2  -0.67]]\n",
            "\n",
            "Message passing using renormalized adjacency matrix\n",
            "[[-0.05216253  0.03790325 -0.35279253]\n",
            " [ 0.61435841 -0.62663067 -0.52403285]\n",
            " [ 0.15212907 -0.46173521 -0.86642731]\n",
            " [ 0.26318309 -0.30175686 -0.38267894]\n",
            " [ 0.7103792  -0.59369053 -0.14161498]\n",
            " [ 0.23038294 -0.44438559  0.08377269]]\n"
          ]
        }
      ],
      "source": [
        "# A * X\n",
        "print(\"Message passing using unnormalized adjacency matrix\")\n",
        "print(adj @ x) # (N x N) @ (N x D) -> (N x D)\n",
        "print()\n",
        "\n",
        "# D^(-1/2) * A * D^(-1/2) * X\n",
        "print(\"Message passing using renormalized adjacency matrix\")\n",
        "print(renorm @ x) # (N x N) @ (N x D) -> (N x D)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "42a38bab-d3cb-462a-8b8c-181d42a7dd64",
      "metadata": {
        "id": "42a38bab-d3cb-462a-8b8c-181d42a7dd64"
      },
      "source": [
        "## GCN Layer"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's implement one layer of GCN now."
      ],
      "metadata": {
        "id": "fZNx6u5ySnyi"
      },
      "id": "fZNx6u5ySnyi"
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "id": "bac20765-ab88-4228-8ef0-403c7f7c2d32",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bac20765-ab88-4228-8ef0-403c7f7c2d32",
        "outputId": "0b8e3ec9-f09d-4f9c-e4df-325d390d3983"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Adjacency matrix shape : (6, 6)\n",
            "Feature matrix shape:  (6, 3)\n",
            "Labels [0 1 1 0 0 1]\n",
            "Labels shape (6,)\n"
          ]
        }
      ],
      "source": [
        "np.random.seed(2) # setting up the seed\n",
        "print(\"Adjacency matrix shape :\", adj_loop.shape)\n",
        "print(\"Feature matrix shape: \", x.shape)\n",
        "\n",
        "# create random labels for node classification task\n",
        "y = np.random.randint(low=0, high=2, size=x.shape[0])\n",
        "print(\"Labels\", y)\n",
        "print(\"Labels shape\", y.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "id": "27091e98-38df-4d60-bec4-35679b0a2b7e",
      "metadata": {
        "id": "27091e98-38df-4d60-bec4-35679b0a2b7e"
      },
      "outputs": [],
      "source": [
        "# convert all the numpy tensor to torch tensor\n",
        "x = torch.tensor(x, dtype=torch.float32)\n",
        "y = torch.tensor(y, dtype=torch.long)\n",
        "renorm = torch.tensor(renorm, dtype=torch.float32)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we will implement 2-layer GCN on our sample graph. We will implement the following:\n",
        "\n",
        "$Z = f(X, A) = \\texttt{softmax} \\biggl( \\tilde{A}\\ ReLU\\bigl(\\tilde{A}XW^{(0)}\\bigr)W^{(1)}\\biggr)$\n"
      ],
      "metadata": {
        "id": "awMdTY7fZ1NB"
      },
      "id": "awMdTY7fZ1NB"
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "id": "e5cfed38-a332-4046-9629-f6c7773f4f84",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e5cfed38-a332-4046-9629-f6c7773f4f84",
        "outputId": "4e0510ec-d47f-4e9e-d67c-c0c5186a1103"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[ 0.3726, -0.4049],\n",
            "        [-0.2735, -0.6526],\n",
            "        [ 0.0312, -0.2535]])\n",
            "torch.Size([3, 2])\n",
            "\n",
            "tensor([0.1519, 0.0329])\n",
            "torch.Size([2])\n"
          ]
        }
      ],
      "source": [
        "# Layer 1\n",
        "fixed_generator = torch.Generator().manual_seed(4)\n",
        "output_dim = 2\n",
        "input_dim = x.shape[1]\n",
        "\n",
        "# Trainable parameters\n",
        "w1 = torch.randn(input_dim, output_dim, generator=fixed_generator) # D x W1\n",
        "b1 = torch.randn(output_dim, generator=fixed_generator) # W1 x 1\n",
        "\n",
        "# Glorot uniform initialization\n",
        "stdv = 1. / math.sqrt(w1.shape[1])\n",
        "w1.uniform_(-stdv, stdv, generator=fixed_generator)\n",
        "b1.uniform_(-stdv, stdv, generator=fixed_generator)\n",
        "\n",
        "print(w1)\n",
        "print(w1.shape)\n",
        "print()\n",
        "print(b1)\n",
        "print(b1.shape)\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Layer 1 forward pass\n",
        "\n",
        "# message passing -> D^(-1/2) * A * D^(-1/2) * X\n",
        "message_agg = renorm @ x # (N x N) @ (N x D) -> (N x D)\n",
        "\n",
        "# projection to output dimension -> D^(-1/2) * A * D^(-1/2) * X * W_1\n",
        "z = message_agg @ w1 + b1 # (N x D) @ (D x W1) + (W1 x 1) -> (N x W1)\n",
        "\n",
        "# apply non-linearity\n",
        "z = F.relu(z)\n",
        "\n",
        "print(\"Output of first layer\")\n",
        "print(z)\n",
        "print(z.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wKW3Ib3dMiTE",
        "outputId": "3b4b08a7-968b-4fba-d811-7289f8a66969"
      },
      "id": "wKW3Ib3dMiTE",
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Output of first layer\n",
            "tensor([[0.3379, 0.0000],\n",
            "        [0.4438, 0.0753],\n",
            "        [0.3701, 0.2639],\n",
            "        [0.3544, 0.0000],\n",
            "        [0.3625, 0.0000],\n",
            "        [0.1385, 0.0000]])\n",
            "torch.Size([6, 2])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "id": "b77e634f-a7a1-4d23-b726-e2781f2899d5",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b77e634f-a7a1-4d23-b726-e2781f2899d5",
        "outputId": "44739624-5e35-4a5a-fd1b-45535d818e79"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[-0.6047,  0.2253],\n",
            "        [ 0.3041,  0.1122]])\n",
            "torch.Size([2, 2])\n",
            "\n",
            "tensor([0.6801, 0.2124])\n",
            "torch.Size([2])\n"
          ]
        }
      ],
      "source": [
        "fixed_generator = torch.Generator().manual_seed(5)\n",
        "\n",
        "# Layer 2\n",
        "output_dim = 2\n",
        "input_dim = z.shape[1]\n",
        "\n",
        "# Trainable parameters\n",
        "w2 = torch.randn(input_dim, output_dim, generator=fixed_generator) # W1 x W2\n",
        "b2 = torch.randn(output_dim, generator=fixed_generator) # W2 x 1\n",
        "\n",
        "# Glorot uniform initialization\n",
        "stdv = 1. / math.sqrt(w2.shape[1])\n",
        "w2.uniform_(-stdv, stdv, generator=fixed_generator)\n",
        "b2.uniform_(-stdv, stdv, generator=fixed_generator)\n",
        "\n",
        "print(w2)\n",
        "print(w2.shape)\n",
        "print()\n",
        "print(b2)\n",
        "print(b2.shape)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# layer 2 forward pass\n",
        "\n",
        "# D^(-1/2) * A * D^(-1/2) * z\n",
        "message_agg = renorm @ z # (N x N) @ (N x W1) -> (N x W1)\n",
        "\n",
        "# D^(-1/2) * A * D^(-1/2) * z * W_2\n",
        "out = message_agg @ w2 + b2 # (N x W1) @ (W1 x W2) + (W2 x 1) -> (N x W2)\n",
        "\n",
        "print(\"Output of second layer\")\n",
        "print(out)\n",
        "print(out.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O5BZE4fTMqgx",
        "outputId": "2062f957-6775-409e-b726-e4e5dc50ddd8"
      },
      "id": "O5BZE4fTMqgx",
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Output of second layer\n",
            "tensor([[0.5053, 0.2813],\n",
            "        [0.4488, 0.3173],\n",
            "        [0.5136, 0.2986],\n",
            "        [0.4867, 0.3032],\n",
            "        [0.5195, 0.2766],\n",
            "        [0.4969, 0.2806]])\n",
            "torch.Size([6, 2])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# compute the loss\n",
        "loss = F.cross_entropy(out, y) # same as F.nll_loss(F.log_softmax(out, dim=1), y)\n",
        "print(f\"Loss of the network =\", loss.item())"
      ],
      "metadata": {
        "id": "lfu4_91yT_ea",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "06f137fa-6eba-4e79-ad21-e32bf788d1b3"
      },
      "id": "lfu4_91yT_ea",
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Loss of the network = 0.6911020874977112\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "88e05e7f-635f-4d4f-a97e-3ca0b1308530",
      "metadata": {
        "id": "88e05e7f-635f-4d4f-a97e-3ca0b1308530"
      },
      "source": [
        "## GCN Definition"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's implement a 2-layer GCN properly using classes."
      ],
      "metadata": {
        "id": "cN01L68ckuIP"
      },
      "id": "cN01L68ckuIP"
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "id": "398e05ca-4e01-4058-baca-03fb1300059a",
      "metadata": {
        "id": "398e05ca-4e01-4058-baca-03fb1300059a"
      },
      "outputs": [],
      "source": [
        "# One layer\n",
        "class GCNLayer(nn.Module):\n",
        "    def __init__(self, in_feat, out_feat):\n",
        "        super().__init__()\n",
        "        self.in_feat = in_feat\n",
        "        self.out_feat = out_feat\n",
        "\n",
        "        # trainable parameters\n",
        "        self.projection = nn.Linear(in_feat, out_feat)\n",
        "\n",
        "    def forward(self, x, A_norm):\n",
        "        x = torch.mm(A_norm, x) # message passing, (N x N) @ (N x D) -> (N x D)\n",
        "        x = self.projection(x) # projection, (N x D) @ (D x W) -> (N x W)\n",
        "        return x\n",
        "\n",
        "    def __repr__(self):\n",
        "        return f\"GCNLayer ({self.in_feat} -> {self.out_feat})\"\n",
        "\n",
        "class GCNModel(nn.Module):\n",
        "    def __init__(self, in_feat, num_hidden, nclass, actn, dropout=None):\n",
        "        super().__init__()\n",
        "\n",
        "        # layer initialization\n",
        "        self.gcn_l1 = GCNLayer(in_feat, num_hidden)\n",
        "        self.gcn_l2 = GCNLayer(num_hidden, nclass)\n",
        "\n",
        "        # sometimes people also add a linear layer after the gcn layers. That's optional though. Kipf hasn't done that.\n",
        "        self.dropout = dropout\n",
        "        self.actn = actn\n",
        "\n",
        "    def forward(self, x, A_norm):\n",
        "        x = self.actn(self.gcn_l1(x, A_norm)) # (N x W1)\n",
        "        if self.dropout is not None:\n",
        "            x = F.dropout(x, p=self.dropout, training=self.training)\n",
        "        x = self.gcn_l2(x, A_norm) # (N x W2)\n",
        "        return x"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "533f2844-4f3c-458b-8766-ffe7fd183d5e",
      "metadata": {
        "id": "533f2844-4f3c-458b-8766-ffe7fd183d5e"
      },
      "source": [
        "## Dataset"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We will use the [Cora dataset](https://paperswithcode.com/dataset/cora) for our demonstration purpose. This is one of the dataset used by the author as well. I have taken the dataset implementation from [Geometric Deep Learning Course](https://geometricdeeplearning.com/lectures/) by [Michael M. Bronstein](https://www.imperial.ac.uk/people/m.bronstein), [Joan Bruna](https://cims.nyu.edu/~bruna/), [Taco Cohen](https://tacocohen.wordpress.com/), and [Petar Veličković](https://petar-v.com/). I highly recommend taking this course if you are interested in Geometric Deep Learning."
      ],
      "metadata": {
        "id": "-eZHX2bnmzVM"
      },
      "id": "-eZHX2bnmzVM"
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "id": "4ea40a18-8cfc-4b0b-b9ba-711e70ba0a0b",
      "metadata": {
        "id": "4ea40a18-8cfc-4b0b-b9ba-711e70ba0a0b"
      },
      "outputs": [],
      "source": [
        "class CoraDataset(object):\n",
        "    def __init__(self, split=\"public\"):\n",
        "        super(CoraDataset, self).__init__()\n",
        "        self.cora_pyg = Planetoid(root='/tmp/Cora', name='Cora', split=split)\n",
        "        self.cora_data = self.cora_pyg[0]\n",
        "        self.train_mask = self.cora_data.train_mask\n",
        "        self.valid_mask = self.cora_data.val_mask\n",
        "        self.test_mask = self.cora_data.test_mask\n",
        "\n",
        "    def train_val_test_split(self):\n",
        "        train_x = self.cora_data.x[self.cora_data.train_mask]\n",
        "        train_y = self.cora_data.y[self.cora_data.train_mask]\n",
        "\n",
        "        valid_x = self.cora_data.x[self.cora_data.val_mask]\n",
        "        valid_y = self.cora_data.y[self.cora_data.val_mask]\n",
        "\n",
        "        test_x = self.cora_data.x[self.cora_data.test_mask]\n",
        "        test_y = self.cora_data.y[self.cora_data.test_mask]\n",
        "        return train_x, train_y, valid_x, valid_y, test_x, test_y\n",
        "\n",
        "    def get_fullx(self):\n",
        "        return self.cora_data.x\n",
        "\n",
        "    def get_adjacency_matrix(self):\n",
        "        # We will ignore this for the first part\n",
        "        adj = to_dense_adj(self.cora_data.edge_index)[0]\n",
        "        return adj"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "id": "dbf1c2d7-28d4-409c-8fe9-3bf44d4a78d3",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dbf1c2d7-28d4-409c-8fe9-3bf44d4a78d3",
        "outputId": "39017219-71e9-4486-f784-7672946e1b0f"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.x\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.tx\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.allx\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.y\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.ty\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.ally\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.graph\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.test.index\n",
            "Processing...\n",
            "Done!\n"
          ]
        }
      ],
      "source": [
        "# Lets download the cora dataset and get the splits\n",
        "cora_data = CoraDataset()\n",
        "train_x, train_y, valid_x, valid_y, test_x, test_y = cora_data.train_val_test_split()\n",
        "A = cora_data.get_adjacency_matrix()\n",
        "X = cora_data.get_fullx()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's get the dataset infromation."
      ],
      "metadata": {
        "id": "V-STJIzrqdxa"
      },
      "id": "V-STJIzrqdxa"
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "id": "73a801ee-a982-42dd-a60a-7ca1597b93b8",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "73a801ee-a982-42dd-a60a-7ca1597b93b8",
        "outputId": "ec50a08b-fccf-4554-e128-81c0a3eecfe6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "======================\n",
            "Number of graphs: 1\n",
            "Number of features: 1433\n",
            "Number of classes: 7\n",
            "\n",
            "Number of nodes/samples: 2708\n",
            "Number of edges: 10556\n",
            "Average node degree: 3.90\n",
            "Number of training nodes: 140\n",
            "Training node label rate: 0.05\n",
            "Contains isolated nodes: False\n",
            "Contains self-loops: False\n",
            "Is undirected: True\n",
            "\n",
            "Adjacency Matrix A: torch.Size([2708, 2708])\n",
            "Feature Matrix X: torch.Size([2708, 1433])\n",
            "\n",
            "Train shape x: torch.Size([140, 1433]), y: torch.Size([140])\n",
            "Val shape x: torch.Size([500, 1433]), y: torch.Size([500])\n",
            "Test shape x: torch.Size([1000, 1433]), y: torch.Size([1000])\n",
            "======================\n"
          ]
        }
      ],
      "source": [
        "print('======================')\n",
        "print(f'Number of graphs: {len(cora_data.cora_pyg)}')\n",
        "print(f'Number of features: {cora_data.cora_data.num_features}')\n",
        "print(f'Number of classes: {cora_data.cora_pyg.num_classes}')\n",
        "print()\n",
        "print(f'Number of nodes/samples: {cora_data.cora_data.num_nodes}')\n",
        "print(f'Number of edges: {cora_data.cora_data.num_edges}')\n",
        "print(f'Average node degree: {cora_data.cora_data.num_edges / cora_data.cora_data.num_nodes:.2f}')\n",
        "print(f'Number of training nodes: {cora_data.cora_data.train_mask.sum()}')\n",
        "print(f'Training node label rate: {int(cora_data.cora_data.train_mask.sum()) / cora_data.cora_data.num_nodes:.2f}')\n",
        "print(f'Contains isolated nodes: {cora_data.cora_data.has_isolated_nodes()}')\n",
        "print(f'Contains self-loops: {cora_data.cora_data.has_self_loops()}')\n",
        "print(f'Is undirected: {cora_data.cora_data.is_undirected()}')\n",
        "print()\n",
        "print(f\"Adjacency Matrix A: {A.shape}\")\n",
        "print(f\"Feature Matrix X: {X.shape}\")\n",
        "print()\n",
        "print(f\"Train shape x: {train_x.shape}, y: {train_y.shape}\")\n",
        "print(f\"Val shape x: {valid_x.shape}, y: {valid_y.shape}\")\n",
        "print(f\"Test shape x: {test_x.shape}, y: {test_y.shape}\")\n",
        "print('======================')"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We observe that the Cora dataset comprises a total of 2708 samples or nodes. There are a total of 10556 edges, and each node is characterized by a 1433-dimensional feature vector. Each sample is classified into one of 7 classes. Another point worth noting is that out of the 2708 nodes, only 140 are utilized for training purposes. We will use 500 samples for validation and 1000 samples for testing."
