ManybodyMPNN_SyntheticZINC_OSQ_Playground.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "UxpH6cSe3kCC",
    "outputId": "88ae1138-f5b1-4d88-e332-c1c93e2340c1"
   },
   "outputs": [],
   "source": [
    "#@title Installation and Imports\n",
    "\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "import scipy.linalg\n",
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "PYB7ZpPP3rdW",
    "outputId": "387c5508-408e-4577-9b2c-07bd6661eef1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input dimensions: torch.Size([10, 4])\n",
      "Output dimensions: torch.Size([10, 12])\n"
     ]
    }
   ],
   "source": [
    "#@title Many-body MPNNConv Layer\n",
    "\n",
    "import scipy.sparse as sp\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.init as init\n",
    "from torch_geometric.nn import ChebConv\n",
    "from torch_geometric.utils import to_networkx, to_scipy_sparse_matrix, add_self_loops, get_laplacian, to_dense_adj\n",
    "\n",
    "class ManyBodyMPNNConv(nn.Module):\n",
    "    def __init__(self, in_channels, out_channels, max_order, edge_feature_dim, K=3):\n",
    "        super(ManyBodyMPNNConv, self).__init__()\n",
    "        self.in_channels = in_channels\n",
    "        self.out_channels = out_channels\n",
    "        self.max_order = max_order\n",
    "        self.K = K\n",
    "        self.U, self.V = self.precompute_motif_eigenvectors(max_order + 1)\n",
    "\n",
    "        self.W_cheb = nn.ParameterList([nn.Parameter(torch.randn(out_channels, in_channels, K)) for _ in range(max_order)])\n",
    "        self.W_cheb_motif = nn.ParameterList([nn.Parameter(torch.randn(in_channels, k, K)) for k in range(2, max_order+1)])\n",
    "        self.W_msg = nn.Linear(in_channels, out_channels)\n",
    "\n",
    "    @staticmethod\n",
    "    def precompute_motif_eigenvectors(n):\n",
    "        U, V = {}, {}\n",
    "        for i in range(2, n + 1):\n",
    "            motif_graph = nx.star_graph(i - 1)\n",
    "            laplacian_matrix = nx.laplacian_matrix(motif_graph).toarray()\n",
    "            eigenvalues, eigenvectors = scipy.linalg.eigh(laplacian_matrix)\n",
    "            U[i] = torch.linalg.inv(torch.tensor(eigenvectors, dtype=torch.float))\n",
    "            V[i] = torch.tensor(eigenvalues, dtype=torch.float)\n",
    "        return U, V\n",
    "\n",
    "    def chebyshev_expansion(self, x, K):\n",
    "        T_0, T_1 = torch.ones_like(x), x\n",
    "        expansion = [T_0, T_1]\n",
    "        for k in range(2, K + 1):\n",
    "            T_k = 2 * x * T_1 - T_0\n",
    "            expansion.append(T_k)\n",
    "            T_0, T_1 = T_1, T_k\n",
    "        return torch.stack(expansion, dim=-1)\n",
    "\n",
    "    def apply_chebyshev(self, L, X, K):\n",
    "        X_0 = X\n",
    "        X_1 = torch.matmul(L, X)\n",
    "        result = self.W_cheb[0][:, :, 0].unsqueeze(1) * X_0 + self.W_cheb[0][:, :, 1].unsqueeze(1) * X_1\n",
    "        for k in range(2, K):\n",
    "            X_k = 2 * torch.matmul(L, X_1) - X_0\n",
    "            result += self.W_cheb[0][:, :, k].unsqueeze(1) * X_k\n",
    "            X_0, X_1 = X_1, X_k\n",
    "        return result\n",
    "\n",
    "    def higher_order_interaction(self, H, edge_index):\n",
    "\n",
    "        # Initialize the output feature matrix\n",
    "        Y = torch.zeros_like(H)\n",
    "\n",
    "        # Iterate through orders from 2 to max_order\n",
    "        for order in range(2, self.max_order + 1):\n",
    "            # Retrieve the precomputed eigenvectors U_k and eigenvalues for the current order\n",
    "            U_k = self.U[order].to(H.device)\n",
    "            lambda_k = self.V[order].to(H.device)\n",
    "\n",
    "            # Scale the eigenvalues for Chebyshev expansion and perform the expansion\n",
    "            scaled_eigenvalues = 2 * lambda_k / lambda_k.max() - 1\n",
    "            T_k = self.chebyshev_expansion(scaled_eigenvalues, self.K)\n",
    "\n",
    "            # Apply the filter defined by the Chebyshev expansion\n",
    "            for i in range(self.K):\n",
    "                # Chebyshev polynomial of degree i on the Laplacian, weighted by W_cheb\n",
    "                filter_response = torch.matmul(U_k, torch.matmul(torch.diag(T_k[:, i]), U_k.t()))\n",
    "                weights = self.W_cheb_motif[order-2][:, :, i]  # Assuming this needs to align with `result`\n",
    "                result = torch.einsum(\"ni,ik->ni\", H, torch.matmul(weights, filter_response.t()))\n",
    "                Y += result\n",
    "\n",
    "        return Y\n",
    "\n",
    "    def forward(self, H, edge_index, edge_features=None):\n",
    "        # Compute Laplacian\n",
    "        edge_index, edge_weight = add_self_loops(edge_index, num_nodes=H.size(0))\n",
    "        edge_weight = torch.ones(edge_index.size(1), device=H.device)\n",
    "        L = get_laplacian(edge_index, edge_weight, normalization='sym', dtype=torch.float, num_nodes=H.size(0))\n",
    "\n",
    "        L_dense = to_dense_adj(L[0], edge_attr=L[1], max_num_nodes=H.size(0)).squeeze(0)\n",
    "        L_scaled = 2 * L_dense - torch.eye(L_dense.size(0), device=H.device)\n",
    "\n",
    "        # Direct interaction via a custom Chebyshev operation\n",
    "        X_2 = self.apply_chebyshev(L_scaled, H, self.K)\n",
    "        # Higher-order interactions\n",
    "        m = self.higher_order_interaction(H, edge_index)\n",
    "        # Combine direct and higher-order interactions\n",
    "        H_next = X_2.transpose(0, 1).sum(-1) + self.W_msg(m)\n",
    "        return H_next\n",
    "\n",
    "    def __initialize_weights(self):\n",
    "        for w in self.W_cheb:\n",
    "            init.kaiming_uniform_(w, a=np.sqrt(5))\n",
    "        for w in self.W_cheb_motif:\n",
    "            init.kaiming_uniform_(w, a=np.sqrt(5))\n",
    "\n",
    "\n",
    "# Dummy data to illustrate usage\n",
    "num_nodes = 10\n",
    "in_channels = 4\n",
    "out_channels = 12\n",
    "max_order = 3\n",
    "edge_feature_dim = 1\n",
    "batch_size = 2\n",
    "\n",
    "# Instantiate the layer with the learnable_ricci set to True or False based on your setup\n",
    "layer = ManyBodyMPNNConv(in_channels, out_channels, max_order, edge_feature_dim)\n",
    "\n",
    "# Dummy node feature matrix\n",
    "H = torch.randn(num_nodes, in_channels)\n",
    "\n",
    "# Generate a dummy sparse edge index for a fully-connected graph for simplicity\n",
    "edge_index = torch.combinations(torch.arange(num_nodes), 2).t()\n",
    "\n",
    "# Simulate edge features if needed\n",
    "edge_features = torch.randint(0, 10, (edge_index.size(1), edge_feature_dim)).to(torch.float32)\n",
    "\n",
    "# Adapt the model call to the new API. Note: Adjust num_nodes if batching logic is different.\n",
    "H_next = layer(H, edge_index, edge_features=edge_features)\n",
    "\n",
    "print(\"Input dimensions:\", H.shape)\n",
    "print(\"Output dimensions:\", H_next.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZL8ohW2PdNcm"
   },
   "source": [
    "To validate Theorem 4.1 using synthetic datasets and GCN models, we'll perform experiments that track the sensitivity of node features in a GCN to the information contained at other nodes at various distances / commute time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 516
    },
    "id": "mrT-jjPqx7hm",
    "outputId": "9d6d72ba-e7be-41cb-e07f-786003899ec7"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Matplotlib created a temporary cache directory at /tmp/matplotlib-c99rp0ya because the default path (/scratch-ssd/oatml/matplotlib) is not a writable directory; it is highly recommended to set the MPLCONFIGDIR environment variable to a writable directory, in particular to speed up the import of Matplotlib and to better support multiprocessing.\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Example Star Graphs with Distorted Structures (Negative Ricci Curvature)\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Helper function to create a star-like structure\n",
    "def create_star(center, leaf_nodes):\n",
    "    star = nx.Graph()\n",
    "    for leaf in leaf_nodes:\n",
    "        star.add_edge(center, leaf)\n",
    "    return star\n",
    "\n",
    "# Main function to generate a graph that resembles the attached image\n",
    "def generate_custom_graph():\n",
    "    # Create a base chain graph\n",
    "    chain = nx.path_graph(6)\n",
    "\n",
    "    # Create branches as star graphs\n",
    "    branch1 = create_star(1, [7, 8, 9])  # First branch\n",
    "    branch2 = create_star(3, [10, 11, 12, 13, 14])  # Second branch\n",
    "    branch3 = create_star(5, [15, 16, 17])  # Third branch\n",
    "\n",
    "    # Combine the branches with the main chain graph\n",
    "    G = nx.disjoint_union(chain, branch1)\n",
    "    G = nx.disjoint_union(G, branch2)\n",
    "    G = nx.disjoint_union(G, branch3)\n",
    "\n",
    "    # Now we need to manually add edges between the main chain and the branches\n",
    "    G.add_edge(1, 7)\n",
    "    G.add_edge(3, 10)\n",
    "    G.add_edge(5, 15)\n",
    "\n",
    "    return G\n",
    "\n",
    "# Generate the graph\n",
    "custom_graph = generate_custom_graph()\n",
    "\n",
    "# Draw the graph\n",
    "nx.draw(custom_graph, with_labels=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cellView": "form",
    "id": "WanyGlvx30xd"
   },
   "outputs": [],
   "source": [
    "# @title Synthetic Dataset Generation (ZINC star graphs)\n",
    "import torch\n",
    "from torch_geometric.data import Data\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "from itertools import combinations\n",
    "from scipy.sparse.csgraph import connected_components\n",
    "from scipy.sparse import csr_matrix\n",
    "\n",
    "def generate_large_star_graph(base_size, branches_per_node):\n",
    "    G = nx.Graph()\n",
    "\n",
    "    # Create the base path (spine of the star)\n",
    "    base_nodes = list(range(base_size))\n",
    "    G.add_nodes_from(base_nodes)\n",
    "    for i in range(len(base_nodes) - 1):\n",
    "        G.add_edge(base_nodes[i], base_nodes[i + 1])\n",
    "\n",
    "    # Generate branches and attach them to the spine nodes\n",
    "    leaf_counter = base_size\n",
    "    for spine_node in base_nodes:\n",
    "        for _ in range(branches_per_node):\n",
    "            G.add_node(leaf_counter)\n",
    "            G.add_edge(spine_node, leaf_counter)\n",
    "            leaf_counter += 1\n",
    "\n",
    "    # Convert to edge_index format for PyTorch Geometric\n",
    "    edge_index = torch.tensor(list(G.edges())).t().contiguous()\n",
    "    return edge_index\n",
    "\n",
    "# Function to generate synthetic ZINC datasets with large star graph structure\n",
    "def generate_synthetic_zinc_star_graphs(num_graphs, base_size, branches_per_node, num_features, num_edge_features):\n",
    "    graphs = []\n",
    "    for _ in range(num_graphs):\n",
    "        edge_indices = generate_large_star_graph(base_size, branches_per_node)\n",
    "        num_nodes = base_size + branches_per_node * base_size\n",
    "        node_features = torch.randn((num_nodes, num_features))\n",
    "        edge_features = torch.randn((edge_indices.size(1), num_edge_features))\n",
    "        y = torch.randn((1,))  # Placeholder target value\n",
    "\n",
    "        data = Data(x=node_features, edge_index=edge_indices, edge_attr=edge_features, y=y)\n",
    "        graphs.append(data)\n",
    "    return graphs\n",
    "\n",
    "# Example usage:\n",
    "base_size = 200  # Increase base size for larger graph\n",