      ],
      "metadata": {
        "id": "C_a2wTMp8P9C"
      },
      "id": "C_a2wTMp8P9C"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Before delving into the training of GCN, let's initially train a basic 2-layer Multi-Layer Perceptron (MLP) to assess performance without incorporating the graph structure."
      ],
      "metadata": {
        "id": "yRZFbss97gSq"
      },
      "id": "yRZFbss97gSq"
    },
    {
      "cell_type": "markdown",
      "id": "b558112f-2806-4c04-954b-43d467990c64",
      "metadata": {
        "id": "b558112f-2806-4c04-954b-43d467990c64"
      },
      "source": [
        "## MLP Definition"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's implement a simple MLP. The code for MLP implementation and training is taken from the [GDL course](https://geometricdeeplearning.com/lectures/)."
      ],
      "metadata": {
        "id": "5lzJvp_-9f9Q"
      },
      "id": "5lzJvp_-9f9Q"
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "id": "df33200d-365a-49e3-beb2-91582d447bef",
      "metadata": {
        "id": "df33200d-365a-49e3-beb2-91582d447bef"
      },
      "outputs": [],
      "source": [
        "class MLP(nn.Module):\n",
        "    def __init__(self, in_feat, num_hidden, nclass):\n",
        "        super().__init__()\n",
        "        self.linear1 = nn.Linear(in_feat, num_hidden)\n",
        "        self.linear2 = nn.Linear(num_hidden, nclass)\n",
        "        self.bn1 = nn.BatchNorm1d(num_hidden)\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = self.bn1(F.relu(self.linear1(x)))\n",
        "        x = F.dropout(x, training=self.training)\n",
        "        x = self.linear2(x)\n",
        "        return x"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "id": "c8ba4484-d5a0-4b01-b409-c244b73ff8a2",
      "metadata": {
        "id": "c8ba4484-d5a0-4b01-b409-c244b73ff8a2"
      },
      "outputs": [],
      "source": [
        "def train_mlp_cora(x, y, model, optimiser):\n",
        "    model.train()\n",
        "    optimiser.zero_grad()\n",
        "    out = model(x)\n",
        "    loss = F.cross_entropy(out, y)\n",
        "    loss.backward()\n",
        "    optimiser.step()\n",
        "    return loss.data\n",
        "\n",
        "def evaluate_mlp_cora(x, y, model):\n",
        "    model.eval()\n",
        "    out = model(x)\n",
        "    out = out.data.max(1)[1]\n",
        "    num_correct = out.eq(y.data).sum()\n",
        "    num_total = len(y)\n",
        "    accuracy = 100.0 * (num_correct/num_total)\n",
        "    return accuracy\n",
        "\n",
        "def train_eval_loop(model, train_x, train_y, valid_x, valid_y, test_x, test_y):\n",
        "    training_stats = []\n",
        "    optimiser = optim.Adam(model.parameters(), lr=LR)\n",
        "\n",
        "    for epoch in range(NUM_EPOCHS):\n",
        "        train_loss = train_mlp_cora(train_x, train_y, model, optimiser)\n",
        "        train_acc = evaluate_mlp_cora(train_x, train_y, model)\n",
        "        valid_acc = evaluate_mlp_cora(valid_x, valid_y, model)\n",
        "        if epoch % 10 == 0:\n",
        "            print(f\"Epoch {epoch} with train loss: {train_loss:.3f} train accuracy: {train_acc:.3f}\",\n",
        "                    f\"validation accuracy: {valid_acc:.3f}\")\n",
        "        training_stats.append([train_acc.detach().cpu(), valid_acc.detach().cpu(), epoch])\n",
        "\n",
        "    test_acc = evaluate_mlp_cora(test_x, test_y, model)\n",
        "    print(f\"Our final test accuracy for the MLP is: {test_acc:.3f}\")\n",
        "    return training_stats\n",
        "\n",
        "def plot_stats(training_stats, model_name):\n",
        "    ts = np.array(training_stats)\n",
        "    epochs = ts[:, 2]\n",
        "    train_acc = ts[:, 0]\n",
        "    val_acc = ts[:, 1]\n",
        "\n",
        "    plt.plot(epochs, train_acc, 'go-', label='Training Accuracy', linewidth=2)\n",
        "    plt.plot(epochs, val_acc, 'bo--', label='Validation Accuracy')\n",
        "    plt.xlabel(f'Epochs')\n",
        "    plt.ylabel(f'Accuracy')\n",
        "    plt.title(f\"Performance of {model_name}\")\n",
        "    plt.legend()\n",
        "    plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Initialize the device\n",
        "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
        "print(device)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "okddEZW8Lx_v",
        "outputId": "5af63e0e-5673-482f-a84b-664d7c603105"
      },
      "id": "okddEZW8Lx_v",
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cuda\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "NUM_EPOCHS = 101\n",
        "LR = 0.01"
      ],
      "metadata": {
        "id": "ejjMcCTfUHDa"
      },
      "id": "ejjMcCTfUHDa",
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5592b84e-75c2-47c0-96d8-0ee4731b6c39",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "5592b84e-75c2-47c0-96d8-0ee4731b6c39",
        "outputId": "067e9699-8de4-4b9f-98b8-0916ef61b2f8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0 with train loss: 2.192 train accuracy: 27.143 validation accuracy: 17.600\n",
            "Epoch 10 with train loss: 0.863 train accuracy: 99.286 validation accuracy: 48.200\n",
            "Epoch 20 with train loss: 0.394 train accuracy: 100.000 validation accuracy: 52.000\n",
            "Epoch 30 with train loss: 0.298 train accuracy: 100.000 validation accuracy: 53.000\n",
            "Epoch 40 with train loss: 0.157 train accuracy: 100.000 validation accuracy: 52.800\n",
            "Epoch 50 with train loss: 0.102 train accuracy: 100.000 validation accuracy: 52.600\n",
            "Epoch 60 with train loss: 0.108 train accuracy: 100.000 validation accuracy: 53.200\n",
            "Epoch 70 with train loss: 0.101 train accuracy: 100.000 validation accuracy: 53.000\n",
            "Epoch 80 with train loss: 0.079 train accuracy: 100.000 validation accuracy: 52.800\n",
            "Epoch 90 with train loss: 0.051 train accuracy: 100.000 validation accuracy: 52.200\n",
            "Epoch 100 with train loss: 0.070 train accuracy: 100.000 validation accuracy: 51.400\n",
            "Our final test accuracy for the MLP is: 53.300\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# training simple 2-layer MLP\n",
        "model = MLP(train_x.shape[-1], 16, 7).to(device)\n",
        "train_x = train_x.to(device)\n",
        "train_y = train_y.to(device)\n",
        "valid_x = valid_x.to(device)\n",
        "valid_y = valid_y.to(device)\n",
        "test_x = test_x.to(device)\n",
        "test_y = test_y.to(device)\n",
        "# Run training loop\n",
        "train_stats_mlp_cora = train_eval_loop(model, train_x, train_y, valid_x, valid_y, test_x, test_y)\n",
        "plot_stats(train_stats_mlp_cora, \"MLP_Cora\")"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Semi-supervised learning: Transductive vs Inductive\n",
        "\n",
        "We will use the **entire adjacency and node feature matrix each time we call the GCNLayer** as opposed to the specific subsets of the train/validation/test we did earlier with the MLP. This is **because nodes from the different splits share edges with those from the other splits and building our representation requires these.** **Hence, the learning performed with our GCNLayer is an instance of transductive semi-supervised learning as the model gets to see all of the observations in the dataset.** This is different to the inductive learning performed on the MLP where the model only sees the train observations during training and only sees validation/test observations for prediction. It is important to note that despite the model using all of the observations and entire adjacency matrix it does not use all of the targets!"
      ],
      "metadata": {
        "id": "W8qEoOQzYfHl"
      },
      "id": "W8qEoOQzYfHl"
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "id": "0aed045b-101c-41c9-a3a6-1078964cd14d",
      "metadata": {
        "id": "0aed045b-101c-41c9-a3a6-1078964cd14d"
      },
      "outputs": [],
      "source": [
        "def train_gnn_cora(A_norm, X, y, mask, model, optimiser):\n",
        "    model.train()\n",
        "    optimiser.zero_grad()\n",
        "    out = model(X, A_norm)[mask] # only using the train samples to calculate the loss\n",
        "    loss = F.cross_entropy(out, y) # this kind of learning is called transductive learning.\n",
        "    loss.backward()\n",
        "    optimiser.step()\n",
        "    return loss.item()\n",
        "\n",
        "def evaluate_gnn_cora(A_norm, X, y, mask, model):\n",
        "    model.eval()\n",
        "    out = model(X, A_norm)[mask]\n",
        "    out = out.data.max(1)[1]\n",
        "    num_correct = out.eq(y.data).sum()\n",
        "    num_total = len(y)\n",
        "    accuracy = 100.0 * (num_correct/num_total)\n",
        "    return accuracy\n",
        "\n",
        "def train_eval_loop_gnn_cora(model, A_norm, train_x, train_y, train_mask,\n",
        "                        valid_x, valid_y, valid_mask,\n",
        "                        test_x, test_y, test_mask\n",
        "                    ):\n",
        "    optimiser = optim.Adam(model.parameters(), lr=LR, weight_decay=5e-4)\n",
        "    training_stats = []\n",
        "    # Training loop\n",
        "    for epoch in range(NUM_EPOCHS):\n",
        "        train_loss = train_gnn_cora(A_norm, train_x, train_y, train_mask, model, optimiser)\n",
        "        train_acc = evaluate_gnn_cora(A_norm, train_x, train_y, train_mask, model)\n",
        "        valid_acc = evaluate_gnn_cora(A_norm, valid_x, valid_y, valid_mask, model)\n",
        "        if epoch % 10 == 0:\n",
        "            print(f\"Epoch {epoch} with train loss: {train_loss:.3f} train accuracy: {train_acc:.3f} validation accuracy: {valid_acc:.3f}\")\n",
        "\n",
        "        training_stats.append([train_acc.detach().cpu(), valid_acc.detach().cpu(), epoch])\n",
        "\n",
        "    test_acc = evaluate_gnn_cora(A_norm, test_x, test_y, test_mask, model)\n",
        "    print(f\"Our final test accuracy for the GCN is: {test_acc:.3f}\")\n",
        "    return training_stats"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e2af80bc-0e77-43e1-9794-53f3d857efaa",
      "metadata": {
        "id": "e2af80bc-0e77-43e1-9794-53f3d857efaa"
      },
      "outputs": [],
      "source": [
        "# get the adjacency matrix\n",
        "A = cora_data.get_adjacency_matrix().to(device) # (2708 x 2708)\n",
        "\n",
        "# get the feature matrix\n",
        "X = cora_data.get_fullx().to(device) # (2708 x 1433)\n",
        "\n",
        "# add self loop\n",
        "A = A + torch.eye(A.shape[0]).to(device) # (2708 x 2708)\n",
        "\n",
        "# apply renormalization trick\n",
        "D = torch.sum(A, dim=1) # (2708 x 1)\n",
        "A_norm = torch.diag(D ** (-1/2)) @ A @ torch.diag(D ** (-1/2)) # (2708 x 2708)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "27b3abff-c954-4a0b-8182-f3825b206a89",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "27b3abff-c954-4a0b-8182-f3825b206a89",
        "outputId": "d33df48a-d816-4482-8c4e-666851f269da"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0 with train loss: 1.959 train accuracy: 30.714 validation accuracy: 14.600\n",
            "Epoch 10 with train loss: 1.056 train accuracy: 95.000 validation accuracy: 71.000\n",
            "Epoch 20 with train loss: 0.391 train accuracy: 99.286 validation accuracy: 77.000\n",
            "Epoch 30 with train loss: 0.134 train accuracy: 100.000 validation accuracy: 79.400\n",
            "Epoch 40 with train loss: 0.086 train accuracy: 100.000 validation accuracy: 78.600\n",
            "Epoch 50 with train loss: 0.065 train accuracy: 100.000 validation accuracy: 78.400\n",
            "Epoch 60 with train loss: 0.056 train accuracy: 100.000 validation accuracy: 77.600\n",
            "Epoch 70 with train loss: 0.063 train accuracy: 100.000 validation accuracy: 78.000\n",
            "Epoch 80 with train loss: 0.048 train accuracy: 100.000 validation accuracy: 77.200\n",
            "Epoch 90 with train loss: 0.050 train accuracy: 100.000 validation accuracy: 77.400\n",
            "Epoch 100 with train loss: 0.056 train accuracy: 100.000 validation accuracy: 77.000\n",
            "Our final test accuracy for the GCN is: 80.900\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# create a 2-layer GCN model where hidden layer feature has 16-dimensions.\n",
        "# These numbers are taken from the paper.\n",
        "model = GCNModel(in_feat=train_x.shape[-1], num_hidden=16, nclass=7, actn=F.relu, dropout=0.5).to(device)\n",
        "\n",
        "train_y = train_y.to(device)\n",
        "valid_y = valid_y.to(device)\n",
        "test_y = test_y.to(device)\n",
        "\n",
        "train_mask = cora_data.train_mask.to(device)\n",
        "valid_mask = cora_data.valid_mask.to(device)\n",
        "test_mask = cora_data.test_mask.to(device)\n",
        "\n",
        "# we are passing full features instead of just training features.\n",
        "train_stats_gnn_cora = train_eval_loop_gnn_cora(model, A_norm, X, train_y, train_mask,\n",
        "                                          X, valid_y, valid_mask,\n",
        "                                          X, test_y, test_mask\n",
        "                                       )\n",
        "plot_stats(train_stats_gnn_cora, model_name=\"GCN Cora\")"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Node Embeddings With Random Weights\n",
        "Untrained GCN model with random weights can serve as a powerful feature extractor for nodes in a graph. We will implement the following GCN model:\n",
        "\n",
        "$Z = \\texttt{tanh} \\biggl(\\tilde{A}\\ \\texttt{tanh} \\bigl( \\tilde{A}\\ \\texttt{tanh} \\bigl(\\tilde{A}XW^{(0)} \\bigr)W^{(1)}\\bigr)W^{(2)}\\biggr)$\n",
        "\n",
        "We are going to use the [Zachary Karate Club Dataset](http://konect.cc/networks/ucidata-zachary/) which has 34 nodes connected by 156 (undirected and unweighted) edges. Every node is labeled by one of four classes. Now, we will start with the feature matrix $X = I_N$ ($N \\times N$ identity matrix) where $N$ being number of nodes. Let's create the graph and get all the information."
      ],
      "metadata": {
        "id": "KnlcfE7HHhBq"
      },
      "id": "KnlcfE7HHhBq"
    },
    {
      "cell_type": "code",
      "source": [
        "dataset = KarateClub()\n",
        "data = dataset[0]\n",
        "adj_karate = to_dense_adj(data.edge_index)[0]\n",
        "x_karate = data.x # Identity matrix of 34 x 34\n",
        "\n",
        "train_x_karate = data.x[data.train_mask]\n",
        "train_y_karate = data.y[data.train_mask]\n",
        "\n",
        "print('======================')\n",
        "print(f'Number of graphs: {len(dataset)}')\n",
        "print(f'Number of features: {data.num_features}')\n",
        "print(f'Number of classes: {dataset.num_classes}')\n",
        "print()\n",
        "print(f'Number of nodes/samples: {data.num_nodes}')\n",
        "print(f'Number of edges: {data.num_edges}')\n",
        "print(f'Average node degree: {data.num_edges / data.num_nodes:.2f}')\n",
        "print(f'Number of training nodes: {data.train_mask.sum()}')\n",
        "print(f'Training node label rate: {int(data.train_mask.sum()) / data.num_nodes:.2f}')\n",
        "print(f'Contains isolated nodes: {data.has_isolated_nodes()}')\n",
        "print(f'Contains self-loops: {data.has_self_loops()}')\n",
        "print(f'Is undirected: {data.is_undirected()}')\n",
        "print()\n",
        "print(f\"Adjacency Matrix A: {adj_karate.shape}\")\n",
        "print(f\"Feature Matrix X: {x_karate.shape}\")\n",
        "print()\n",
        "print(f\"Train shape x: {train_x_karate.shape}, y: {train_y_karate.shape}\")\n",
        "print('======================')\n",
        "\n",
        "# plot the network\n",
        "G_karate = nx.karate_club_graph()\n",
        "cmap = {0:'c', 1:'b', 2:'g', 3:'r'}\n",
        "color = [cmap[c] for c in data.y.numpy().tolist()]\n",
        "plt.figure(figsize=(5, 4))\n",
        "nx.draw_spring(G_karate, with_labels=False, node_size=80, font_size=10, font_color='black', node_color=color,\n",
        "              cmap='hsv', edge_color='grey', vmin=-2, vmax=3, width=0.8)\n",
        "plt.title(\"Karate Club Graph\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 836
        },
        "id": "lkAb2cTDRTnN",
        "outputId": "9765af41-f5e3-45a0-d440-e56062cea190"
      },
      "id": "lkAb2cTDRTnN",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "======================\n",
            "Number of graphs: 1\n",
            "Number of features: 34\n",
            "Number of classes: 4\n",
            "\n",
            "Number of nodes/samples: 34\n",
            "Number of edges: 156\n",
            "Average node degree: 4.59\n",
            "Number of training nodes: 4\n",
            "Training node label rate: 0.12\n",
            "Contains isolated nodes: False\n",
            "Contains self-loops: False\n",
            "Is undirected: True\n",
            "\n",
            "Adjacency Matrix A: torch.Size([34, 34])\n",
            "Feature Matrix X: torch.Size([34, 34])\n",
            "\n",
            "Train shape x: torch.Size([4, 34]), y: torch.Size([4])\n",
            "======================\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/networkx/drawing/nx_pylab.py:437: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap', 'vmin', 'vmax' will be ignored\n",
            "  node_collection = ax.scatter(\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's construct the 3-layer GCN model as discussed for this task. Following the paper's recommendations, we will employ 4-dimensional hidden layers and a 2-dimensional output layer for direct plotting and visualization of the outputs. At this stage, we won't be training the GCN model; instead, we'll perform a single forward pass of the input data to obtain the node features. Additionally, I'm making a slight modification to the GCN implementation: given the highly random weights initialization and the absence of training, I am introducing batch normalization between the GCN layers to ensure the activations follow a specific distribution."