    "branches_per_node = 4  # Increase branches per node\n",
    "num_features = 8 # Increase the dimensionality of node features\n",
    "num_edge_features = 2  # Increase the dimensionality of edge features\n",
    "num_graphs = 1\n",
    "\n",
    "large_synthetic_zinc_star_graphs = generate_synthetic_zinc_star_graphs(\n",
    "    num_graphs, base_size, branches_per_node, num_features, num_edge_features\n",
    ")\n",
    "# Function to plot the histogram of pairwise commute times for a given graph\n",
    "def plot_commute_times_histogram(graph, num_nodes):\n",
    "    # Convert the edge index to a NetworkX graph for easier manipulation\n",
    "    G = nx.Graph()\n",
    "    G.add_edges_from(graph.edge_index.t().numpy())\n",
    "\n",
    "    # Calculate commute times for all pairs of nodes\n",
    "    commute_times = {}\n",
    "    for i in range(num_nodes):\n",
    "        for j in range(i + 1, num_nodes):\n",
    "            _, commute_time = simulate_random_walk(G, i, j)\n",
    "            commute_times[(i,j)] = commute_time\n",
    "\n",
    "    # Plot the histogram of commute times\n",
    "    plt.hist(list(commute_times.values()), bins=20)\n",
    "    plt.xlabel('Commute Time')\n",
    "    plt.ylabel('Frequency')\n",
    "    plt.title('Histogram of Pairwise Commute Times')\n",
    "    plt.show()\n",
    "\n",
    "    return commute_times\n",
    "\n",
    "# Select one graph to illustrate\n",
    "# commute_times = plot_commute_times_histogram(large_synthetic_zinc_star_graphs[0], num_nodes=base_size + branches_per_node)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "cellView": "form",
    "id": "pbgj3hVV4A2b"
   },
   "outputs": [],
   "source": [
    "#@title Many-Body MPNN, GCN, GraphSage, ChebNet Models\n",
    "import torch\n",
    "import torch.nn.functional as F\n",
    "from torch.nn import ModuleList, BatchNorm1d, Linear\n",
    "from torch_geometric.nn import (\n",
    "    ChebConv,\n",
    "    GCNConv,\n",
    "    SAGEConv,\n",
    "    GatedGraphConv,\n",
    "    global_mean_pool,\n",
    ")\n",
    "\n",
    "\n",
    "class BaseGNN(nn.Module):\n",
    "    def __init__(self, in_channels, hidden_channels, out_channels, num_layers, conv_layer_type, dropout=0.5, *args, **kwargs):\n",
    "        super(BaseGNN, self).__init__()\n",
    "        self.convs = nn.ModuleList()\n",
    "        self.bns = nn.ModuleList()\n",
    "        self.dropout = dropout\n",
    "        self.saved_grads = {}  # To store gradients\n",
    "\n",
    "        # Initialize convolutional and batch norm layers\n",
    "        self.convs.append(conv_layer_type(in_channels, hidden_channels, *args, **kwargs))\n",
    "        self.bns.append(BatchNorm1d(hidden_channels))\n",
    "        for _ in range(1, num_layers):\n",
    "            self.convs.append(conv_layer_type(hidden_channels, hidden_channels, *args, **kwargs))\n",
    "            self.bns.append(BatchNorm1d(hidden_channels))\n",
    "\n",
    "        self.lin1 = Linear(hidden_channels, out_channels)\n",
    "\n",
    "        self.__initialize_weights()\n",
    "        # Register backward hooks for all convolutional layers\n",
    "        for idx, conv in enumerate(self.convs):\n",
    "            conv.register_backward_hook(self.__make_hook(f'conv_{idx}'))\n",
    "\n",
    "    def forward(self, data):\n",
    "        x, edge_index, batch = data.x, data.edge_index, data.batch\n",
    "        for i, (conv, bn) in enumerate(zip(self.convs, self.bns)):\n",
    "            x = conv(x, edge_index)\n",
    "            x = bn(x)\n",
    "            x = F.leaky_relu(x)\n",
    "            x = F.dropout(x, p=self.dropout, training=self.training)\n",
    "        x = global_mean_pool(x, batch)\n",
    "        x = self.lin1(x)\n",
    "        return x\n",
    "\n",
    "    def __initialize_weights(self):\n",
    "        for conv in self.convs:\n",
    "            if hasattr(conv, 'weight'):\n",
    "                nn.init.kaiming_uniform_(conv.weight, nonlinearity='leaky_relu')\n",
    "            if hasattr(conv, 'bias') and conv.bias is not None:\n",
    "                nn.init.zeros_(conv.bias)\n",
    "        nn.init.kaiming_uniform_(self.lin1.weight, nonlinearity='leaky_relu')\n",
    "        nn.init.zeros_(self.lin1.bias)\n",
    "\n",
    "    def __make_hook(self, layer_name):\n",
    "        def hook(module, grad_input, grad_output):\n",
    "            self.saved_grads[layer_name] = grad_output[0].detach()\n",
    "        return hook\n",
    "\n",
    "    def get_gradients(self, layer_name):\n",
    "        \"\"\"Retrieve the saved gradients by layer name.\"\"\"\n",
    "        return self.saved_grads.get(layer_name, None)\n",
    "\n",
    "\n",
    "class ManyBodyMPNN(BaseGNN):\n",
    "    def __init__(self, in_channels, hidden_channels, out_channels, num_layers, max_order, edge_feature_dim, K=3, dropout=0.5):\n",
    "        super(ManyBodyMPNN, self).__init__(in_channels, hidden_channels, out_channels,\n",
    "                                  num_layers, ManyBodyMPNNConv, dropout, max_order, edge_feature_dim, K)\n",
    "\n",
    "class GCN(BaseGNN):\n",
    "    def __init__(self, in_channels, hidden_channels, out_channels, num_layers, dropout=0.5):\n",
    "        super(GCN, self).__init__(in_channels, hidden_channels, out_channels, num_layers, GCNConv, dropout)\n",
    "\n",
    "class ChebNet(BaseGNN):\n",
    "    def __init__(self, in_channels, hidden_channels, out_channels, num_layers, K, dropout=0.5):\n",
    "        super(ChebNet, self).__init__(in_channels, hidden_channels, out_channels, num_layers, ChebConv, dropout, K)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {
    "cellView": "form",
    "id": "aFUOfh6Td6ci"
   },
   "outputs": [],
   "source": [
    "#@title Define Training Loops and Parameters\n",
    "import torch\n",
    "import torch.nn.functional as F\n",
    "from torch_geometric.nn import GCNConv\n",
    "from torch_geometric.utils import add_self_loops\n",
    "from scipy.sparse.csgraph import shortest_path\n",
    "from tqdm.auto import tqdm\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "\n",
    "from collections import defaultdict\n",
    "\n",
    "def compute_J(h_v_m, h_u_m, h_v_k, h_u_k, dv, du):\n",
    "    # Ensure gradient computation is enabled for the scope of this function\n",
    "    J = torch.max((1 / dv) * (h_v_m / h_v_k) - (1 / torch.sqrt(dv * du)) * (h_v_m / h_u_k))\n",
    "    return J\n",
    "\n",
    "def compute_aggregate_J(model, num_of_layers, node_group, degrees):\n",
    "    \"\"\"\n",
    "    Computes the aggregate J values (average and maximum) for a group of nodes.\n",
    "\n",
    "    model: The trained GNN model.\n",
    "    num_of_layers: Number of layers in the model.\n",
    "    node_group: List of node indices in the group.\n",
    "    degrees: Degrees of the nodes in the group.\n",
    "    \"\"\"\n",
    "    # Store all J values for combinations within the group\n",
    "    model.eval()\n",
    "    J_values = {}\n",
    "\n",
    "    # Iterate over all pairs within the group to compute pairwise J\n",
    "    for i in range(len(node_group)):\n",
    "        for j in range(i + 1, len(node_group)):\n",
    "            u, v = node_group[i], node_group[j]\n",
    "            du, dv = degrees[i], degrees[j]\n",
    "\n",
    "            h_m_grad = model.get_gradients(f\"conv_{num_of_layers-1}\")\n",
    "            h_v_m_grad, h_u_m_grad = h_m_grad[v], h_m_grad[u]\n",
    "\n",
    "            J_values[(u,v)] = []\n",
    "            \n",
    "            for k in range(num_of_layers-1):  # Exclude the last layer for comparison\n",
    "                h_k_grad = model.get_gradients(f\"conv_{k}\")\n",
    "                h_v_k_grad, h_u_k_grad = h_k_grad[v], h_k_grad[u]\n",
    "    \n",
    "                # Compute J using the explicitly computed gradients\n",
    "                J = compute_J(h_v_m_grad, h_u_m_grad, h_v_k_grad, h_u_k_grad, \n",
    "                              torch.tensor(dv, dtype=torch.float32), \n",
    "                              torch.tensor(du, dtype=torch.float32))\n",
    "                J_values[(u,v)].append(J.item())\n",
    "\n",
    "    return J_values\n",
    "\n",
    "def simulate_random_walk(graph, node_a, node_b, num_simulations=100):\n",
    "    \"\"\"\n",
    "    Simulate a random walk to calculate the access and commute times\n",
    "    between two nodes in a graph.\n",
    "    \"\"\"\n",
    "    access_times = []\n",
    "    for _ in range(num_simulations):\n",
    "        current_node = node_a\n",
    "        steps_to_reach_b = 0\n",
    "        reached_b = False\n",
    "        while not reached_b:\n",
    "            neighbors = list(graph.neighbors(current_node))\n",
    "            current_node = np.random.choice(neighbors)\n",
    "            steps_to_reach_b += 1\n",
    "            if current_node == node_b and not reached_b:\n",
    "                reached_b = True\n",
    "                access_times.append(steps_to_reach_b)\n",
    "    return np.mean(access_times)\n",
    "\n",
    "def run_experiments(model_name, model, dataset, device, num_of_layers, layer_width, num_epochs=10):\n",
    "    data = dataset.to(device)  # assuming dataset is a Data object\n",
    "    model.to(device)\n",
    "    model.train()\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr=0.01)\n",
    "    J_statistics = defaultdict(dict)\n",
    "\n",
    "    for epoch in tqdm(range(num_epochs), desc=f\"Training Epochs for {model_name}\"):\n",
    "        model.train()\n",
    "        optimizer.zero_grad()\n",
    "        out = model(data)\n",
    "        loss = F.mse_loss(out.squeeze(), data.y)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "\n",
    "    # After training, we compute the J quantity\n",
    "\n",
    "    # Select some pairs of nodes: (for better computational efficiency on estimating commute time)\n",
    "    # node_pairs_with_neighbors = [\n",
    "    #     [0, 1, 5, 6],     # Spine nodes at the beginning have 5 and 6 neighbors, respectively\n",
    "    #     [198, 199, 6, 5], # Spine nodes at the end have 6 and 5 neighbors, respectively\n",
    "    #     [50, 70, 6, 6],   # Middle spine nodes, both have 6 neighbors\n",
    "    #     [100, 125, 6, 6], # Another pair of middle spine nodes, both have 6 neighbors\n",
    "    #     [0, 199, 5, 5],   # First and last spine nodes\n",
    "    #     [10, 190, 6, 6],  # Spine nodes slightly inwards from the ends\n",
    "    #     [200, 201, 1, 1], # Branch nodes from the same spine node have 1 neighbor each\n",
    "    #     [202, 205, 1, 1], # Branch nodes from adjacent spine nodes have 1 neighbor each\n",
    "    #     [0, 200, 5, 1],   # Direct connection between a spine node and its branch\n",
    "    #     [199, 998, 5, 1]  # Direct connection from the other end of the spine to one of its branches\n",
    "    # ]\n",
    "\n",
    "    node_groups = [\n",
    "        # 3-Node Interactions\n",
    "        [0, 200, 201],  # Central node 0; branches 200, 201\n",
    "        [4, 216, 217],  # Central node 4; branches 216, 217\n",
    "        [10, 240, 241],  # Central node 10; branches 240, 241\n",
    "        [15, 260, 261],  # Central node 15; branches 260, 261\n",
    "        \n",
    "        # 4-Node Interactions\n",
    "        [1, 2, 204, 208],  # Central nodes 1 and 2; branches 204 (from 1) and 208 (from 2)\n",
    "        [3, 7, 212, 228],  # Central nodes 3 and 7; branches 212 (from 3) and 228 (from 7)\n",
    "        [11, 12, 244, 248],  # Central nodes 11 and 12; branches 244 (from 11) and 248 (from 12)\n",