      ],
      "metadata": {
        "id": "bR33WieOTMkf"
      },
      "id": "bR33WieOTMkf"
    },
    {
      "cell_type": "code",
      "source": [
        "# define the 3-layer GCN model\n",
        "class GCNModel_karate(nn.Module):\n",
        "    def __init__(self, in_feat, num_hidden, nclass, actn, dropout=True):\n",
        "        super().__init__()\n",
        "        self.gcn_l1 = GCNLayer(in_feat, num_hidden)\n",
        "        self.gcn_l2 = GCNLayer(num_hidden, num_hidden)\n",
        "        self.gcn_l3 = GCNLayer(num_hidden, nclass)\n",
        "        self.bn1 = nn.BatchNorm1d(num_hidden)\n",
        "        self.bn2 = nn.BatchNorm1d(num_hidden)\n",
        "\n",
        "        self.dropout = dropout\n",
        "        self.actn = actn\n",
        "\n",
        "    def forward(self, x, A_norm):\n",
        "        x = self.bn1(self.actn(self.gcn_l1(x, A_norm)))\n",
        "        x = self.bn2(self.actn(self.gcn_l2(x, A_norm)))\n",
        "        x = self.actn(self.gcn_l3(x, A_norm))\n",
        "        return x\n",
        "\n",
        "# add self loop to the adjacency matrix\n",
        "adj_karate_loop = adj_karate + torch.eye(adj_karate.shape[0])\n",
        "\n",
        "# get the degree matrix\n",
        "D_karate = torch.sum(adj_karate_loop, dim=1)\n",
        "\n",
        "# renormalize the adjacency matrix\n",
        "adj_karate_norm = torch.diag(D_karate ** -0.5) @ adj_karate_loop @ torch.diag(D_karate ** -0.5)"
      ],
      "metadata": {
        "id": "vwBcHJCdRfvD"
      },
      "id": "vwBcHJCdRfvD",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# create the GCN model with 4-dimensional hidden layers and 2-dimensional output layer\n",
        "model_karate = GCNModel_karate(in_feat=34, num_hidden=4, nclass=2, actn=F.tanh, dropout=False)\n",
        "\n",
        "# print the model\n",
        "print(model_karate)\n",
        "model_karate.train()\n",
        "\n",
        "# lets do just a forward pass and get the outputs from the model\n",
        "out = model_karate(x_karate, adj_karate_norm)\n",
        "out_numpy = out.detach().numpy()\n",
        "\n",
        "# plot the 2-dimensional outputs with the node labels depicted in colors\n",
        "plt.scatter(out_numpy[:, 0], out_numpy[:, 1], c=color)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 549
        },
        "id": "L2Sq_uv1Rj_M",
        "outputId": "de1fbfd8-6d0d-4629-826e-eb8870ea83cd"
      },
      "id": "L2Sq_uv1Rj_M",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GCNModel_karate(\n",
            "  (gcn_l1): GCNLayer (34 -> 4)\n",
            "  (gcn_l2): GCNLayer (4 -> 4)\n",
            "  (gcn_l3): GCNLayer (4 -> 2)\n",
            "  (bn1): BatchNorm1d(4, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
            "  (bn2): BatchNorm1d(4, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
            ")\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "This illustrates the effectiveness of GCN. It's evident that a single pass through the GCN model, even with an untrained model and features set to an identity matrix, can generate embeddings that readily form distinguishable clusters corresponding to their classes. The model captures meaningful representations through the relationships between the samples."
      ],
      "metadata": {
        "id": "cDrr_6n6ZjIi"
      },
      "id": "cDrr_6n6ZjIi"
    },
    {
      "cell_type": "markdown",
      "source": [
        "## GCN Variants\n",
        "Next we will implement all the GCN variants mentioned in the paper. These variants are defined as follows:\n",
        "- Single Parameter Model - $(I_N + D^{\\frac{-1}{2}}AD^{\\frac{-1}{2}})XΘ$\n",
        "- 1st Order term only - $(D^{\\frac{-1}{2}}AD^{\\frac{-1}{2}})XΘ$\n",
        "- 1st order model - $XΘ_0 + (D^{\\frac{-1}{2}}AD^{\\frac{-1}{2}})XΘ_1$\n",
        "- Chebyshev Polynomials - $\\sum_{k=0}^KT_k(\\tilde{L})X\\theta_k$ for k = 2"
      ],
      "metadata": {
        "id": "kNRfw6CPbgud"
      },
      "id": "kNRfw6CPbgud"
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Single Parameter model\n",
        "This model is defined as follows:\n",
        "\n",
        "$(I_N + D^{\\frac{-1}{2}}AD^{\\frac{-1}{2}})XΘ$\n",
        "\n"
      ],
      "metadata": {
        "id": "klddX7jYo_l1"
      },
      "id": "klddX7jYo_l1"
    },
    {
      "cell_type": "code",
      "source": [
        "A = cora_data.get_adjacency_matrix().to(device)\n",
        "X = cora_data.get_fullx().to(device)\n",
        "\n",
        "# implement the adjacency part of the variant here.\n",
        "D = torch.sum(A, dim=1)\n",
        "I = torch.eye(A.shape[0]).to(device)\n",
        "A_norm = I + (torch.diag(D ** (-1/2)) @ A @ torch.diag(D ** (-1/2)))"
      ],
      "metadata": {
        "id": "XKmPaaAio25e"
      },
      "id": "XKmPaaAio25e",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model = GCNModel(in_feat=train_x.shape[-1], num_hidden=16, nclass=7, actn=F.relu, dropout=0.5).to(device)\n",
        "\n",
        "train_y = train_y.to(device)\n",
        "valid_y = valid_y.to(device)\n",
        "test_y = test_y.to(device)\n",
        "\n",
        "train_mask = cora_data.train_mask.to(device)\n",
        "valid_mask = cora_data.valid_mask.to(device)\n",
        "test_mask = cora_data.test_mask.to(device)\n",
        "\n",
        "train_stats_gnn_cora = train_eval_loop_gnn_cora(model, A_norm, X, train_y, train_mask,\n",
        "                                          X, valid_y, valid_mask,\n",
        "                                          X, test_y, test_mask\n",
        "                                       )\n",
        "plot_stats(train_stats_gnn_cora, model_name=\"GCN Cora Single Parameter\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "ppVqhJ8qo7UA",
        "outputId": "3dd060d4-72ea-4495-db2d-a0cbb8fab6e5"
      },
      "id": "ppVqhJ8qo7UA",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0 with train loss: 1.964 train accuracy: 60.714 validation accuracy: 38.400\n",
            "Epoch 10 with train loss: 0.354 train accuracy: 100.000 validation accuracy: 75.000\n",
            "Epoch 20 with train loss: 0.054 train accuracy: 100.000 validation accuracy: 78.200\n",
            "Epoch 30 with train loss: 0.041 train accuracy: 100.000 validation accuracy: 76.800\n",
            "Epoch 40 with train loss: 0.040 train accuracy: 100.000 validation accuracy: 77.000\n",
            "Epoch 50 with train loss: 0.020 train accuracy: 100.000 validation accuracy: 76.200\n",
            "Epoch 60 with train loss: 0.036 train accuracy: 100.000 validation accuracy: 76.400\n",
            "Epoch 70 with train loss: 0.017 train accuracy: 100.000 validation accuracy: 77.200\n",
            "Epoch 80 with train loss: 0.031 train accuracy: 100.000 validation accuracy: 77.200\n",
            "Epoch 90 with train loss: 0.025 train accuracy: 100.000 validation accuracy: 77.000\n",
            "Epoch 100 with train loss: 0.017 train accuracy: 100.000 validation accuracy: 77.000\n",
            "Our final test accuracy for the GCN is: 79.800\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1st order term only\n",
        "This model is defined as follows:\n",
        "\n",
        "$(D^{\\frac{-1}{2}}AD^{\\frac{-1}{2}})XΘ$"
      ],
      "metadata": {
        "id": "8L6F_KuGrum5"
      },
      "id": "8L6F_KuGrum5"
    },
    {
      "cell_type": "code",
      "source": [
        "A = cora_data.get_adjacency_matrix().to(device)\n",
        "X = cora_data.get_fullx().to(device)\n",
        "\n",
        "# implement the adjacency part of the variant here.\n",
        "D = torch.sum(A, dim=1)\n",
        "A_norm = torch.diag(D ** (-1/2)) @ A @ torch.diag(D ** (-1/2))"
      ],
      "metadata": {
        "id": "BZLtMnIlsATz"
      },
      "id": "BZLtMnIlsATz",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model = GCNModel(in_feat=train_x.shape[-1], num_hidden=16, nclass=7, actn=F.relu, dropout=0.5).to(device)\n",
        "\n",
        "train_y = train_y.to(device)\n",
        "valid_y = valid_y.to(device)\n",
        "test_y = test_y.to(device)\n",
        "\n",
        "train_mask = cora_data.train_mask.to(device)\n",
        "valid_mask = cora_data.valid_mask.to(device)\n",
        "test_mask = cora_data.test_mask.to(device)\n",
        "\n",
        "train_stats_gnn_cora = train_eval_loop_gnn_cora(model, A_norm, X, train_y, train_mask,\n",
        "                                          X, valid_y, valid_mask,\n",
        "                                          X, test_y, test_mask\n",
        "                                       )\n",
        "plot_stats(train_stats_gnn_cora, model_name=\"GCN Cora 1st order term only\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "7R0cB1M8sCzT",
        "outputId": "ba9ff5b6-959f-45f6-8f4a-9ee2df3e99fe"
      },
      "id": "7R0cB1M8sCzT",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0 with train loss: 1.952 train accuracy: 29.286 validation accuracy: 35.600\n",
            "Epoch 10 with train loss: 1.145 train accuracy: 96.429 validation accuracy: 69.600\n",
            "Epoch 20 with train loss: 0.487 train accuracy: 98.571 validation accuracy: 78.400\n",
            "Epoch 30 with train loss: 0.241 train accuracy: 100.000 validation accuracy: 76.000\n",
            "Epoch 40 with train loss: 0.146 train accuracy: 100.000 validation accuracy: 75.800\n",
            "Epoch 50 with train loss: 0.155 train accuracy: 100.000 validation accuracy: 76.400\n",
            "Epoch 60 with train loss: 0.097 train accuracy: 100.000 validation accuracy: 77.800\n",
            "Epoch 70 with train loss: 0.060 train accuracy: 100.000 validation accuracy: 76.600\n",
            "Epoch 80 with train loss: 0.082 train accuracy: 100.000 validation accuracy: 78.200\n",
            "Epoch 90 with train loss: 0.060 train accuracy: 100.000 validation accuracy: 76.400\n",