    "        [16, 17, 264, 268],  # Central nodes 16 and 17; branches 264 (from 16) and 268 (from 17)\n",
    "        \n",
    "        # 5-Node Interactions\n",
    "        [5, 220, 221, 222, 223],  # Central node 5; branches 220, 221, 222, 223\n",
    "        [6, 224, 225, 226, 227],  # Central node 6; branches 224, 225, 226, 227\n",
    "        [18, 272, 273, 274, 275],  # Central node 18; branches 272, 273, 274, 275\n",
    "        [19, 276, 277, 278, 279],  # Central node 19; branches 276, 277, 278, 279\n",
    "    ]\n",
    "    \n",
    "    degrees = [\n",
    "        # 3-Node Interaction degrees\n",
    "        [base_size, 1, 1],\n",
    "        [base_size, 1, 1],\n",
    "        [base_size, 1, 1],\n",
    "        [base_size, 1, 1],\n",
    "        \n",
    "        # 4-Node Interaction degrees\n",
    "        [base_size, base_size, 1, 1],\n",
    "        [base_size, base_size, 1, 1],\n",
    "        [base_size, base_size, 1, 1],\n",
    "        [base_size, base_size, 1, 1],\n",
    "        \n",
    "        # 5-Node Interaction degrees\n",
    "        [base_size, 1, 1, 1, 1],\n",
    "        [base_size, 1, 1, 1, 1],\n",
    "        [base_size, 1, 1, 1, 1],\n",
    "        [base_size, 1, 1, 1, 1],\n",
    "    ]\n",
    "\n",
    "\n",
    "    for nodes, degs in zip(node_groups, degrees):\n",
    "        J_values = compute_aggregate_J(model, num_of_layers, nodes, degs)\n",
    "        if tuple(nodes) not in J_statistics[f\"{model_name} - {num_of_layers} layers - {layer_width} hidden dims\"]:\n",
    "            J_statistics[f\"{model_name} - {num_of_layers} layers - {layer_width} hidden dims\"][tuple(nodes)] = []\n",
    "        J_statistics[f\"{model_name} - {num_of_layers} layers - {layer_width} hidden dims\"][tuple(nodes)] = J_values\n",
    "\n",
    "    # print(f\"Nodes: {nodes}, J_avg: {J_avg}, J_max: {J_max}\")\n",
    "\n",
    "    # Store results for analysis\n",
    "    print(f\"Finished training {model_name}. J_values collected for analysis.\")\n",
    "    return J_statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 596,
     "referenced_widgets": [
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    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "== Running 4 layers with 8 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7436cada46de4d6fa56b285f3fe4195a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for GCN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2114004/4043381514.py:84: UserWarning: Using a target size (torch.Size([1])) that is different to the input size (torch.Size([8])). This will likely lead to incorrect results due to broadcasting. Please ensure they have the same size.\n",
      "  loss = F.mse_loss(out.squeeze(), data.y)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "93f061bb58094058be4302b8846c400b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for ChebNet:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0a9648148afc4ecb8170053c340b8ad1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for ManyBodyMPNN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 4 layers with 32 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6e3946a149cb48dfac97add6891d039c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for GCN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2114004/4043381514.py:84: UserWarning: Using a target size (torch.Size([1])) that is different to the input size (torch.Size([32])). This will likely lead to incorrect results due to broadcasting. Please ensure they have the same size.\n",
      "  loss = F.mse_loss(out.squeeze(), data.y)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2030db159a264350916afcb4cc3e8550",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bc9fd08de7684ca099f30322322f08ca",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 4 layers with 128 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c95b4e78f926408f95e0f7bfb42b3e92",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2114004/4043381514.py:84: UserWarning: Using a target size (torch.Size([1])) that is different to the input size (torch.Size([128])). This will likely lead to incorrect results due to broadcasting. Please ensure they have the same size.\n",
      "  loss = F.mse_loss(out.squeeze(), data.y)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6724a6e304db42e7b3c1c640ea576b26",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a6c0383db1254ab59586118a676fb2d2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 4 layers with 256 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8be0893112a74bc68ebe30fc811c0636",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2114004/4043381514.py:84: UserWarning: Using a target size (torch.Size([1])) that is different to the input size (torch.Size([256])). This will likely lead to incorrect results due to broadcasting. Please ensure they have the same size.\n",
      "  loss = F.mse_loss(out.squeeze(), data.y)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "afdc786ea2244c6dbfc1019af475a35d",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9cc7334572f346a3849d78eadc2b26a8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for ManyBodyMPNN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 8 layers with 8 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0dddba579e924187a44d9c3816273cf1",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1e5b91d284f7437d8e9e6e6cd63c5389",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "056b61c1c7a5411798ae77378b431fff",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for ManyBodyMPNN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 8 layers with 32 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "28a9b7e5a4354610b05ce244c2561e58",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ca857e952c02406781a4aa4fba5be516",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1427b5612db549cbbd320580fa593827",
       "version_major": 2,
       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 8 layers with 128 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "29d5983f2700475e93f8cbda67cb52e2",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "102d3ad3fc9c4fd8bf9deebef4db1a5e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "879a517a98014ee88bb4e939462ce5c1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 8 layers with 256 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "35ed01a53711423290993d36c68c010e",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "92f0244fc4b041f78bde473656389446",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2b3a6152217a4ba390b90aa185eb2065",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 13 layers with 8 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6bc0fe4e9a1d4c3c9cb1f720531ee5ec",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a48255df1c844cf391a57d0c0eb0d14f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a02a8c43cc404e25abf86b9f60eab6b3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 13 layers with 32 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1ec015bdb8d1413a8a1949e89a4c862a",
       "version_major": 2,
       "version_minor": 0
      },
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       "Training Epochs for GCN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ee009f1899ce4988b6a9eb9b63dc9189",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ac07259ca98d40bc966e2015c8ada385",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for ManyBodyMPNN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 13 layers with 128 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "defecf0923d449d7a8295cbf3e2d2e57",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for GCN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ad47fab643f148d6b4ea59c89ea0a20a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for ChebNet:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c3da21d9686d4d00ac5e80ba99b432d0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for ManyBodyMPNN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 13 layers with 256 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c1702bc9b1b54d5ba2b2449c84c8f081",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for GCN:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f2bb698e6b70428193c556bac4992884",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training Epochs for ChebNet:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "64189b9709134b7a9b4af449d7d84696",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 25 layers with 8 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "78512906d94e43b2bd02e56a548a5578",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8f7fd4ef30c14826b7a7f92d36aa3636",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 25 layers with 32 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
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       "model_id": "71bc01a6d6834364923f25e530b37e94",
       "version_major": 2,
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1c991702e2b948f49ed3bbba56e6b7ae",
       "version_major": 2,
       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5d3eb60715a645a5af693874ac427ca0",
       "version_major": 2,
       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 25 layers with 128 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8e7f936d54af4d7e95473d313fd3e249",
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       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1dde0aa014954cfcb2b6abde746d69eb",
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       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f395dbf378a2489cb9044ae202b6b55b",
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       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "\n",
      "== Running 25 layers with 256 hidden dimensions ==\n",
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b7386eea40884a6daa56ace9a6579564",
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       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training GCN. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cdb19d7ae04d429693968f6bae3c2ba1",
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       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ChebNet. J_values collected for analysis.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "004d4d4e1d2b4974a44c898f643c78a4",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished training ManyBodyMPNN. J_values collected for analysis.\n",
      "defaultdict(<class 'dict'>, {'GCN': {'GCN - 4 layers - 8 hidden dims': {(0, 200, 201): {(0, 200): [22.85019874572754, 140.0528106689453, 588.4586181640625], (0, 201): [723.3408813476562, 0.872650682926178, 62.375789642333984], (200, 201): [1129.1478271484375, 15.336589813232422, 294.68157958984375]}, (4, 216, 217): {(4, 216): [6022.31787109375, 9.023730278015137, 62.03780746459961], (4, 217): [38.35300064086914, 12.503005027770996, 40.067237854003906], (216, 217): [12.990274429321289, 21.447010040283203, 31.303678512573242]}, (10, 240, 241): {(10, 240): [703.8297729492188, 91.57502746582031, 75.67516326904297], (10, 241): [185.4275665283203, 42.188804626464844, 27.89792251586914], (240, 241): [128.99960327148438, 19.238271713256836, 237.7349395751953]}, (15, 260, 261): {(15, 260): [916.0797729492188, 15813.9033203125, 561.7665405273438], (15, 261): [1374.73291015625, 35.89352035522461, 289.26031494140625], (260, 261): [115980.8671875, 927.6982421875, 83.49787902832031]}, (1, 2, 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276): [114.9813461303711, 