            "Epoch 100 with train loss: 0.089 train accuracy: 100.000 validation accuracy: 78.000\n",
            "Our final test accuracy for the GCN is: 78.900\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1st order model\n",
        "This model is defined as follows:\n",
        "\n",
        "$XΘ_0 + (D^{\\frac{-1}{2}}AD^{\\frac{-1}{2}})XΘ_1$"
      ],
      "metadata": {
        "id": "VSqIhe4ftXu8"
      },
      "id": "VSqIhe4ftXu8"
    },
    {
      "cell_type": "code",
      "source": [
        "class GCNLayer1stOrderModel(nn.Module):\n",
        "    def __init__(self, in_feat, out_feat):\n",
        "        super().__init__()\n",
        "        self.in_feat = in_feat\n",
        "        self.out_feat = out_feat\n",
        "\n",
        "        self.projection1 = nn.Linear(in_feat, out_feat)\n",
        "        self.projection2 = nn.Linear(in_feat, out_feat)\n",
        "\n",
        "    def forward(self, x, A_norm):\n",
        "        first_term = self.projection1(x) # X @ W0\n",
        "        x = torch.mm(A_norm, x) # message passing\n",
        "        x = first_term + self.projection2(x) # projection\n",
        "        return x\n",
        "\n",
        "    def __repr__(self):\n",
        "        return f\"GCNLayer ({self.in_feat} -> {self.out_feat})\"\n",
        "\n",
        "class GCNModel1stOrderModel(nn.Module):\n",
        "    def __init__(self, in_feat, num_hidden, nclass, actn, dropout=None):\n",
        "        super().__init__()\n",
        "        self.gcn_l1 = GCNLayer1stOrderModel(in_feat, num_hidden)\n",
        "        self.gcn_l2 = GCNLayer1stOrderModel(num_hidden, nclass)\n",
        "\n",
        "        self.dropout = dropout\n",
        "        self.actn = actn\n",
        "\n",
        "    def forward(self, x, A_norm):\n",
        "        x = self.actn(self.gcn_l1(x, A_norm))\n",
        "        if self.dropout is not None:\n",
        "            x = F.dropout(x, p=self.dropout, training=self.training)\n",
        "        x = self.gcn_l2(x, A_norm)\n",
        "        return x"
      ],
      "metadata": {
        "id": "chj96WpWtVI1"
      },
      "id": "chj96WpWtVI1",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "A = cora_data.get_adjacency_matrix().to(device)\n",
        "X = cora_data.get_fullx().to(device)\n",
        "\n",
        "D = torch.sum(A, dim=1)\n",
        "A_norm = torch.diag(D ** (-1/2)) @ A @ torch.diag(D ** (-1/2))"
      ],
      "metadata": {
        "id": "yTHPUw-9ulZG"
      },
      "id": "yTHPUw-9ulZG",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model = GCNModel1stOrderModel(in_feat=train_x.shape[-1], num_hidden=16, nclass=7, actn=F.relu, dropout=0.5).to(device)\n",
        "\n",
        "train_y = train_y.to(device)\n",
        "valid_y = valid_y.to(device)\n",
        "test_y = test_y.to(device)\n",
        "\n",
        "train_mask = cora_data.train_mask.to(device)\n",
        "valid_mask = cora_data.valid_mask.to(device)\n",
        "test_mask = cora_data.test_mask.to(device)\n",
        "\n",
        "train_stats_gnn_cora = train_eval_loop_gnn_cora(model, A_norm, X, train_y, train_mask,\n",
        "                                          X, valid_y, valid_mask,\n",
        "                                          X, test_y, test_mask\n",
        "                                       )\n",
        "plot_stats(train_stats_gnn_cora, model_name=\"GCN Cora 1st order model\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "PILuqerRunsd",
        "outputId": "ef86b96a-8b5c-4a1c-a2c9-cb574cf11082"
      },
      "id": "PILuqerRunsd",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0 with train loss: 1.977 train accuracy: 31.429 validation accuracy: 35.000\n",
            "Epoch 10 with train loss: 0.409 train accuracy: 100.000 validation accuracy: 76.400\n",
            "Epoch 20 with train loss: 0.075 train accuracy: 100.000 validation accuracy: 74.000\n",
            "Epoch 30 with train loss: 0.022 train accuracy: 100.000 validation accuracy: 76.000\n",
            "Epoch 40 with train loss: 0.014 train accuracy: 100.000 validation accuracy: 76.200\n",
            "Epoch 50 with train loss: 0.020 train accuracy: 100.000 validation accuracy: 76.600\n",
            "Epoch 60 with train loss: 0.024 train accuracy: 100.000 validation accuracy: 77.000\n",
            "Epoch 70 with train loss: 0.016 train accuracy: 100.000 validation accuracy: 76.800\n",
            "Epoch 80 with train loss: 0.036 train accuracy: 100.000 validation accuracy: 77.400\n",
            "Epoch 90 with train loss: 0.027 train accuracy: 100.000 validation accuracy: 76.800\n",
            "Epoch 100 with train loss: 0.026 train accuracy: 100.000 validation accuracy: 77.400\n",
            "Our final test accuracy for the GCN is: 79.500\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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FVlZWqF+/vtZ2b29vuLm54cqVK1rbg4KCSj1XnTp1tJ5rfjEX7V+i2a5SqZCdnY2aNWsCAA4ePIgpU6bg0KFDuHfvntbx2dnZWr/ki18HAGrUqKHVJ+HSpUuIiYkpNVZAfV/Pnz8v9cEoTtOxWBfNfWnQoEGJfSEhIThw4ECZ19ZFkzzk5eWV2Pf5558jNzcXmZmZGDhwoLTdxcUFgPrDvzI6dOiAp59+GnPnzsXIkSP1fp2Li4ve1yztXtna2qJu3bol3mOlvX///PNPTJo0CXv27JE+GDWKJ8SVFRkZiZiYGEybNg3z589Hx44d0bt3b7z00ktQKBSVOueVK1e0EgGN0NBQaX/jxo2l7cV/xjT3R9fPf4MGDXDy5Enp+cWLF5GdnQ1PT0+dsRR/T5f186yLn59fiflqXF1ddf6MA5B+Jm/cuIF79+7p/HkJDQ2FSqVCamoqGjVqVOr9Kv7aixcvAvivf2Nxmp8NMh4mO1RhTz31lDQaqziVSgWZTIYdO3ZALpeX2F+8JaAyoyn0nXCrrHPriq2s7UIIAOrEpHPnzggJCcG8efPg7+8PW1tb/PTTT5g/f36JjonlnU9fKpUKTZo0wbx583TuL/4L3NhcXV3h4+NTYuQU8N9fysUnVKtfvz6sra1x5syZSl93ypQp6NixIz7//HO9RowB6oQuKSkJBQUFBp/GQNd7LCsrC5GRkXBxccGHH36IevXqwc7ODidPnsQ777xTaufVipLJZNiyZQsOHz6M77//Hrt27cLQoUPx6aef4vDhwzpb3QztUUZDqVQqeHp6Yt26dTr3F0/sK3qtyv6MG4Pme7527Vqdnc+trflRbGy8w2RQ9erVgxACQUFBeOKJJwx67oCAAKhUKly8eFH6SxNQTxaXlZWlNZeLsXz//ffIz8/H9u3btVptHqUZul69ejqThuLHnD59Gp07d67w7Kqa+3LhwoUSf1leuHCh0vetR48e+OKLL3D06FGtZvzSODg4oFOnTtizZw9SU1MrlaBFRkaiY8eOmDNnDj744AO9XtOzZ08cOnQI3377bblTIxS9V0VLGAUFBUhOTtZr7qF9+/bh1q1bSEhIQIcOHaTtRUcrGlKbNm3Qpk0bzJw5E+vXr8eAAQOwceNGvPLKK5V6r1y4cKHEdk3prbz3ima/piWjqOLnrVevHn755Re0a9euSg0h9/DwgIODQ6n3wcrKSnrvBgQE6P21AoCnp6de7yEyPPbZIYOKjo6GXC7HtGnTSvylJITArVu3Kn3u7t27AwAWLFigtV3T2tGjR49Kn1tfmr8Ki35t2dnZiI+Pr/Q5Y2JicPr0aZ3DczXX6devH9LS0nTOB3P//n3cvXu31PO3bNkSnp6eWL58udYw9R07duD8+fOVvm8TJkyAg4MDhg4dqnMGbV1/KU+ZMgVCCLz88ss6S2AnTpzAmjVryryupu/OihUr9Ipz5MiR8PHxwdtvv42///67xP7r169jxowZANT90WxtbbFo0SKt+FetWoXs7Gy97pWu90hBQQE+++wzveLV1507d0rcY82yKprvs2bOH31niO7evTuOHj2KQ4cOSdvu3r2LFStWIDAwsES/m+J8fHzQvHlzrFmzRqtct3v37hL9ffr16welUonp06eXOM/Dhw/NNqu1XC7Hs88+i++++06rdTIzMxPr169H+/btpbJT9+7dcfjwYRw9elQ67saNGyVaq6KiouDi4oKPPvpIZ/+qGzduGOeLIQlbdsig6tWrhxkzZmDixIm4fPkyevfuDWdnZyQnJ2Pr1q0YMWIExo8fX6lzN2vWDHFxcVixYoVUKjh69CjWrFmD3r174+mnnzbwV1PSs88+C1tbW/Ts2ROvvvoq8vLysHLlSnh6eiI9Pb1S5/zf//6HLVu24IUXXsDQoUMRFhaG27dvY/v27Vi+fDmaNWuGl19+GZs2bcLIkSOxd+9etGvXDkqlEn/99Rc2bdokzT+ii42NDebMmYMhQ4YgMjISsbGxyMzMxMKFCxEYGIg333yzUnEHBwdj/fr1iI2NRYMGDaQZlIUQSE5Oxvr162FlZQU/Pz/pNW3btsXSpUvx+uuvIyQkRGsG5X379mH79u1S4lGayMhIREZG4tdff9Urzho1amDr1q3o3r07mjdvrjWD8smTJ7FhwwaEh4cDUP9VP3HiREybNg1du3bF888/jwsXLuCzzz5Dq1attPoglaZt27aoUaMG4uLi8MYbb0Amk2Ht2rUVKpMsWbIEWVlZuHbtGgB1i+LVq1cBAGPGjIGrqyvWrFmDzz77DH369EG9evWQm5uLlStXwsXFRfrDwN7eHg0bNsQ333yDJ554Au7u7mjcuLFWv5ui3n33XWzYsAHdunXDG2+8AXd3d6xZswbJycn49ttv9ZowcNasWejRowfat2+PoUOH4vbt21i8eDEaNWqkleBGRkbi1VdfxaxZs5CUlIRnn30WNjY2uHjxIjZv3oyFCxeib9++et8zQ5oxYwZ2796N9u3b4/XXX4e1tTU+//xz5OfnY+7cudJxEyZMwNq1a9G1a1eMHTsWjo6OWLFiBQICArSWSnFxccGyZcvw8ssvo0WLFujfvz88PDyQkpKCH3/8Ee3atcOSJUvM8aVWHyYf/0WPLX2H+gohxLfffivat28vHB0dhaOjowgJCRGjRo0SFy5ckI6JjIwUjRo10vl6XUPPhRCisLBQTJs2TQQFBQkbGxvh7+8vJk6cWGI4b0BAgOjRo0eJ12uGzG7evFmvr00zDPTGjRvStu3bt4umTZsKOzs7ERgYKObMmSO+/PLLEvNqlBZDZGSkiIyM1Np269YtMXr0aFG7dm1ha2sr/Pz8RFxcnLh586Z0TEFBgZgzZ45o1KiRUCgUokaNGiIsLExMmzZNZGdnl7yJxXzzzTfiySefFAqFQri7u4sBAwaIq1ev6nUfyvLPP/+I1157TdSvX1/Y2dkJe3t7ERISIkaOHCmSkpJ0vubEiRPipZdeEr6+vsLGxkbUqFFDdO7cWaxZs0ZryDeKDD0vSvN9rEis165dE2+++aZ44oknhJ2dnXBwcBBhYWFi5syZJe7fkiVLREhIiLCxsRFeXl7itdde05ojSoiy378HDx4Ubdq0Efb29sLX11dMmDBBGuJc1vwwGpqh1roemvfYyZMnRWxsrKhTp45QKBTC09NTPPfcc+L48eNa5/r9999FWFiYsLW11WsY+qVLl0Tfvn2Fm5ubsLOzE0899ZT44YcftI4p7edI49tvvxWhoaFCoVCIhg0bioSEBBEXF1diGgchhFixYoUICwsT9vb2wtnZWTRp0kRMmDBBXLt2Tet+6PpZKk1p35vSzqPrfXby5EkRFRUlnJychIODg3j66ad1zjv1xx9/iMjISGFnZydq164tpk+fLlatWlXi94EQ6vsWFRUlXF1dhZ2dnahXr54YPHiw1veMQ8+NQyaEEXtlEREREZkZ++wQERGRRWOyQ0RERBaNyQ4RERFZNCY7REREZNGY7BAREZFFY7JDREREFo2TCkK9bsm1a9fg7Oxc4enViYiIyDyEEMjNzYWvr2+Zk14y2QFw7do1ky+kSERERIaRmpqqNVt7cUx2ADg7OwNQ3yzNmidERERUteXk5MDf31/6HC8Nkx1AKl25uLgw2SEiInrMlNcFhR2UiYiIyKIx2SEiIiKLxmSHiIiILBqTHSIiIrJoTHaIiIjIojHZISIiIovGZIeIiIgsGpMdIiIismhMdoiIiMiicQblx5BSpcT+lP1Iz02Hj7MP2vq1xe9Xf5eeR9SJAAAeY+HHmPv6PIbH8Bj+fFfmGLmVHKZm1mTnt99+w8cff4wTJ04gPT0dW7duRe/evaX9QghMmTIFK1euRFZWFtq1a4dly5YhODhYOub27dsYM2YMvv/+e1hZWSEmJgYLFy6Ek5OTGb4i40s4n4CxO8fias5VaZtcJodSKKXnNe1rAgBu3b/FYyz4GHNfn8fwGB7Dn++KHuPn4oeFXRciOjQapiQTQgiTXrGIHTt24ODBgwgLC0N0dHSJZGfOnDmYNWsW1qxZg6CgIEyePBlnzpzBuXPnYGdnBwDo1q0b0tPT8fnnn6OwsBBDhgxBq1atsH79er3jyMnJgaurK7Kzs6v02lgJ5xPQd1NfCJjtW0ZERFRpMqjXsNrSb4tBEh59P7/NmuwUJZPJtJIdIQR8fX3x9ttvY/z48QCA7OxseHl5YfXq1ejfvz/Onz+Phg0b4tixY2jZsiUAYOfOnejevTuuXr0KX19fva5dlZMdTckqLScNb+56Ezfu3TB3SERERJUmgwx+Ln5IHpv8yCUtfT+/q2wH5eTkZGRkZKBLly7SNldXV7Ru3RqHDh0CABw6dAhubm5SogMAXbp0gZWVFY4cOVLqufPz85GTk6P1qIoSzicgcGEgnl7zNAZuHchEh4iIHnsCAqk5qdifst9k16yyyU5GRgYAwMvLS2u7l5eXtC8jIwOenp5a+62treHu7i4do8usWbPg6uoqPfz9/Q0c/aPTlKyK9s0hIiKyFOm56Sa7VpVNdoxp4sSJyM7Olh6pqanmDkmLUqXE2J1j2TeHiIgslo+zj8muVWWHnnt7ewMAMjMz4ePz3w3JzMxE8+bNpWOuX7+u9bqHDx/i9u3b0ut1USgUUCgUhg/aQPan7GeLDhERWSRNnx3NUHVTqLItO0FBQfD29kZiYqK0LScnB0eOHEF4eDgAIDw8HFlZWThx4oR0zJ49e6BSqdC6dWuTx2wopmzaIyIiMhXNaKwFXReYdL4dsyY7eXl5SEpKQlJSEgB1p+SkpCSkpKRAJpNh3LhxmDFjBrZv344zZ85g0KBB8PX1lUZshYaGomvXrhg+fDiOHj2KgwcPYvTo0ejfv7/eI7Gqooo27cll2m+YmvY1pfkOeIzlHmPu6/MYHsNj+PNd0WP8XPwMNuy8Isxaxjp+/Diefvpp6flbb70FAIiLi8Pq1asxYcIE3L17FyNGjEBWVhbat2+PnTt3SnPsAMC6deswevRodO7cWZpUcNGiRSb/WgxFqVJCqVLC3d4dt+/fLvU4DwcPzI+aj9outc0+GyaP4QyrPIbH8Bj+fFflGZSrzDw75lRV5tnRNTtycYaekImIiOhxpe/nd5XtoFzd6Ds7sp+LHxZ0XcBEh4iISE9MdqoAfYaau9u7Y1PfTegY2NEsTYBERESPqyo7Gqs60Weo+e37tyG3kjPRISIiqiAmO1WAvkPNOSSdiIio4pjsVAH6DjU35WyTREREloLJThUQUScCfi5+pe6XQQZ/F3+TzjZJRERkKZjsVAFyKzkWdl2oc5+5ZpskIiKyFEx2qojo0GiE1Aopsd1cs00SERFZCg49ryLuFtzFP7f/AQDUdq6Nj5/52KyzTRIREVkKJjtVxIGUA3ioeggAeO6J5xDbJNbMEREREVkGlrGqiD3Je6T/dwrqZMZIiIiILAuTnSpiz+X/kp2OgR3NFwgREZGFYbJTBdy5fwcn008CAJp4NoGno6eZIyIiIrIcTHaqgN+u/AaVUAFgCYuIiMjQmOxUAeyvQ0REZDxMdqoATX8dK5kVOgR0MHM0REREloVDz81IqVLiuwvf4ez1swCAFt4t4GbnZt6giIiILAxbdswk4XwCAhcGImZTjLTtwq0LSDifYMaoiIiILA+THTNIOJ+Avpv64mrOVa3tuQW56LupLxMeIiIiA2KyY2JKlRJjd46FgCj1mHE7x0GpUpowKiIiIsvFZMfE9qfsL9GiU5SAQGpOKvan7DdhVERERJaLyY6JpeemG/Q4IiIiKhuTHRPzcfYx6HFERERUNiY7JhZRJwJ+Ln6QQaZzvwwy+Lv4I6JOhIkjIyIiskxMdkxMbiXHwq4Lde7TJEALui6A3EpuyrCIiIgsFpMdM4gOjcaWfltKTCDo5+KHLf22IDo02jyBERERWSAmO2YSHRqNie0nSs+ndJiC5LHJTHSIiIgMjMmOGd0tuCv9v41/G5auiIiIjIDJjhnlFuRK/3e2dTZjJERERJaLyY4Z5RXkSf93snUyYyRERESWi8mOGWm17CjYskNERGQMTHbMKDefZSwiIiJjY7JjRkVbdljGIiIiMg4mO2ak6bMjl8lhZ21n5miIiIgsE5MdM9KUsZwVzpDJdC8fQURERI+GyY4ZacpY7K9DRERkPEx2zEhTxmJ/HSIiIuNhsmMmKqGSkh0OOyciIjKeKp/s5ObmYty4cQgICIC9vT3atm2LY8eOSfuFEPjggw/g4+MDe3t7dOnSBRcvXjRjxPopulQEy1hERETGU+WTnVdeeQW7d+/G2rVrcebMGTz77LPo0qUL0tLSAABz587FokWLsHz5chw5cgSOjo6IiorCgwcPzBx52Th7MhERkWlU6WTn/v37+PbbbzF37lx06NAB9evXx9SpU1G/fn0sW7YMQggsWLAAkyZNQq9evdC0aVN89dVXuHbtGrZt22bu8MvE2ZOJiIhMo0onOw8fPoRSqYSdnfYcNPb29jhw4ACSk5ORkZGBLl26SPtcXV3RunVrHDp0qNTz5ufnIycnR+thapw9mYiIyDSqdLLj7OyM8PBwTJ8+HdeuXYNSqcTXX3+NQ4cOIT09HRkZGQAALy8vrdd5eXlJ+3SZNWsWXF1dpYe/v79Rvw5dWMYiIiIyjSqd7ADA2rVrIYRA7dq1oVAosGjRIsTGxsLKqvKhT5w4EdnZ2dIjNTXVgBHrR6uMxZYdIiIio6nyyU69evXw66+/Ii8vD6mpqTh69CgKCwtRt25deHt7AwAyMzO1XpOZmSnt00WhUMDFxUXrYWpaZSz22SEiIjKaKp/saDg6OsLHxwd37tzBrl270KtXLwQFBcHb2xuJiYnScTk5OThy5AjCw8PNGG35WMYiIiIyDWtzB1CeXbt2QQiBBg0a4J9//sH//vc/hISEYMiQIZDJZBg3bhxmzJiB4OBgBAUFYfLkyfD19UXv3r3NHXqZWMYiIiIyjSqf7GRnZ2PixIm4evUq3N3dERMTg5kzZ8LGxgYAMGHCBNy9excjRoxAVlYW2rdvj507d5YYwVXVsIxFRERkGjIhhDB3EOaWk5MDV1dXZGdnm6z/zv9+/h8+OfQJAOC3wb8hIiDCJNclIiKyFPp+fj82fXYsTdEyFvvsEBERGQ+THTPhDMpERESmwWTHTIqOxmIHZSIiIuNhsmMmRTsos4xFRERkPEx2zERTxrKSWcHBxsHM0RAREVkuJjtmoiljOdk6QSaTmTkaIiIiy8Vkx0w0ZSyWsIiIiIyLyY6ZaMpY7JxMRERkXEx2zEAIIZWxOOyciIjIuJjsmMH9h/ehEioALGMREREZG5MdM9BaF4tlLCIiIqNismMGnD2ZiIjIdJjsmAFnTyYiIjIdJjtmwNmTiYiITIfJjhlolbHYskNERGRUTHbMQKuMxT47RERERsVkxwxYxiIiIjIdJjtmwDIWERGR6TDZMQOWsYiIiEyHyY4ZsIxFRERkOkx2zIBlLCIiItNhsmMGLGMRERGZDpMdMyjassMyFhERkXEx2TEDLgRKRERkOkx2zKBoGcvR1tGMkRAREVk+JjtmoCljOdk6wUrGbwEREZEx8ZPWDDRlLPbXISIiMj4mO2agKWOxvw4REZHxMdkxMSGEVMbisHMiIiLjY7JjYvnKfDxUPQTAMhYREZEpMNkxMa0JBVnGIiIiMjomOyamNccOy1hERERGx2THxLRmT7ZhGYuIiMjYmOyYGNfFIiIiMi0mOybGpSKIiIhMi8mOiXERUCIiItNismNiLGMRERGZFpMdE2MZi4iIyLSqdLKjVCoxefJkBAUFwd7eHvXq1cP06dMhhJCOEULggw8+gI+PD+zt7dGlSxdcvHjRjFGXrWgZiy07RERExlelk505c+Zg2bJlWLJkCc6fP485c+Zg7ty5WLx4sXTM3LlzsWjRIixfvhxHjhyBo6MjoqKi8ODBAzNGXrqiZSz22SEiIjI+a3MHUJbff/8dvXr1Qo8ePQAAgYGB2LBhA44ePQpA3aqzYMECTJo0Cb169QIAfPXVV/Dy8sK2bdvQv39/s8VeGpaxiIiITKtKt+y0bdsWiYmJ+PvvvwEAp0+fxoEDB9CtWzcAQHJyMjIyMtClSxfpNa6urmjdujUOHTpU6nnz8/ORk5Oj9TAVlrGIiIhMq0q37Lz77rvIyclBSEgI5HI5lEolZs6ciQEDBgAAMjIyAABeXl5ar/Py8pL26TJr1ixMmzbNeIGXgUPPiYiITKtKt+xs2rQJ69atw/r163Hy5EmsWbMGn3zyCdasWfNI5504cSKys7OlR2pqqoEiLh8XAiUiIjKtKt2y87///Q/vvvuu1PemSZMmuHLlCmbNmoW4uDh4e3sDADIzM+Hj4yO9LjMzE82bNy/1vAqFAgqFwqixl6Zonx227BARERlflW7ZuXfvHqystEOUy+VQqVQAgKCgIHh7eyMxMVHan5OTgyNHjiA8PNyksepLU8ayt7aH3Epu5miIiIgsX5Vu2enZsydmzpyJOnXqoFGjRjh16hTmzZuHoUOHAgBkMhnGjRuHGTNmIDg4GEFBQZg8eTJ8fX3Ru3dv8wZfCk0Zi52TiYiITKNKJzuLFy/G5MmT8frrr+P69evw9fXFq6++ig8++EA6ZsKECbh79y5GjBiBrKwstG/fHjt37oSdnZ0ZIy+dpozF/jpERESmIRNFpyOupnJycuDq6ors7Gy4uLgY9VqKGQoUKAvQzKsZkkYmGfVaRERkOEolsH8/kJ4O+PgAERHq7cW3ydlDwWT0/fyu0i07lqZAWYACZQEAlrGIiKqS8hKZixeBlSuBq1f/e03Nmup/b936b1vt2sCIEUBwMJOfqoTJjglx2DkRkekZKpEpTte+tDRgypT/nvv5AfPmAR4e/12/bVvg99+rRwuRrntvjq+LyY4JaS0VwZYdIotSVX6pV0TxmHV9CFf1r6E8CQnA2LGGSWQq4+pVoF8/7W1yufrelxWPriTpcft+6Lr3fn7AwoVAdLRpY2GyY0Jai4DacI4doqqoMv0y9P2lrk9yUfxalU1AyrvWzZvAm29qx1z8Q9hcH0yPSvO1f/cdsGBByf2GSmQqq+g9BnTHoytJqmrfj7IS/IQEoG9foHiv4LQ09fYtW0z7dTDZMaHHcV2sx/GvVbI8+iQghmiV0LcVoGi/jIsXgalTS/5Sv3oViIkBxo0DevXSL7nQdS1dCUh5ZRF9rqVL8f1paeqvYdq0svugVKXfE7q+h5ai+HvK1Pe56PdZV+lPk4z16qX+Huga/iQEIJP99zWYKn6OxoLpRmPtvrQbz379LABgUsQkTO803WjXMoSq1ARJulWlDxldKpukFD1G3/4UlUkKil6rtFaAx4E+iYyhFO+AqyuxquzviUdt+Sot8bRUhix1lfe7RJ8kUiZT3/vBg4HVq8u/5t69QMeOFY+1KI7GqoK0ylgmXipCnw/F4lm7rl8a5mqCpJIMWTox1F/q5f3lp0+SUtn+FMU/7CvbV+JxZKpEByjZAVeXyrRA6Ho/V6blqzrR9R6vzGgwXfden9bL4jT79Ul0APXvCVNhsmNC5ipjlfahWPQvAl0fTLpo3szDhwOuruqsvCq1JJibqVpaSquHV6Z0os97obKlk+L0SVKMmXiY8lqkbilbsKD8JLy0D1N9vl/VNdEpTUVHg5X1h215Se2jKrKkpdGxjAXTlbGWHl2K0TtGAwC+6v0VXm72stGupVHah6KhVPeylj417MoMOy3rmLQ0dVJx44bpv96iqvNf1FQxmvKGpu+Pvn9cVXWPa8uguX92ZTL178bk5Ef/Y5BlrCooJz9H+v/lrMtQqpRGXQxUqSy9k5ihVKeyVvFWG31aMipbSnkcyi1MdEhfmt9Bxm4pMKTShoMPH65dIgLK/oOnKjJ3ogOoW/xMWRVgyw5M07KTcD4Bg7cN1ipl+bn4YWHXhYgONU6WsG8f8PTTRjm1Fn2y9KrWkbai/VgseYQHUXVTmURG399b+vxR9Dj8MWMs/v7qRMdQfxzr+/nNZAfGT3YSzieg76a+ENC+1TKoU9wt/bYYJeHZsAF46SWDn7ZUpfWsr2qjuvTpCFm0/PQ4j9IhqghzlzeMrWiHacB0f4BVZpSZPi3Hj5v584ExYwx7n5nsVIAxkx2lSonAhYG4mqP7HSuDDH4ufkgem2zQkpZSCSxerP5hMZX164HYWO1t5fUZMsV8Efp0hCQqjT5/dRftk3Lnjjo51mwriylHGxU/j78/8Omn5XdcBR7/nxdDtyaYSvHJEfV5T1VFhuyjUxz77FQR+1P2l5roAICAQGpOKvan7EfHwI4Guaa5Si7nzqlLZ5pfmJqOtGX9cBYdrWGMqdFZfrJMphiCXForQGkd0Yt+mEZElHzflZdc6NtZXZ+yiL7X0vXzVbR1tnHjx+/np3hn6KpQNq8suVz9/ejYUfd7ytyKlv5KS47N1UenOLbswLgtOxvObMBLCeXXktZHr0dsk9hyjyuPIUdfaX5pTJmibiW6fVu/1xnqQ+dRJyZj+anqqWxnbH36U1QmKdB1LX1aASo6b5WhP3BNuaZVeSMOiyZWhm6BqEzL1+PaiqOPygySMBR9kkhdf1wa+/vBMlYFGDPZ2Xd5H55eU34v4b1xex+5ZUepBAIDDffGL/om1SRRgOmbUR91YjJL5+Gh7pu1cGHlSifGVJkkxZD9KSrTV+JxbQUwFUPMtKuLrg9TY64dZinKS0b1oc/UAPomLaYejMJkpwJM0WcnLSetRAdlwLB9dvQdfTV/vvpDSNcU78U/mKrSiKTySl3GnlOoqtE0D2uG/Zf2V1V55YzSpvsv+l6obOmkun3wkJqufnJA2T+bltwiY0qVGQ2m695XtRG0pWGyUwGWMhpL39FXmo7ElXkza16TmAjMmPHIIT8yzZTm9epVjYn2KpMkVLa0Y8hfUJUpy1T3v6hJf6WNyCzrjysyHEv+2WWyUwGmmmcn9ttYFCgLpG3+Lv5Y0HWBwYad69uyY4jF10w9rL0q0rcl41EXN2S5hSzB49JSQI8XJjsVYKrlIlp83gKnMk5BLpPjl0G/IKJOhMGHmwcGqkdB6fquGnL4n6kmLDSVivRjMcVweSIiKp++n99WJoyp2nuoeggAUFgr0DGwo8GXipDL1Z1Ugf/6c2gYevhfRIQ6cSp+nbJ4eKibsnXFZ0qaa0+bpi7p7d0L3Lun/lfzfPNm9ddXlL8/8O236j5PXACViOjxwXl2TKhQVQgAsLGyMdo1oqPVHVZ11ccN2flPk1j17Vv+CCBNcrF8ufr6HTqYv6OzrntRvLTXpw+b3YmILAGTHRPS9NexkRsv2QGAK1eAV19Vd9oFjPdBXVpipWvphaLJRXS0ugxk6vkiKlp+0kzoRUREjzcmOyZUqFS37NjKbY16nUWLgMuXgR07gK5djXopnYmLPj39dSUSmpYUQ09MxiGtRETVG5MdEzJFGSs5WZ3oWFsD7dsb7TJadCUulWkRMeTU6B4e6r41tWuz/EREVN0x2TEhU5Sx9u5V//vUU4CTk9EuY3SVLXUV7x9ERETEZMeETFHG0iQ7ljAsvKxSl74LMhIRETHZMSFjl7GE+C/Z6dTJKJcwu+IJ0Pvvc8QUERGVjcmOCRm7jHXxonpCQVtbIDzcKJeocjhiioiIysNkx0RUQgWVUAEwXhnr4kXA0RFo1QqwtzfKJYiIiB47THZMRNNfBzB8GUuz5kxODrBtG/DEEwY9PRER0WONyY6JFF0A1JBlrNJWE164kJ10iYiIAK6NZTKazsmA4cpYCQnq5RqKD8VOS1NvT0gwyGWIiIgea0x2TMTQZSylUt2io2uGYc22ceP0X8mbiIjIUlU42QkMDMSHH36IlJQUY8RjsQxdxtq/v+zJ9YQAUlPVxxEREVVnFU52xo0bh4SEBNStWxfPPPMMNm7ciPz8fGPEZlEMXcZKTzfscURERJaqUslOUlISjh49itDQUIwZMwY+Pj4YPXo0Tp48aYwYLYKhy1g+PoY9joiIyFJVus9OixYtsGjRIly7dg1TpkzBF198gVatWqF58+b48ssvIQyxXLUF0SpjGSDZiYhQj7rSrAVVnEymXu07IuKRL0VERPRYq3SyU1hYiE2bNuH555/H22+/jZYtW+KLL75ATEwM3nvvPQwYMMAgAQYGBkImk5V4jBo1CgDw4MEDjBo1CjVr1oSTkxNiYmKQmZlpkGsbkqHLWHK5eni5LpoEaMECLp1ARERU4Xl2Tp48ifj4eGzYsAFWVlYYNGgQ5s+fj5CQEOmYPn36oFWrVgYJ8NixY1AWGVJ09uxZPPPMM3jhhRcAAG+++SZ+/PFHbN68Ga6urhg9ejSio6Nx8OBBg1zfULTKWAaaZyc6Ghg6FFi1Sns7F8MkIiL6T4WTnVatWuGZZ57BsmXL0Lt3b9jYlPzgDgoKQv/+/Q0SoIeHh9bz2bNno169eoiMjER2djZWrVqF9evXo9P/r3wZHx+P0NBQHD58GG3atDFIDIZQtGXHkDMov/46YGUFuLoCLVpwMUwiIqLiKpzs/PvvvwgICCjzGEdHR8THx1c6qNIUFBTg66+/xltvvQWZTIYTJ06gsLAQXbp0kY4JCQlBnTp1cOjQoVKTnfz8fK0RZDk5OQaPtUTsRfrsGHJtrBYtgBUrDHY6IiIii1PhPjvXr1/HkSNHSmw/cuQIjh8/bpCgSrNt2zZkZWVh8ODBAICMjAzY2trCzc1N6zgvLy9kZGSUep5Zs2bB1dVVevj7+xsxajVjlLGIiIiofBVOdkaNGoXU1NQS29PS0qROw8ayatUqdOvWDb6+vo90nokTJyI7O1t66Pp6DM2QZSylEti7F4iJAZYsAR4+fNToiIiILFeFk51z586hRYsWJbY/+eSTOHfunEGC0uXKlSv45Zdf8Morr0jbvL29UVBQgKysLK1jMzMz4e3tXeq5FAoFXFxctB7GZqgZlBMSgMBAoFMn9f/HjAECArgOFhERUWkqnOwoFAqdQ7vT09NhbW28RdTj4+Ph6emJHj16SNvCwsJgY2ODxMREaduFCxeQkpKC8PBwo8VSGUXLWJXts1Pawp/p6Vz4k4iIqDQVTnaeffZZqQykkZWVhffeew/PPPOMQYPTUKlUiI+PR1xcnFZC5erqimHDhuGtt97C3r17ceLECQwZMgTh4eFVaiQW8OhlLC78SUREVDkVbor55JNP0KFDBwQEBODJJ58EACQlJcHLywtr1641eIAA8MsvvyAlJQVDhw4tsW/+/PmwsrJCTEwM8vPzERUVhc8++8wocTyKRy1jVWThz44dKxEgERGRhapwslO7dm388ccfWLduHU6fPg17e3sMGTIEsbGxOufcMYRnn3221OUn7OzssHTpUixdutQo1zaURy1jceFPIiKiyqlUJxtHR0eMGDHC0LFYtEctY3HhTyIiosqpdI/ic+fOISUlBQUFBVrbn3/++UcOyhI9ahlLs/BnWprufjsymXo/F/4kIiLSVqkZlPv06YMzZ85AJpNJ5SXZ/68+qWQPWZ0etYylWfizb191YlM04eHCn0RERKWr8GissWPHIigoCNevX4eDgwP+/PNP/Pbbb2jZsiX27dtnhBAtgyEmFYyOBrZsAWrX1t7u56fezoU/iYiISqpwy86hQ4ewZ88e1KpVC1ZWVrCyskL79u0xa9YsvPHGGzh16pQx4nzsGWpSwehooFcv9air9HQu/ElERFSeCic7SqUSzs7OAIBatWrh2rVraNCgAQICAnDhwgWDB2gpDDGpIKBOdhQKYNo0DjEnIiLSR4WTncaNG+P06dMICgpC69atMXfuXNja2mLFihWoW7euMWK0CIYoY92/D3z/vXotrNmzDRUZERGRZatwsjNp0iTcvXsXAPDhhx/iueeeQ0REBGrWrIlvvvnG4AFaCkOUsU6eVCc63t5AnTqGioyIiMiyVTjZiYqKkv5fv359/PXXX7h9+zZq1KghjciikgxRxjp8WP1vmzb/jcAiIiKislVoNFZhYSGsra1x9uxZre3u7u5MdMphiDJW0WSHiIiI9FOhZMfGxgZ16tThXDqVYIgyFpMdIiKiiqvwPDvvv/8+3nvvPdy+fdsY8Visoi07lSljXb2qflhZAS1bGjIyIiIiy1bhPjtLlizBP//8A19fXwQEBMDR0VFr/8mTJw0WnCUp2menMmWsmzeBFi3UyU6xW05ERERlqHCy07t3byOEYfketYzVvDlw4gTACiIREVHFVDjZmTJlijHisHiV7aCsVJacLZmIiIj0V+lVz6liKjP0PCEBGDtW3VdHw89PvSAo18EiIiLST4U7KFtZWUEul5f6IN0qWsZKSFCvcF400QGAtDT19oQEQ0dIRERkmSrcsrN161at54WFhTh16hTWrFmDadOmGSwwS1ORMpZSqW7REaLkPiHUEwqOG6deEJT5JRERUdkqnOz06tWrxLa+ffuiUaNG+OabbzBs2DCDBGZpNGUsayvrcidg3L+/ZItOUUIAqanq47gYKBERUdkqXMYqTZs2bZCYmGio01kcTcuOPp2T09P1O6e+xxEREVVnBkl27t+/j0WLFqF27dqGOJ1F0vTZ0ae/jo+PfufU9zgiIqLqrMJlrOILfgohkJubCwcHB3z99dcGDc6SaMpY+ozEiohQj7pKS9Pdb0cmU+/nMHQiIqLyVTjZmT9/vlayY2VlBQ8PD7Ru3Ro1atQwaHCWpCJlLLlcPbw8JqbkPs2tX7CAnZOJiIj0UeFkZ/DgwUYIw/JVpIwFqOfR2bABeP114M6d/7b7+akTHc6zQ0REpJ8KJzvx8fFwcnLCCy+8oLV98+bNuHfvHuLi4gwWnCWpSBlLo39