1443.4891357421875, 482.94586181640625, 2515.08935546875, 714.934814453125, 1850.9942626953125, 8235.572265625, 29163.185546875, 7205.0693359375, 644.860595703125, 681.0404052734375, 793.3272705078125, 1098.50830078125, 1683.503662109375, 2717.8876953125, 783.291015625, 715.1615600585938, 3920.094970703125, 14347.849609375, 873.2567138671875, 25499.48828125, 2231.39599609375, 4593.46435546875, 589.1221923828125], (19, 277): [841.9672241210938, 553.6762084960938, 347.0018310546875, 387.00982666015625, 15058.9619140625, 507.80438232421875, 4221.89599609375, 2374.86962890625, 1211.9085693359375, 922.2559204101562, 1416.9273681640625, 1371.9921875, 5370.76416015625, 1598.697265625, 5107.185546875, 769.6580200195312, 5149.9326171875, 3192.553466796875, 25403.9609375, 4011.473876953125, 4858.77001953125, 29326.146484375, 1552.10400390625, 2875.028564453125], (19, 278): [365.69464111328125, 4919.69287109375, 13560.044921875, 2543.90234375, 8828.302734375, 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1049.1492919921875, 18420.923828125, 652.201904296875, 5137.51220703125, 15042.3408203125, 23514.056640625, 3943.838623046875, 4153.154296875, 12059.345703125, 11057.5830078125, 2964.29638671875], (276, 278): [415.1500244140625, 4223.26513671875, 13553.4052734375, 2512.82666015625, 8851.365234375, 2417.142578125, 8116.2021484375, 2716.60986328125, 1413.2738037109375, 3134.7919921875, 13356.4140625, 28146.728515625, 938.0498657226562, 25681.443359375, 49366.67578125, 7416.4326171875, 118570.9765625, 20293.373046875, 368472.46875, 15556.84375, 4198.0859375, 2564.883544921875, 12576.46484375, 4627.58837890625], (276, 279): [71.42646789550781, 755.400146484375, 1580.349365234375, 3567.439453125, 6734.33740234375, 2230.370361328125, 7818.2548828125, 2895.374755859375, 16820.5859375, 1901.0860595703125, 94513.296875, 644.111083984375, 76270.765625, 19737.734375, 23197.9921875, 640.710205078125, 881.8594970703125, 3447.51171875, 16446.25, 13653.908203125, 17833.544921875, 1184.7713623046875, 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1026.13671875, 8788.5224609375, 3285.137939453125, 16699.861328125, 1279.0489501953125, 96173.7578125, 1447.778564453125, 76755.046875, 19629.548828125, 22276.232421875, 4217.24365234375, 98171.1015625, 3082.278076171875, 3568.24609375, 1176.3685302734375, 8752.7421875, 2691.3095703125, 2233.92822265625, 3940.837890625]}}}})\n"
     ]
    }
   ],
   "source": [
    "#@title Make Training Runs (100 epochs for 36 configs)\n",
    "# Hyperparameters\n",
    "layers = [4, 8, 13, 25]\n",
    "widths = [8, 32, 128, 256]\n",
    "max_order = 5 # NOTE: correpond to the number of neighbors\n",
    "K = 3  # Chebyshev filter size\n",
    "nepochs = 100\n",
    "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
    "\n",
    "# Run experiments and get statistics\n",
    "synthetic_data = large_synthetic_zinc_star_graphs[0]  # Use the first graph for demonstration\n",
    "\n",
    "J_stats = defaultdict(dict)\n",
    "\n",
    "# Run experiments\n",
    "for n_layer in layers:\n",
    "    for width in widths:\n",
    "        print(f\"\\n== Running {n_layer} layers with {width} hidden dimensions ==\\n\")\n",
    "        hidden_channels = output_channels = width\n",
    "        num_of_layers = n_layer\n",
    "\n",
    "        gcn = GCN(num_features, hidden_channels, output_channels, num_of_layers)\n",
    "        chebnet = ChebNet(num_features, hidden_channels, output_channels, num_of_layers, K)\n",
    "        manybodympnn = ManyBodyMPNN(num_features, hidden_channels, output_channels, num_of_layers, max_order, 1, K)\n",
    "\n",
    "        GCN_J_stats = run_experiments(\"GCN\", gcn, synthetic_data, device, n_layer, output_channels, nepochs)\n",
    "        ChebNet_J_stats = run_experiments(\"ChebNet\", chebnet, synthetic_data, device, num_of_layers, output_channels, nepochs)\n",
    "        MPNN_J_stats = run_experiments(\"ManyBodyMPNN\", manybodympnn, synthetic_data, device, num_of_layers, output_channels, nepochs)\n",
    "\n",
    "        # Aggregate J values into a single dictionary for plotting\n",
    "        J_stats[\"GCN\"].update(GCN_J_stats)\n",
    "        J_stats[\"ChebNet\"].update(ChebNet_J_stats)\n",
    "        J_stats[\"ManyBodyMPNN\"].update(MPNN_J_stats)\n",
    "\n",
    "print(J_stats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 79,
     "referenced_widgets": [
      "a7368771a221479293c7e8fcc9423893",
      "64951d57d2904ca38fbc96bfee69173c",
      "aa4105fc9fd54ef98bd00ae290057bc1",
      "ee4e59aff4664b9187dbc808ad611cbe",
      "2e9ad5cb991540378afa7a111bc5a0e9",
      "7b6d90e51a1c40c5be2dac5e6215cd62"
     ]
    },
    "id": "LQo2HS2ExvZt",
    "outputId": "2318a740-ed28-4659-d6fc-c2530a660db7"
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e6520e7e629042fc9adcbdc46c6ee8ae",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Dropdown(description='Model Config:', options=('GCN - 4 layers - 8 hidden dims', 'GCN - 4 layers - 32 hidden d…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "51daadc6f36d4bde836a97e9afd1d116",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Dropdown(description='Choose:', options=([0, 200, 201], [4, 216, 217], [10, 240, 241], [15, 260, 261], [1, 2, …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title Choose from Dropdown the Configs to Visualize\n",
    "from ipywidgets import widgets, Dropdown, interact\n",
    "\n",
    "# Define model names, layers, and widths for creating model configurations\n",
    "model_names = ['GCN', 'ChebNet', 'ManyBodyMPNN']\n",
    "\n",
    "# Create model configurations\n",
    "model_configs = [f\"{model_name} - {num_layers} layers - {width} hidden dims\"\n",
    "                 for model_name in model_names\n",
    "                 for num_layers in layers\n",
    "                 for width in widths]\n",
    "\n",
    "# Create the dropdown for model configurations\n",
    "model_config_dropdown = Dropdown(options=model_configs, description='Model Config:')\n",
    "\n",
    "# Create a dropdown menu widget\n",
    "# node_pair_dropdown = widgets.Dropdown(\n",
    "#     options= [\n",
    "#     [0, 1, 5, 6],     # Spine nodes at the beginning have 5 and 6 neighbors, respectively\n",
    "#     [198, 199, 6, 5], # Spine nodes at the end have 6 and 5 neighbors, respectively\n",
    "#     [50, 70, 6, 6],   # Middle spine nodes, both have 6 neighbors\n",
    "#     [100, 125, 6, 6], # Another pair of middle spine nodes, both have 6 neighbors\n",
    "#     [0, 199, 5, 5],   # First and last spine nodes\n",
    "#     [10, 190, 6, 6],  # Spine nodes slightly inwards from the ends\n",
    "#     [200, 201, 1, 1], # Branch nodes from the same spine node have 1 neighbor each\n",
    "#     [202, 205, 1, 1], # Branch nodes from adjacent spine nodes have 1 neighbor each\n",
    "#     [0, 200, 5, 1],   # Direct connection between a spine node and its branch\n",
    "#     [199, 998, 5, 1]  # Direct connection from the other end of the spine to one of its branches\n",
    "#     ],  # List of options\n",
    "#     value=[0, 1, 5, 6],  # Default selected value\n",
    "#     description='Choose:',  # Description label\n",
    "# )\n",
    "\n",
    "node_pair_dropdown =  widgets.Dropdown(\n",
    "    options = [\n",
    "        # 3-Node Interactions\n",
    "        [0, 200, 201],  # Central node 0; branches 200, 201\n",
    "        [4, 216, 217],  # Central node 4; branches 216, 217\n",
    "        [10, 240, 241],  # Central node 10; branches 240, 241\n",
    "        [15, 260, 261],  # Central node 15; branches 260, 261\n",
    "        \n",
    "        # 4-Node Interactions\n",
    "        [1, 2, 204, 208],  # Central nodes 1 and 2; branches 204 (from 1) and 208 (from 2)\n",
    "        [3, 7, 212, 228],  # Central nodes 3 and 7; branches 212 (from 3) and 228 (from 7)\n",
    "        [11, 12, 244, 248],  # Central nodes 11 and 12; branches 244 (from 11) and 248 (from 12)\n",
    "        [16, 17, 264, 268],  # Central nodes 16 and 17; branches 264 (from 16) and 268 (from 17)\n",
    "        \n",
    "        # 5-Node Interactions\n",
    "        [5, 220, 221, 222, 223],  # Central node 5; branches 220, 221, 222, 223\n",
    "        [6, 224, 225, 226, 227],  # Central node 6; branches 224, 225, 226, 227\n",
    "        [18, 272, 273, 274, 275],  # Central node 18; branches 272, 273, 274, 275\n",
    "        [19, 276, 277, 278, 279],  # Central node 19; branches 276, 277, 278, 279\n",
    "    ],  # List of options\n",
    "    value=[0, 200, 201],  # Default selected value\n",
    "    description='Choose:',  # Description label\n",
    ")   \n",
    "\n",
    "# Display the dropdowns\n",
    "display(model_config_dropdown, node_pair_dropdown)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 507
    },
    "id": "XnFNQjpdjcpd",
    "outputId": "452fa4fe-edaa-4a30-e822-291624934b10"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{(0, 200): [119.63104248046875, 318.6832275390625, 127.93414306640625, 162.4609375, 539.4739990234375, 536.0497436523438, 515.6968383789062, 128.86801147460938, 319.3278503417969, 380.7975769042969, 175.28285217285156, 21.506927490234375], (0, 201): [1401.8109130859375, 34.282066345214844, 505.67193603515625, 300.2069396972656, 306.9381408691406, 324.305419921875, 831.8245239257812, 134.02719116210938, 206.45187377929688, 29.755460739135742, 125.67475891113281, 137.0595703125], (200, 201): [1559.8199462890625, 5.5070343017578125, 48.344024658203125, 8.968036651611328, 8.309944152832031, 64.35113525390625, 395.01275634765625, 29.647525787353516, 163.78945922851562, 370.9432067871094, 71.11344146728516, 171.54507446289062]}\n"
     ]
    }
   ],
   "source": [
    "#@title Make Visualization (Histograms of Jacobian values)\n",
    "import matplotlib.pyplot as plt\n",
    "# Node pairs\n",
    "\n",
    "# Good pairs for further report: 25 layers - 32 hidden dims - [0,1,5,6] / [10,190,6,6]\n",
    "selected_model_config = model_config_dropdown.value\n",
    "\n",
    "model_name = selected_model_config.split(' - ')[0]\n",
    "\n",
    "selected_node_config = node_pair_dropdown.value\n",
    "\n",
    "selected_pair_data = J_stats[model_name][selected_model_config][tuple(selected_node_config)]\n",
    "\n",
    "print(selected_pair_data)\n",
    "\n",
    "# # Relative Jacobians of u and v across layers (compared with the last layer)\n",
    "# relative_jacobians = np.array(selected_pair_data)\n",
    "\n",
    "# # X-axis: range of epochs\n",
    "# epochs = np.arange(len(relative_jacobians))\n",
    "\n",
    "# # Initialize plot\n",
    "# fig, ax = plt.subplots(figsize=(10, 5))\n",
    "\n",
    "# # Plot\n",
    "# ax.bar(epochs, relative_jacobians.T[0], label=f'{selected_model_config} - Node Pair {selected_node_config}')\n",
    "# ax.set_title(f'Average Jacobians for {selected_model_config}')\n",
    "# ax.set_xlabel('Epoch')\n",
    "# ax.set_ylabel('Average Jacobian')\n",
    "# ax.legend()\n",
    "\n",
    "# # Adjust layout\n",
    "# plt.tight_layout()\n",
    "# plt.show()\n",
    "\n",
    "# NOTE: Formulate it in the zinc context."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "FtU6--Nm0tIk",
    "outputId": "22d82d80-ccef-49d1-db4b-84f8a6525e66"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "J_stats written to ./J_stats.pkl\n"
     ]
    }
   ],
   "source": [
    "#@title Save Experimental Outcomes (Optional)\n",
    "import pickle\n",
    "f = open('./J_stats.pkl', \"wb\")\n",
    "pickle.dump(J_stats, f)\n",
    "f.close()\n",
    "print(\"J_stats written to ./J_stats.pkl\")"
   ]
  }
 ],
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