/4IUXSs6gzBYdIiIi/VW4g/KsWbNQq1atEts9PT3x0UcfGSQoS6RvGUupBPbtU7fq7Nun3taxIxAbq/6XiQ4REVHFVLhlJyUlBUFBQSW2BwQEICUlxSBBWSJ9yli6loeoXRtYtIhlKyIiosqqcMuOp6cn/vjjjxLbT58+jZo1axokKEtUXhmrtOUhrl3j8hBERESPosLJTmxsLN544w3s3bsXSqUSSqUSe/bswdixY9G/f39jxPjYUwkVlEIJQHcZq7zlIQD18hBKpRGDJCIislAVLmNNnz4dly9fRufOnWFtrX65SqXCoEGD2GenFEVXPNdVxuLyEERERMZT4WTH1tYW33zzDWbMmIGkpCTY29ujSZMmCAgIMEZ8FqHoIqC6ylhcHoKIiMh4KpzsaAQHByM4ONiQsVgsrZadImUspVLdWnPunH7n4fIQREREFVfhPjsxMTGYM2dOie1z584tMfcOqWlGYgH/lbESEoDAQODpp4EZM8p+vUwG+PtzeQgiIqLKqHCy89tvv6F79+4ltnfr1g2//fabQYKyNEXLWDZWNqWOvNKFy0MQERE9mgonO3l5ebC1LdnvxMbGBjk5OQYJytIULWNZQ1HqyCtd/PyALVs4zw4REVFlVTjZadKkCb755psS2zdu3IiGDRsaJChLU7SMdefvxnq16EyaBOzdCyQnM9EhIiJ6FBXuoDx58mRER0fj0qVL6NSpEwAgMTER69evx5YtWwweoCUoWsYqyNJv4sWGDTnMnIiIyBAqnOz07NkT27Ztw0cffYQtW7bA3t4ezZo1w549e+Du7m6MGB97RctYLjXv6vUajrwiIiIyjAqXsQCgR48eOHjwIO7evYt///0X/fr1w/jx49GsWTNDx4e0tDQMHDgQNWvWlOb0OX78uLRfCIEPPvgAPj4+sLe3R5cuXXDx4kWDx/Eoipax6jS5Aj+//zoeF8eRV0RERIZVqWQHUI/KiouLg6+vLz799FN06tQJhw8fNmRsuHPnDtq1awcbGxvs2LED586dw6effooaNWpIx8ydOxeLFi3C8uXLceTIETg6OiIqKgoPHjwwaCyPomgZS2FrjYULdR/HkVdERESGV6EyVkZGBlavXo1Vq1YhJycH/fr1Q35+PrZt22aUzslz5syBv78/4uPjpW1FV1wXQmDBggWYNGkSevXqBQD46quv4OXlhW3btlWZtbqKlrFs5baIjlaPsBo6FMjO/u84Pz91osMOyURERIajd8tOz5490aBBA/zxxx9YsGABrl27hsWLFxszNmzfvh0tW7bECy+8AE9PTzz55JNYuXKltD85ORkZGRno0qWLtM3V1RWtW7fGoUOHSj1vfn4+cnJytB7GpDWp4P/PoBwdDbz0knrb889z5BUREZGx6J3s7NixA8OGDcO0adPQo0cPyE1QZ/n333+xbNkyBAcHY9euXXjttdfwxhtvYM2aNQDULU0A4OXlpfU6Ly8vaZ8us2bNgqurq/Tw9/c33heBYpMKFlkINDlZ/e9zz6lHXrF0RUREZHh6JzsHDhxAbm4uwsLC0Lp1ayxZsgQ3b940ZmxQqVRo0aIFPvroIzz55JMYMWIEhg8fjuXLlz/SeSdOnIjs7GzpkZqaaqCIdStextKYOxfYsAEo0jBFREREBqZ3stOmTRusXLkS6enpePXVV7Fx40b4+vpCpVJh9+7dyM3NNXhwPj4+JfoChYaGIiUlBQDg7e0NAMjMzNQ6JjMzU9qni0KhgIuLi9bDmIovF6HRpAnQvz9QpBsSERERGViFR2M5Ojpi6NChOHDgAM6cOYO3334bs2fPhqenJ55//nmDBteuXTtcuHBBa9vff/+NgIAAAOrOyt7e3khMTJT25+Tk4MiRIwgPDzdoLI9C10KgREREZBqVHnoOAA0aNMDcuXNx9epVbNiwwVAxSd58800cPnwYH330Ef755x+sX78eK1aswKhRowAAMpkM48aNw4wZM7B9+3acOXMGgwYNgq+vL3r37m3weCpLVxnr77+BRYuAffvMFBQREVE1UeEZlHWRy+Xo3bu3wROMVq1aYevWrZg4cSI+/PBDBAUFYcGCBRgwYIB0zIQJE3D37l2MGDECWVlZaN++PXbu3Ak7OzuDxvIodJWx9u8Hxo4FoqK4LAQREZExGSTZMabnnnsOzz33XKn7ZTIZPvzwQ3z44YcmjKpidJWxLl1SP69XzxwRERERVR+PVMYi/egqYzHZISIiMg0mOyagq4ylSXbq1jVHRERERNUHkx0T0FXG+vdf9XO27BARERkXkx0TKF7GunMHuHNH/ZwtO0RERMbFZMcEipexNCUsLy/A0dFMQREREVUTVX40liUoXsZq1Ag4fBjIyjJfTERERNUFkx0TKFrGsrGygb090Lq1GQMiIiKqRljGMoGiZayiC4ESERGR8bFlxwSKl7GWLgWEAPr0AWrXNmNgRERE1QCTHRMo3kF57lwgJQVo0YLJDhERkbGxjGUCRfvsQGmL1FT1fznHDhERkfEx2TGBomWszDR7CKEecu7pacagiIiIqgkmOyZQtIx19bICgHoyQZnMXBERERFVH0x2TKBoGSvtyn/JDhERERkfkx0TKFrGunJZ3Sec/XWIiIhMg8mOCUhlLJUVThyTAwAePgSUSjMGRUREVE0w2TGBQmUhcK4PsOAyDh9SJzuLFgGBgUBCgnljIyIisnRMdkwg81g7YNMWIEd7Up20NKBvXyY8RERExsRkx8iUSiD1m7f//5n27RZC/e+4cSxpERERGQuTHSPbvx8ozPJGabdaCCA1VX0cERERGR6THSNLTzfscURERFQxTHaMzMfHsMcRERFRxTDZMbKICMDK9RoAlc79Mhng768+joiIiAyPyY6RyeWA4/Pv/f8zobVPs1zEggXq44iIiMjwmOyYgKzhVqBfX8gUd7W2+/kBW7YA0dFmCoyIiKgaYLJjAoXKQqDhVrg99SMAoE8fYO9eIDmZiQ4REZGxWZs7gOpAs1yErNARABAeDnTsaMaAiIiIqhG27BiZEAIPVQ8BAIF9P8fJk8DAgWYOioiIqBphy46RSYuAAnB0z8aTT5oxGCIiomqILTtGVqj8L9mxlduaMRIiIqLqicmOkRUoC6T/p/0Sg1mz1MtDEBERkWkw2TGyomWslJ198N576tXOiYiIyDSY7BhZ0TKWMt8eAODkZK5oiIiIqh8mO0ZWtIz18IEdACY7REREpsRkx8ikMpbKCsoCBQAmO0RERKbEZMfIpDJWgaO0jckOERGR6TDZMTKpjFWgznDkckChMGNARERE1QyTHSOTylj/n+w4Of232jkREREZX5VOdqZOnQqZTKb1CAkJkfY/ePAAo0aNQs2aNeHk5ISYmBhkZmaaMeKSpDKWawoGLpmPHTvMGw8REVF1U6WTHQBo1KgR0tPTpceBAwekfW+++Sa+//57bN68Gb/++iuuXbuG6Cq2jLhUxrLJh1+D6wgPN288RERE1U2VXxvL2toa3t7eJbZnZ2dj1apVWL9+PTp16gQAiI+PR2hoKA4fPow2bdqYOlSdik4qaCO3MWMkRERE1VOVb9m5ePEifH19UbduXQwYMAApKSkAgBMnTqCwsBBdunSRjg0JCUGdOnVw6NChMs+Zn5+PnJwcrYexSGWszMY4/E0ktm0z2qWIiIhIhyqd7LRu3RqrV6/Gzp07sWzZMiQnJyMiIgK5ubnIyMiAra0t3NzctF7j5eWFjIyMMs87a9YsuLq6Sg9/f3+jfQ1SGetqa+z+vDNWrTLapYiIiEiHKl3G6tatm/T/pk2bonXr1ggICMCmTZtgb29f6fNOnDgRb731lvQ8JyfHaAmPrtFYREREZDpVumWnODc3NzzxxBP4559/4O3tjYKCAmRlZWkdk5mZqbOPT1EKhQIuLi5aD2P5b1JBdZbj7Gy0SxEREZEOj1Wyk5eXh0uXLsHHxwdhYWGwsbFBYmKitP/ChQtISUlBeBUa8sSWHSIiIvOq0mWs8ePHo2fPnggICMC1a9cwZcoUyOVyxMbGwtXVFcOGDcNbb70Fd3d3uLi4YMyYMQgPD68yI7GAkjMoM9khIiIyrSqd7Fy9ehWxsbG4desWPDw80L59exw+fBgeHh4AgPnz58PKygoxMTHIz89HVFQUPvvsMzNHra14GYvJDhERkWlV6WRn48aNZe63s7PD0qVLsXTpUhNFVHEsYxEREZnXY9Vn53EklbE6v4ep8b+hZ0/zxkNERFTdMNkxMqmMVesiWoRnw4hT+hAREZEOTHaMrOhyEbZyWzNGQkREVD0x2TEyqYx1fDh2bAjEjRvmjYeIiKi6YbJjZFIZa++HWPhBA5SzkgUREREZGJMdI/tvNJZ66mSOxiIiIjItJjtGVqAsAFRWQKEjACY7REREpsZkx8gKlYVAoYP0nMkOERGRaTHZMbJCVaE0oaCVlYCdnZkDIiIiqmaY7BhZgbIAyFf313FwFJDJzBwQERFRNcNkx8iKtuw4OavMHA0REVH1w2THyAqVhYD7P8CgTlj8ea65wyEiIqp2mOwYWYGyALDLBeruRafOwtzhEBERVTtMdoys6HIRNlY2ZoyEiIioemKyY2SFykIgszFw7FUcOqAwdzhERETVDpMdIytQFgDJTwM/LseXX7Blh4iIyNSY7BhZ0dFYzk4cd05ERGRqTHaMrFBZyHWxiIiIzIjJjpEVKAv+m2eHyQ4REZHJMdkxMq1JBZnsEBERmRyTHSNTl7GY7BAREZkLkx0jYxmLiIjIvJjsGFmhqhB4ejK8ho1Ex47mjoaIiKj6sTZ3AJauUFkI1D4Bt5p5CAgwdzRERETVD1t2jEyzXISt3NbMkRAREVVPbNkxsgJlAXB6IHLd6yAnB3BxMXdERERE1QuTHSMSQuCh6iHwwzJcLnTCzfeY7BAREZkay1hG9FD1EFDJgEKOxiIiIjIXJjtGVKAsAAodpOdMdoiIiEyPyY4RFZ09GTIl7O3NGw8REVF1xGTHiIouAmpt9wAyLnpORERkckx2jKjo7MnWdg/MHA0REVH1xGTHiIqWsWzs8s0cDRERUfXEZMeICpWFQK3zQL9otByy0dzhEBERVUucZ8eICpQFgOMtoOFWBDWvYe5wiIiIqiW27BiRZqkIALCR25gxEiIiouqLLTtGVKgsBK43BDKb4E6NIHOHQ0REVC2xZceICpQFwIXngW834txPHc0dDhERUbX0WCU7s2fPhkwmw7hx46RtDx48wKhRo1CzZk04OTkhJiYGmZmZ5guyiEJVIZCvnmdH4VBYztFERERkDI9NsnPs2DF8/vnnaNq0qdb2N998E99//z02b96MX3/9FdeuXUN0dLSZotSmnlRQPfTczuGhmaMhIiKqnh6LZCcvLw8DBgzAypUrUaPGf6OasrOzsWrVKsybNw+dOnVCWFgY4uPj8fvvv+Pw4cNmjFit6KSC9g5KM0dDRERUPT0Wyc6oUaPQo0cPdOnSRWv7iRMnUFhYqLU9JCQEderUwaFDh0o9X35+PnJycrQexlB0UkF7RyY7RERE5lDlR2Nt3LgRJ0+exLFjx0rsy8jIgK2tLdzc3LS2e3l5ISMjo9Rzzpo1C9OmTTN0qCUULWM5OKiMfj0iIiIqqUq37KSmpmLs2LFYt24d7OzsDHbeiRMnIjs7W3qkpqYa7NxFqctY6g7KDk5MdoiIiMyhSrfsnDhxAtevX0eLFi2kbUqlEr/99huWLFmCXbt2oaCgAFlZWVqtO5mZmfD29i71vAqFAgqFwpihA/j/MlbHqUC2P+o17lLu8URERGR4VTrZ6dy5M86cOaO1bciQIQgJCcE777wDf39/2NjYIDExETExMQCACxcuICUlBeHh4eYIWUuhshCouwcA4F07wszREBERVU9VOtlxdnZG48aNtbY5OjqiZs2a0vZhw4bhrbfegru7O1xcXDBmzBiEh4ejTZs25ghZS4GyQPq/rdzWjJEQERFVX1U62dHH/PnzYWVlhZiYGOTn5yMqKgqfffaZucMC8P9lrHPRgPV9iELD9TkiIipKqVSisJATl5LlsbGxgVwuf+TzPHbJzr59+7Se29nZYenSpVi6dKl5AipDfmEhsGkzACsUvvqDucMhIgsjhEBGRgaysrLMHQqR0bi5ucHb2xsymazS53jskp3Hyf37gGbAm4tzlR74RkSPIU2i4+npCQcHh0f6MCCqaoQQuHfvHq5fvw4A8PHxqfS5mOwYUV6e5n8qODoy2SEiw1EqlVKiU7NmTXOHQ2QU9vb2AIDr16/D09Oz0iUtfgIb0d28/7+9tnehsLYxbzBEZFE0fXQcHBzMHAmRcWne44/SL43JjhHdu6dJdvI4GouIjIKlK7J0hniPM9kxontSy04ubORs2SEiMobAwEAsWLBA7+P37dsHmUzGjt3VCJMdI3pw7/+7RNnmwcaKyQ4RVT1KlRL7Lu/DhjMbsO/yPihVxlu0WCaTlfmYOnVqpc577NgxjBgxQu/j27Zti/T0dLi6ulbqepUREhIChUJR5rqNZDzsoGxEzv5XgF5DANtc2MqnmDscIiItCecTMHbnWFzNuSpt83Pxw8KuCxEdGm3w66Wnp0v//+abb/DBBx/gwoUL0jYnJyfp/0IIKJVKWFuX/zHl4eFRoThsbW3LXFLI0A4cOID79++jb9++WLNmDd555x2TXVuXwsJC2NhUrz/A2bJjRLY1rgNPrgYafcsyFhFVKQnnE9B3U1+tRAcA0nLS0HdTXyScTzD4Nb29vaWHq6srZDKZ9Pyvv/6Cs7MzduzYgbCwMCgUChw4cACXLl1Cr1694OXlBScnJ7Rq1Qq//PKL1nmLl7FkMhm++OIL9OnTBw4ODggODsb27dul/cXLWKtXr4abmxt27dqF0NBQODk5oWvXrlrJ2cOHD/HGG2/Azc0NNWvWxDvvvIO4uDj07t273K971apVeOmll/Dyyy/jyy+/LLH/6tWriI2Nhbu7OxwdHdGyZUscOXJE2v/999+jVatWsLOzQ61atdCnTx+tr3Xbtm1a53Nzc8Pq1asBAJcvX4ZMJsM333yDyMhI2NnZYd26dbh16xZiY2NRu3ZtODg4oEmTJtiwYYPWeVQqFebOnYv69etDoVCgTp06mDlzJgCgU6dOGD16tNbxN27cgK2tLRITE8u9J6bGZMeIClX/9RxnGYuIqgqlSomxO8dCQJTYp9k2buc4o5a0SvPuu+9i9uzZOH/+PJo2bYq8vDx0794diYmJOHXqFLp27YqePXsiJSWlzPNMmzYN/fr1wx9//IHu3btjwIABuH37dqnH37t3D5988gnWrl2L3377DSkpKRg/fry0f86cOVi3bh3i4+Nx8OBB5OTklEgydMnNzcXmzZsxcOBAPPPMM8jOzsb+/ful/Xl5eYiMjERaWhq2b9+O06dPY8KECVCpVACAH3/8EX369EH37t1x6tQpJCYm4qmnnir3usW9++67GDt2LM6fP4+oqCg8ePAAYWFh+PHHH3H27FmMGDECL7/8Mo4ePSq9ZuLEiZg9ezYmT56Mc+fOYf369fDy8gIAvPLKK1i/fj3y8/Ol47/++mvUrl0bnTp1qnB8xsYylhHdSvEALnYFalxiyw4RmUTLFS2RkVd2v5D8h/m4ef9mqfsFBFJzUuH9iTcU1opyr+nt5I3jI45XOFZdPvzwQzzzzDPSc3d3dzRr1kx6Pn36dGzduhXbt28v0bJQ1ODBgxEbGwsA+Oijj7Bo0SIcPXoUXbt21Xl8YWEhli9fjnr16gEARo8ejQ8//FDav3jxYkycOFFqVVmyZAl++umncr+ejRs3Ijg4GI0aNQIA9O/fH6tWrUJEhHpx6PXr1+PGjRs4duwY3N3dAQD169eXXj9z5kz0798f06ZNk7YVvR/6GjduHKKjtUuTRZO5MWPGYNeuXdi0aROeeuop5ObmYuHChViyZAni4uIAAPXq1UP79u0BANHR0Rg9ejS+++479OvXD4C6hWzw4MFVcoQgkx0j+vfXdsC2BcBTizj0nIhMIiMvA2m5aQY5V1kJkbG0bNlS63leXh6mTp2KH3/8Eenp6Xj48CHu379fbstO06ZNpf87OjrCxcVFmolXFwcHBynRAdSz9WqOz87ORmZmplaLilwuR1hYmNQCU5ovv/wSAwcOlJ4PHDgQkZGRWLx4MZydnZGUlIQnn3xSSnSKS0pKwvDhw8u8hj6K31elUomPPvoImzZtQlpaGgoKCpCfny/NaXP+/Hnk5+ejc+fOOs9nZ2cnleX69euHkydP4uzZs1rlwqqEyY4RFd7//wSHo7GIyES8ncrveFtey45GLftaerfsGIqjo6PW8/Hjx2P37t345JNPUL9+fdjb26Nv374oKCgo8zzFO+DKZLIyExNdxwtRssxXEefOncPhw4dx9OhRrU7JSqUSGzduxPDhw6UZgktT3n5dceqafK/4ff3444+xcOFCLFiwAE2aNIGjoyPGjRsn3dfyrguoS1nNmzfH1atXER8fj06dOiEgIKDc15kDkx0jUSqB3PT/X8fjXi1YgckOERmfPuUkpUqJwIWBSMtJ09lvRwYZ/Fz8kDw2GXKrR19x+lEcPHgQgwcPlspHeXl5uHz5skljcHV1hZeXF44dO4YOHToAUCcsJ0+eRPPmzUt93apVq9ChQ4cSC1XHx8dj1apVGD58OJo2bYovvvgCt2/f1tm607RpUyQmJmLIkCE6r+Hh4aHVkfrixYu4d+9euV/TwYMH0atXL6nVSaVS4e+//0bDhg0BAMHBwbC3t0diYiJeeeUVnedo0qQJWrZsiZUrV2L9+vVYsmRJudc1F3ZQNoKEBCAwELj1x/83eZ4cgSYNnJFg+MENREQVJreSY2HXhQDUiU1RmucLui4we6IDqD90ExISkJSUhNOnT+Oll14qt3RkDGPGjMGsWbPw3Xff4cKFCxg7dizu3LlTav+UwsJCrF27FrGxsWjcuLHW45VXXsGRI0fw559/IjY2Ft7e3ujduzcOHjyIf//9F99++y0OHToEAJgyZQo2bNiAKVOm4Pz58zhz5gzmzJkjXadTp05YsmQJTp06hePHj2PkyJF6DSsPDg7G7t278fvvv+P8+fN49dVXkZmZKe23s7PDO++8gwkTJuCrr77CpUuXcPjwYaxatUrrPK+88gpmz54NIYTWKLGqhsmOgSUkAH37Ale1R3PiWpp6OxMeIqoKokOjsaXfFtR2qa213c/FD1v6bTHKPDuVMW/ePNSoUQNt27ZFz549ERUVhRYtWpg8jnfeeQexsbEYNGgQwsPD4eTkhKioKNjZ2ek8fvv27bh165bOBCA0NBShoaFYtWoVbG1t8fPPP8PT0xPdu3dHkyZNMHv2bGnBy44dO2Lz5s3Yvn07mjdvjk6dOmmNmPr000/h7++PiIgIvPTSSxg/frxe66VNmjQJLVq0QFRUFDp27CglXEVNnjwZb7/9Nj744AOEhobixRdfLNHvKTY2FtbW1oiNjS31XlQFMvGoRUkLkJOTA1dXV2RnZ8PFxaXS51Eq1S06xRMdDZkM8PMDkpOBSi7cSkQEAHjw4AGSk5MRFBT0SB8ySpUS+1P2Iz03HT7OPoioE1ElWnSqOpVKhdDQUPTr1w/Tp083dzhmc/nyZdSrVw/Hjh0zWhJa1ntd389v9tkxoP37S090AEAIIDVVfVzHjiYLi4ioVHIrOToGdjR3GFXelStX8PPPPyMyMhL5+flYsmQJkpOT8dJLL5k7NLMoLCzErVu3MGnSJLRp08YsrW0VwTKWARXpI2aQ44iIqGqwsrLC6tWr0apVK7Rr1w5nzpzBL7/8gtDQUHOHZhYHDx6Ej48Pjh07huXLl5s7nHKxZceAfHwMexwREVUN/v7+OHjwoLnDqDI6duz4yEPzTYktOwYUEaHuk1Pa5JEyGeDvrz6OiIiITIPJjgHJ5cBC9WjOEgmP5vmCBeycTEREZEpMdgwsOhrYsgWorT2aE35+6u3RVWM0JxERUbXBPjtGEB0N9OoFuL72HO7edoZ/bRskz/uKLTpERERmwGTHSORyQATuBWrfg6tnYyY6REREZsIylhEVKtWLsXERUCIiIvNhsmMkQggUqtTJjq3c1szREBFZjo4dO2LcuHHS88DAQCxYsKDM18hkMmzbtu2Rr22o85BpMdkxkoeqh9L/beRs2SGiqkmpBPbtAzZsUP+rVBrvWj179kTXrl117tu/fz9kMhn++OOPCp/32LFjGDFixKOGp2Xq1Kk6VzRPT09Ht27dDHqt0ty/fx/u7u6oVasW8vPzTXJNS8Vkx0g0rToAy1hEVDUlJKjX83v6aeCll9T/BgYab8HiYcOGYffu3biqY12d+Ph4tGzZEk2bNq3weT08PPRa/NIQvL29oVAoTHKtb7/9Fo0aNUJISIjZW5OEEHj48GH5B1ZRTHaMRNNfB2DLDhFVPQkJQN++JdfzS0tTbzdGwvPcc8/Bw8MDq1ev1tqel5eHzZs3Y9iwYbh16xZiY2NRu3ZtODg4oEmTJtiwYUOZ5y1exrp48SI6dOgAOzs7NGzYELt37y7xmnfeeQdPPPEEHBwcULduXUyePBmFherf26tXr8a0adNw+vRpyGQyyGQyKebiZawzZ86gU6dOsLe3R82aNTFixAjk5eVJ+wcPHozevXvjk08+gY+PD2rWrIlRo0ZJ1yrLqlWrMHDgQAwcOBCrVq0qsf/PP//Ec889BxcXFzg7OyMiIgKXLl2S9n/55Zdo1KgRFAoFfHx8MHr0aADqxTtlMhmSkpKkY7OysiCTybBv3z4AwL59+yCTybBjxw6EhYVBoVDgwIEDuHTpEnr16gUvLy84OTmhVatW+OWXX7Tiys/PxzvvvAN/f38oFArUr18fq1atghAC9evXxyeffKJ1fFJSEmQyGf75559y70llMdkxkgJlgfR/9tkhIlO6e7f0x4MH6lLV2LHqxYmL02wbOxYo8pld6nkrwtraGoMGDcLq1au1lhrYvHkzlEolYmNj8eDBA4SFheHHH3/E2bNnMWLECLz88ss4evSoXtdQqVSIjo6Gra0tjhw5guXLl+Odd94pcZyzszNWr16Nc+fOYeHChVi5ciXmz58PAHjxxRfx9ttvo1GjRkhPT0d6ejpefPHFEue4e/cuoqKiUKNGDRw7dgybN2/GL7/8IiUVGnv37sWlS5ewd+9erFmzBqtXry6R8BV36dIlHDp0CP369UO/fv2wf/9+XLlyRdqflpaGDh06QKFQYM+ePThx4gSGDh0qtb4sW7YMo0aNwogRI3DmzBls374d9evX1+seFvXuu+9i9uzZOH/+PJo2bYq8vDx0794diYmJOHXqFLp27YqePXsiJSVFes2gQYOwYcMGLFq0COfPn8fnn38OJycnyGQyDB06FPHx8VrXiI+PR4cOHSoVn94EiezsbAFAZGdnG+ycKVkpAlMhMBWi/ar24qHyocHOTUR0//59ce7cOXH//v0S+9Qpi+5H9+5C7N1b9jGaR7Nm2uetVavkMRV1/vx5AUDs3btX2hYRESEGDhxY6mt69Ogh3n77bel5ZGSkGDt2rPQ8ICBAzJ8/XwghxK5du4S1tbVIS0uT9u/YsUMAEFu3bi31Gh9//LEICwuTnk+ZMkU0K34DhNA6z4oVK0SNGjVEXl6etP/HH38UVlZWIiMjQwghRFxcnAgICBAPH/73GfDCCy+IF198sdRYhBDivffeE71795ae9+rVS0yZMkV6PnHiRBEUFCQKCgp0vt7X11e8//77OvclJycLAOLUqVPStjt37mh9X/bu3SsAiG3btpUZpxBCNGrUSCxevFgIIcSFCxcEALF7926dx6alpQm5XC6OHDkihBCioKBA1KpVS6xevbrU85f1Xtf385stO0aQcD4Brb9oLT0/kHoAgQsDkXDeSIVwIqIKSE/X77iCgvKPqaiQkBC0bdsWX375JQDgn3/+wf79+zFs2DAAgFKpxPTp09GkSRO4u7vDyckJu3bt0mo5KMv58+fh7+8PX19faVt4eHiJ47755hu0a9cO3t7ecHJywqRJk/S+RtFrNWvWDI6OjtK2du3aQaVS4cKFC9K2Ro0aQV5ksjUfHx9cv3691PMqlUqsWbMGAwcOlLYNHDgQq1evhkqlAqAu/URERMDGpmQ3ievXr+PatWvo3Llzhb4eXVq2bKn1PC8vD+PHj0doaCjc3Nzg5OSE8+fPS/cuKSkJcrkckZGROs/n6+uLHj16SN//77//Hvn5+XjhhRceOdayMNkxsITzCei7qS/S87R/m6TlpKHvpr5MeIjI6PLySn98+y3g46Pfef6/qiO5fLnk+Spj2LBh+Pbbb5Gbm4v4+HjUq1dP+nD8+OOPsXDhQrzzzjvYu3cvkpKSEBUVhQIDZl6HDh3CgAED0L17d/zwww84deoU3n//fYNeo6jiCYlMJpOSFl127dqFtLQ0vPjii7C2toa1tTX69++PK1euIDExEQBgb29f6uvL2gcAVlbqj35RpJRYWh+iookcAIwfPx5bt27FRx99hP379yMpKQlNmjSR7l151waAV155BRs3bsT9+/cRHx+PF1980egdzJnsGJBSpcTYnWMhULIQrtk2buc4KFVGHNtJRNWeo2PpDzs7ICJCvV5f8QWLNWQywN8f6NKl/PNWRr9+/WBlZYX169fjq6++wtChQyH7/2AOHjyIXr16YeDAgWjWrBnq1q2Lv//+W+9zh4aGIjU1FelFmq8OHz6sdczvv/+OgIAAvP/++2jZsiWCg4O1+sMAgK2tLZTljMMPDQ3F6dOncbdI56WDBw/CysoKDRo00Dvm4latWoX+/fsjKSlJ69G/f3+po3LTpk2xf/9+nUmKs7MzAgMDpcSoOA8PDwDQukdFOyuX5eDBgxg8eDD69OmDJk2awNvbG5cvX5b2N2nSBCqVCr/++mup5+jevTscHR2xbNky7Ny5E0OHDtXr2o+CyY4B7U/Zj6s5JYdUaggIpOakYn/KfhNGRUSkTS4HFi5U/794wqN5vmABjLbMjZOTE1588UVMnDgR6enpGDx4sLQvODgYu3fvxu+//47z58/j1VdfRWZmpt7n7tKlC5544gnExcXh9OnT2L9/P95//32tY4KDg5GSkoKNGzfi0qVLWLRoEbZu3ap1TGBgIJKTk5GUlISbN2/qnOdmwIABsLOzQ1xcHM6ePYu9e/dizJgxePnll+Hl5VWxm/L/bty4ge+//x5xcXFo3Lix1mPQoEHYtm0bbt++jdGjRyMnJwf9+/fH8ePHcfHiRaxdu1Yqn02dOhWffvopFi1ahIsXL+LkyZNYvHgxAHXrS5s2baSOx7/++ismTZqkV3zBwcFISEhAUlISTp8+jZdeekmrlSowMBBxcXEYOnQotm3bhuTkZOzbtw+bNm2SjpHL5Rg8eDAmTpyI4OBgnWVGQ2OyY0DpufoVwvU9jojIWKKjgS1bgNq1tbf7+am3R0cb9/rDhg3DnTt3EBUVpdW/ZtKkSWjRogWioqLQsWNHeHt7o3fv3nqf18rKClu3bsX9+/fx1FNP4ZVXXsHMmTO1jnn++efx5ptvYvTo0WjevDl+//13TJ48WeuYmJgYdO3aFU8//TQ8PDx0Dn93cHDArl27cPv2bbRq1Qp9+/ZF586dsWTJkordjCK++uorODo66uxv07lzZ9jb2+Prr79GzZo1sWfPHuTl5SEyMhJhYWFYuXKlVDKLi4vDggUL8Nlnn6FRo0Z47rnncPHiRelcX375JR4+fIiwsDCMGzcOM2bM0Cu+efPmoUaNGmjbti169uyJqKgotGjRQuuYZcuWoW/fvnj99dcREhKC4cOHa7V+Aervf0FBAYYMGVLRW1QpMiF0DT6sXnJycuDq6ors7Gy4uLhU+jz7Lu/D02ueLve4vXF70TGwY6WvQ0T04MEDJCcnIygoCHZ2dpU+j1IJ7N+v7rTs46MucXHhYjK2/fv3o3PnzkhNTS23Fays97q+n99c9dyAIupEwM/FD2k5aTr77cggg5+LHyLqRJghOiKikuRyoGNHc0dB1UV+fj5u3LiBqVOn4oUXXqh0ua+iqnQZa9myZWjatClcXFzg4uKC8PBw7NixQ9r/4MEDjBo1CjVr1oSTkxNiYmIqVNs1NLmVHAu7qgvhMmgXwjXPF3RdALkV/2wiIqLqZ8OGDQgICEBWVhbmzp1rsutW6WTHz88Ps2fPxokTJ3D8+HF06tQJvXr1wp9//gkAePPNN/H9999j8+bN+PXXX3Ht2jVEG7vQXI7o0Ghs6bcFtV20C+F+Ln7Y0m8LokPNGx8REZG5DB48GEqlEidOnEDt4h3GjOix67Pj7u6Ojz/+GH379oWHhwfWr1+Pvn37AgD++usvhIaG4tChQ2jTpo3e5zRUn52ilCol9qfsR3puOnycfRBRJ4ItOkRkMIbqs0NU1VWrPjtKpRKbN2/G3bt3ER4ejhMnTqCwsBBdikwEERISgjp16pSb7OTn52sNI8zJyTF4vHIrOTshExERVQFVuowFqFeUdXJygkKhwMiRI7F161Y0bNgQGRkZsLW1hZubm9bxXl5eyMjIKPOcs2bNgqurq/Tw9/c34ldARGQ8j1njPFGFGeI9XuWTnQYNGiApKQlHjhzBa6+9hri4OJw7d+6Rzjlx4kRkZ2dLj9TUVANFS0RkGpr5VO7du2fmSIiMS/Me17UOmL6qfBnL1tZWWvY9LCwMx44dw8KFC/Hiiy+ioKAAWVlZWq07mZmZ8Pb2LvOcCoUCCoXCmGETERmVXC6Hm5ubtKCkg4ODtOQCkSUQQuDevXu4fv063NzctBZTragqn+wUp1KpkJ+fj7CwMNjY2CAxMRExMTEAgAsXLiAlJcUkU08TEZmb5g+7slbQJnrcubm5lduIUZ4qnexMnDgR3bp1Q506dZCbm4v169dj37592LVrF1xdXTFs2DC89dZbcHd3h4uLC8aMGYPw8PAKjcQiInpcyWQy+Pj4wNPTs9RVq4keZzY2No/UoqNRpZOd69evY9CgQUhPT4erqyuaNm2KXbt24ZlnngEAzJ8/H1ZWVoiJiUF+fj6ioqLw2WefmTlqIiLTksvlBvlAILJUj908O8ZgjHl2iIiIyLj0/fyu8qOxiIiIiB4Fkx0iIiKyaFW6z46paCp5xphJmYiIiIxD87ldXo8cJjsAcnNzAYAzKRMRET2GcnNz4erqWup+dlCGeu6ea9euwdnZ2aCTcuXk5MDf3x+pqans+GxEvM+mw3ttGrzPpsH7bBrGvM9CCOTm5sLX1xdWVqX3zGHLDgArKyv4+fkZ7fwuLi78QTIB3mfT4b02Dd5n0+B9Ng1j3eeyWnQ02EGZiIiILBqTHSIiIrJoTHaMSKFQYMqUKVx01Mh4n02H99o0eJ9Ng/fZNKrCfWYHZSIiIrJobNkhIiIii8Zkh4iIiCwakx0iIiKyaEx2iIiIyKIx2TGipUuXIjAwEHZ2dmjdujWOHj1q7pAea7NmzUKrVq3g7OwMT09P9O7dGxcuXNA65sGDBxg1ahRq1qwJJycnxMTEIDMz00wRP/5mz54NmUyGcePGSdt4jw0nLS0NAwcORM2aNWFvb48mTZrg+PHj0n4hBD744AP4+PjA3t4eXbp0wcWLF80Y8eNHqVRi8uTJCAoKgr29PerVq4fp06drraXE+1xxv/32G3r27AlfX1/IZDJs27ZNa78+9/T27dsYMGAAXFxc4ObmhmHDhiEvL884AQsyio0bNwpbW1vx5Zdfij///FMMHz5cuLm5iczMTHOH9tiKiooS8fHx4uzZsyIpKUl0795d1KlTR+Tl5UnHjBw5Uvj7+4vExERx/Phx0aZNG9G2bVszRv34Onr0qAgMDBRNmzYVY8eOlbbzHhvG7du3RUBAgBg8eLA4cuSI+Pfff8WuXbvEP//8Ix0ze/Zs4erqKrZt2yZOnz4tnn/+eREUFCTu379vxsgfLzNnzhQ1a9YUP/zwg0hOThabN28WTk5OYuHChdIxvM8V99NPP4n3339fJCQkCABi69atWvv1uaddu3YVzZo1E4cPHxb79+8X9evXF7GxsUaJl8mOkTz11FNi1KhR0nOlUil8fX3FrFmzzBiVZbl+/boAIH799VchhBBZWVnCxsZGbN68WTrm/PnzAoA4dOiQucJ8LOXm5org4GCxe/duERkZKSU7vMeG884774j27duXul+lUglvb2/x8ccfS9uysrKEQqEQGzZsMEWIFqFHjx5i6NChWtuio6PFgAEDhBC8z4ZQPNnR556eO3dOABDHjh2TjtmxY4eQyWQiLS3N4DGyjGUEBQUFOHHiBLp06SJts7KyQpcuXXDo0CEzRmZZsrOzAQDu7u4AgBMnTqCwsFDrvoeEhKBOnTq87xU0atQo9OjRQ+teArzHhrR9+3a0bNkSL7zwAjw9PfHkk09i5cqV0v7k5GRkZGRo3WtXV1e0bt2a97oC2rZti8TERPz9998AgNOnT+PAgQPo1q0bAN5nY9Dnnh46dAhubm5o2bKldEyXLl1gZWWFI0eOGDwmLgRqBDdv3oRSqYSXl5fWdi8vL/z1119misqyqFQqjBs3Du3atUPjxo0BABkZGbC1tYWbm5vWsV5eXsjIyDBDlI+njRs34uTJkzh27FiJfbzHhvPvv/9i2bJleOutt/Dee+/h2LFjeOONN2Bra4u4uDjpfur6PcJ7rb93330XOTk5CAkJgVwuh1KpxMyZMzFgwAAA4H02An3uaUZGBjw9PbX2W1tbw93d3Sj3nckOPZZGjRqFs2fP4sCBA+YOxaKkpqZi7Nix2L17N+zs7MwdjkVTqVRo2bIlPvroIwDAk08+ibNnz2L58uWIi4szc3SWY9OmTVi3bh3Wr1+PRo0aISkpCePGjYOvry/vczXCMpYR1KpVC3K5vMQIlczMTHh7e5spKssxevRo/PDDD9i7dy/8/Pyk7d7e3igoKEBWVpbW8bzv+jtx4gSuX7+OFi1awNraGtbW1vj111+xaNEiWFtbw8vLi/fYQHx8fNCwYUOtbaGhoUhJSQEA6X7y98ij+d///od3330X/fv3R5MmTfDyyy/jzTffxKxZswDwPhuDPvfU29sb169f19r/8OFD3L592yj3ncmOEdja2iIsLAyJiYnSNpVKhcTERISHh5sxssebEAKjR4/G1q1bsWfPHgQFBWntDwsLg42NjdZ9v3DhAlJSUnjf9dS5c2ecOXMGSUlJ0qNly5YYMGCA9H/eY8No165diakT/v77bwQEBAAAgoKC4O3trXWvc3JycOTIEd7rCrh37x6srLQ/6uRyOVQqFQDeZ2PQ556Gh4cjKysLJ06ckI7Zs2cPVCoVWrdubfigDN7lmYQQ6qHnCoVCrF69Wpw7d06MGDFCuLm5iYyMDHOH9th67bXXhKurq9i3b59IT0+XHvfu3ZOOGTlypKhTp47Ys2ePOH78uAgPDxfh4eFmjPrxV3Q0lhC8x4Zy9OhRYW1tLWbOnCkuXrwo1q1bJxwcHMTXX38tHTN79mzh5uYmvvvuO/HHH3+IXr16cUh0BcXFxYnatWtLQ88TEhJErVq1xIQJE6RjeJ8rLjc3V5w6dUqcOnVKABDz5s0Tp06dEleuXBFC6HdPu3btKp588klx5MgRceDAAREcHMyh54+jxYsXizp16ghbW1vx1FNPicOHD5s7pMcaAJ2P+Ph46Zj79++L119/XdSoUUM4ODiIPn36iPT0dPMFbQGKJzu8x4bz/fffi8aNGwuFQiFCQkLEihUrtParVCoxefJk4eXlJRQKhejcubO4cOGCmaJ9POXk5IixY8eKOnXqCDs7O1G3bl3x/vvvi/z8fOkY3ueK27t3r87fx3FxcUII/e7prVu3RGxsrHBychIuLi5iyJAhIjc31yjxyoQoMo0kERERkYVhnx0iIiKyaEx2iIiIyKIx2SEiIiKLxmSHiIiILBqTHSIiIrJoTHaIiIjIojHZISIiIovGZIeICIBMJsO2bdvMHQYRGQGTHSIyu8GDB0Mmk5V4dO3a1dyhEZEFsDZ3AEREANC1a1fEx8drbVMoFGaKhogsCVt2iKhKUCgU8Pb21nrUqFEDgLrEtGzZMnTr1g329vaoW7cutmzZovX6M2fOoFOnTrC3t0fNmjUxYsQI5OXlaR3z5ZdfolGjRlAoFPDx8cHo0aO19t+8eRN9+vSBg4MDgoODsX37dmnfnTt3MGDAAHh4eMDe3h7BwcElkjMiqpqY7BDRY2Hy5MmIiYnB6dOnMWDAAPTv3x/nz58HANy9exdRUVGoUaMGjh07hs2bN+OXX37RSmaWLVuGUaNGYcSIEThz5gy2b9+O+vXra11j2rRp6NevH/744w90794dAwYMwO3bt6Xrnzt3Djt27MD58+exbNky1KpVy3Q3gIgqzyjLixIRVUBcXJyQy+XC0dFR6zFz5kwhhHrF+5EjR2q9pnXr1uK1114TQgixYsUKUaNGDZGXlyft//HHH4WVlZXIyMgQQgjh6+sr3n///VJjACAmTZokPc/LyxMAxI4dO4QQQvTs2VMMGTLEMF8wEZkU++wQUZXw9NNPY9myZVrb3N3dpf+Hh4dr7QsPD0dSUhIA4Pz582jWrBkcHR2l/e3atYNKpcKFCxcgk8lw7do1dO7cucwYmjZtKv3f0dERLi4uuH79OgDgtddeQ0xMDE6ePIlnn30WvXv3Rtu2bSv1tRKRaTHZIaIqwdHRsURZyVDs7e31Os7GxkbruUwmg0qlAgB069YNV65cwU8//YTdu3ejc+fOGDVqFD755BODx0tEhsU+O0T0WDh8+HCJ56GhoQCA0NBQnD59Gnfv3pX2Hzx4EFZWVmjQoAGcnZ0RGBiIxMTER4rBw8MDcXFx+Prrr7FgwQKsWLHikc5HRKbBlh0iqhLy8/ORkZGhtc3a2lrqBLx582a0bNkS7du3x7p163D06FGsWrUKADBgwABMmTIFcXFxmDp1Km7cuIExY8bg5ZdfhpeXFwBg6tSpGDlyJDw9PdGtWzfk5ubi4MGDGDNmjF7xffDBBwgLC0OjRo2Qn5+PH374QUq2iKhqY7JDRFXCzp074ePjo7WtQYMG+OuvvwCoR0pt3LgRr7/+Onx8fLBhwwY0bNgQAODg4IBdu3Zh7NixaNWqFRwcHBATE4N58+ZJ54qLi8ODBw8wf/58jB8/HrVq1ULfvn31js/W1hYTJ07E5cuXYW9vj4iICGzcuNEAXzkRGZtMCCHMHQQRUVlkMhm2bt2K3r17mzsUInoMsc8OERERWTQmO0RERGTR2GeHiKo8VtuJ6FGwZYeIiIgsGpMdIiIismhMdoiIiMiiMdkhIiIii8Zkh4iIiCwakx0iIiKyaEx2iIiIyKIx2SEiIiKLxmSHiIiILNr/ARKh75TBgIhXAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Chebyshev Polynomials\n",
        "This model is defined as follows:\n",
        "\n",
        "$\\sum_{k=0}^KT_k(\\tilde{L})X\\theta_k$\n",
        "\n",
        "We set K = 2"
      ],
      "metadata": {
        "id": "pw2N2g7jwSbS"
      },
      "id": "pw2N2g7jwSbS"
    },
    {
      "cell_type": "code",
      "source": [
        "A = cora_data.get_adjacency_matrix().to(device)\n",
        "X = cora_data.get_fullx().to(device)\n",
        "\n",
        "D = torch.sum(A, dim=1)\n",
        "A_norm = torch.diag(D ** (-1/2)) @ A @ torch.diag(D ** (-1/2))"
      ],
      "metadata": {
        "id": "ZuxW_lXMwOd1"
      },
      "id": "ZuxW_lXMwOd1",
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# define one layer of Chebyshev polynomial\n",
        "class ChebyshevPolyLayer(nn.Module):\n",
        "    def __init__(self, in_feat, out_feat, A_norm, k):\n",
        "        super().__init__()\n",
        "        self.in_feat = in_feat\n",
        "        self.out_feat = out_feat\n",
        "        self.k = k\n",
        "        self.out_shape = (A_norm.shape[0], out_feat)\n",
        "\n",
        "        # Trainable weights\n",
        "        self.linear_layers = []\n",
        "        for i in range(k+1):\n",
        "            self.linear_layers.append(nn.Linear(in_feat, out_feat))\n",
        "        self.linear_layers = nn.ModuleList(self.linear_layers)\n",
        "\n",
        "        # Get the normalized Laplcian matrix\n",
        "        I = torch.eye(A_norm.shape[0]).to(device) # I_N\n",
        "        laplacian = I - A_norm # I_N - A_tilde\n",
        "\n",
        "        # get the eigen value of Laplacian\n",
        "        largest_eigval = torch.linalg.eigvalsh(laplacian).max()\n",
        "\n",
        "        # scale the Laplacian -> (2/eig_val) * Laplacian - I_N\n",
        "        scaled_laplacian = (2. / largest_eigval) * laplacian - I\n",
        "\n",
        "        # create list for the Chebyshev polynomials\n",
        "        self.t_k = []\n",
        "\n",
        "        # first term is Identity matrix\n",
        "        self.t_k.append(I)\n",
        "\n",
        "        # second term is scaled Laplacian\n",
        "        self.t_k.append(scaled_laplacian)\n",
        "\n",
        "        # define the Chebyshev recurrence ->\n",
        "        # T_k[x] = 2xT_(k-1)[x] - T_(k−2)(x), with T_0(x) = 1 and T_1(x) = x.\n",
        "        def chebyshev_recurrence(t_k_minus_one, t_k_minus_two, scaled_lap):\n",
        "            return (2. * (scaled_lap @ t_k_minus_one)) - t_k_minus_two\n",
        "\n",
        "        # fill the Chebyshev polynomial list for k terms\n",
        "        for i in range(2, k+1):\n",
        "            self.t_k.append(chebyshev_recurrence(self.t_k[-1],\n",
        "                                                 self.t_k[-2],\n",
        "                                                 scaled_laplacian))\n",
        "\n",
        "    def forward(self, x):\n",
        "        out = torch.zeros(self.out_shape).to(device)\n",
        "        for i in range(self.k + 1):\n",
        "            x1 = self.t_k[i] @ x\n",
        "            x2 = self.linear_layers[i](x1)\n",
        "            out += x2\n",
        "        return out\n",
        "\n",
        "    def __repr__(self):\n",
        "        return f\"Chebyshev Layer ({self.in_feat} -> {self.out_feat})\"\n",
        "\n",
        "# create the Chebyshev polynomial model\n",
        "class ChebyshevPolyModel(nn.Module):\n",
        "    def __init__(self, in_feat, num_hidden, nclass, A_norm, k, actn, dropout=None):\n",
        "        super().__init__()\n",
        "        self.cheb_l1 = ChebyshevPolyLayer(in_feat, num_hidden, A_norm, k)\n",
        "        self.cheb_l2 = ChebyshevPolyLayer(num_hidden, nclass, A_norm, k)\n",
        "\n",
        "        self.dropout = dropout\n",
        "        self.actn = actn\n",
        "\n",
        "    def forward(self, x, A_norm):\n",
        "        x = self.actn(self.cheb_l1(x))\n",
        "        if self.dropout is not None:\n",
        "            x = F.dropout(x, p=self.dropout, training=self.training)\n",
        "        x = self.cheb_l2(x)\n",
        "        return x"
      ],
      "metadata": {
        "id": "WkSmxiYF1mTX"
      },
      "id": "WkSmxiYF1mTX",
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model = ChebyshevPolyModel(in_feat=train_x.shape[-1],\n",
        "                           num_hidden=16, nclass=7,\n",
        "                           A_norm=A_norm, k=2,\n",
        "                           actn=F.relu, dropout=0.5).to(device)\n",
        "\n",
        "train_y = train_y.to(device)\n",
        "valid_y = valid_y.to(device)\n",
        "test_y = test_y.to(device)\n",
        "\n",
        "train_mask = cora_data.train_mask.to(device)\n",
        "valid_mask = cora_data.valid_mask.to(device)\n",
        "test_mask = cora_data.test_mask.to(device)\n",
        "\n",
        "train_stats_gnn_cora = train_eval_loop_gnn_cora(model, A_norm, X, train_y, train_mask,\n",
        "                                          X, valid_y, valid_mask,\n",
        "                                          X, test_y, test_mask\n",
        "                                       )\n",
        "plot_stats(train_stats_gnn_cora, model_name=\"Chebyshev Cora Model\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "3HIwtC4i-tUX",
        "outputId": "a6c44d37-5d61-4ee1-ca44-9b79c2f09531"
      },
      "id": "3HIwtC4i-tUX",
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch 0 with train loss: 2.000 train accuracy: 36.429 validation accuracy: 18.400\n",
            "Epoch 10 with train loss: 0.202 train accuracy: 100.000 validation accuracy: 74.000\n",
            "Epoch 20 with train loss: 0.039 train accuracy: 100.000 validation accuracy: 74.400\n",
            "Epoch 30 with train loss: 0.017 train accuracy: 100.000 validation accuracy: 75.400\n",
            "Epoch 40 with train loss: 0.005 train accuracy: 100.000 validation accuracy: 76.000\n",
            "Epoch 50 with train loss: 0.009 train accuracy: 100.000 validation accuracy: 74.400\n",
            "Epoch 60 with train loss: 0.009 train accuracy: 100.000 validation accuracy: 76.600\n",
            "Epoch 70 with train loss: 0.030 train accuracy: 100.000 validation accuracy: 78.000\n",
            "Epoch 80 with train loss: 0.019 train accuracy: 100.000 validation accuracy: 77.200\n",
            "Epoch 90 with train loss: 0.015 train accuracy: 100.000 validation accuracy: 75.800\n",
            "Epoch 100 with train loss: 0.005 train accuracy: 100.000 validation accuracy: 77.200\n",
            "Our final test accuracy for the GCN is: 80.600\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Final thoughts\n",
        "That's it for this post. I have tried explaining GCN in the most simplest way. There are some topics I haven't covered in this post:\n",
        "- The mathematical concepts behind graph convolution, as I felt, would make the post too lengthy, and readers might lose interest. Also, the reader needs to understand spectral graph theory to comprehend the derivation of the GCN equation. I have added some links in the References that try to explain the math behind the paper.\n",
        "\n",
        "- Sparse implementation: As the adjacency matrix contains mostly zero values, doing sparse implementation is beneficial and the author has used this approach in the official released code. As this post was to explain GCN and not the \"efficient implementation of GCN\", I have skipped the sparse implementation. Keen readers are encouraged to explore the official code for an in-depth examination of the sparse implementation (Link provided in references).\n",
        "\n",
        "- Training GCN on Zachary Karate Club dataset using self-supervised mechanism. I feel that the training output is too trivial to understand.\n",
        "\n",
        "- Discussion on time complexity of GCN model and it's variants. I'll try to cover it in the next revision whenever it get time for it.\n",
        "\n",
        "- Limitations of the GCN model: Ferenc Huszár has done a great job in his post explaining the limitations of GCN model. Furthermore, the author has acknowledged and discussed these limitations in the comments section of his blog post. I recommend all the interested readers to go through his post. I have provided the link in the references.\n",
        "\n",
        "\n",
        "I would like to recommend reading the GCN paper in detail to understand the most of it. I would also recommend going through the code released by the author to understand the experiments in detail. I have added the link to it in the references. Lastly, I invite readers to find any kind of errors in this post and reach out to me on my [Email ID](mailto:nitinnilesh49@gmail.com)."
      ],
      "metadata": {
        "id": "vglk2byq2WoQ"
      },
      "id": "vglk2byq2WoQ"
    },
    {
      "cell_type": "markdown",
      "source": [
        "## References\n",
        "1. Blog by Thomas Kipf (Author of the paper) - https://tkipf.github.io/graph-convolutional-networks/\n",
        "2. A great post by Matthew Bernstein on GCN - https://mbernste.github.io/posts/gcn/\n",
        "3. A critical post by Ferenc Huszár - https://www.inference.vc/how-powerful-are-graph-convolutions-review-of-kipf-welling-2016-2/\n",
        "4. Understanding GNNs (Distill pub post 🙏) - https://distill.pub/2021/gnn-intro/, https://distill.pub/2021/understanding-gnns/\n",
        "5. Code by the author - https://github.com/tkipf/gcn\n",
        "6. Geometric Deep Learning Course - https://geometricdeeplearning.com/lectures/\n",
        "7. A Medium post explaining the math behind Spectral Graph Convolutions - https://medium.com/@jlcastrog99/spectral-graph-convolutions-c7241af4d8e2\n",
        "8. https://www.topbots.com/graph-convolutional-networks/\n",
        "9. Lectures on Spectral Graph Theory by Fan R. K. Chung - https://mathweb.ucsd.edu/~fan/research/cbms.pdf\n"
      ],
      "metadata": {
        "id": "VodvC5s8v0Ef"
      },
      "id": "VodvC5s8v0Ef"
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
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