00_GNN_Definition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Graph Neural Networks for Solving Combinatorial Optimization Problems\n",
    "\n",
    "#### Author: Ivan Carvalho (@IvanIsCoding)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/IvanIsCoding/GNN-for-Combinatorial-Optimization/blob/main/00_GNN_Definition.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Welcome to Graph Neural Networks for Solving Combinatorial Optimization Problems! In this series of Jupyter notebooks, we will investigate the paper [Combinatorial Optimization with Physics-Inspired Graph Neural Networks](https://arxiv.org/abs/2107.01188) by Schuetz et al.\n",
    "\n",
    "After working through this notebook, we will have a deeper understanding of the core ideas of the paper. Firstly, we will review QUBO formulations, a way to encode optimization problems. Secondly, we will discuss GNNs and the architecture proposed in the paper for unsupervised learning. Lastly, we will train the GNN to solve the QUBO!\n",
    "\n",
    "Before we jump ahead, let's check we have the GPU enabled. GPUs will be important on speeding up the training of the GNN."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GPU 0: Tesla T4 (UUID: GPU-7060d45f-6c2b-093c-2256-ea38603ee946)\n"
     ]
    }
   ],
   "source": [
    "!nvidia-smi -L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "During this notebook we will be using:\n",
    "* [JAX](https://github.com/google/jax): a numerical computation library for Python, supports automatic differentiation and many other cool things\n",
    "* [Flax](https://github.com/google/flax): a machine learning library for Python built on top of JAX; Flax is very fexible and provides all the tools we need to implement the paper\n",
    "* [PyQUBO](https://arxiv.org/abs/2103.01708): a library for building quadratic unconstrained binary optimization (QUBO) models; this paper is all about QUBOs, and PyQUBO lets us write them in a straightforward way\n",
    "\n",
    "Also, during the notebook you will see some comments on the cells to export code. This is because we use [nbdev](https://nbdev.fast.ai/) to create a package from this notebook. This will allow us to reuse all the code from this on the next ones!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -q flax pyqubo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | default_exp core"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import numpy as np\n",
    "import networkx as nx  # for making graphs\n",
    "import optax  # for optimizing GNN with Adam\n",
    "\n",
    "from flax import linen as nn  # for defining the GNN\n",
    "from flax.training import train_state  # utility for training\n",
    "from pyqubo import Array  # for defining the QUBO\n",
    "from tqdm.notebook import trange, tqdm  # visualizing notebook progress"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QUBO Background\n",
    "\n",
    "Now that we have installed and imported the libraries we need, let's dicuss QUBO formulations. \n",
    "\n",
    "QUBOs are a specific way to encode optimization problems. You have binary variables $x_{i} \\in \\{0, 1\\}$ and write a Hamiltonian:\n",
    "\n",
    "$$\n",
    "H = \\sum_{i=1}^{N} \\sum_{j=i+1}^{N} b_{i,j}x_{i}x_{j} \\sum_{i=1}^{N} a_{i} x_{i} + c\n",
    "$$\n",
    "\n",
    "Then, you give your Hamiltonian to a QUBO solver and (hopefully) the solver outputs a solution that minimizes $H$. Generally, the output from the solver is decoded and mapped back to a combinatorial optimization problem that is useful in the real-world. I recommend reading [Ising formulations of many NP problems](https://www.frontiersin.org/articles/10.3389/fphy.2014.00005/full) by Lucas if you are interested more in the topic. Many, many problems can be encoded as QUBOs.\n",
    "\n",
    "There is also another convenient way of writing QUBO problems using matrices. Let $Q$ be the matrix describe the QUBO coefficients, then:\n",
    "\n",
    "$$\n",
    "H = x^\\intercal Q x\n",
    "$$\n",
    "\n",
    "They are equivalent, but for this specific case the matrix version is the one used in the paper. This makes sense given that the authors also want to reach the Deep Learning community that is familiar with linear algebra."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two combinatorial optimization problems appear in the paper. The first one is the Max Cut problem. In the Max-Cut problem, you are given an undirected graph and a set of vertices. Your goal is to divide the vertices into two sets such that the number of edges connecting vertices in different sets is maximized. The Max-Cut problem has attracted a lot of interested from the research community (e.g. quantum computing), hence it is not surprising the authors chose it.\n",
    "\n",
    "The QUBO formulation for the Max-Cut given a weighted-graph $G = (V, E)$ is:\n",
    "\n",
    "$$\n",
    "H = \\sum_{(u, v) \\in E} W_{u, v} (x_{u} - x_{v})^{2}\n",
    "$$\n",
    "\n",
    "The hamiltonian $H$ encodes the cost of the cut. If $x_{u} = 0$, then the vertex $u$ is in the first set. Analogously, if $x_{u} = 1$ then $u$ is in the other set. Notice that $(x_{u} - x_{v})^{2}$ evaluates to $1$ if and only if the vertices are in different sets. There are two details worth noticing in our implementation: we assume the ede weights $W_{u, v}$ are all one; and we feed $-H$ to our solver, because the solver finds a minimum (not a maximum).\n",
    "\n",
    "The second optimization problem is the Maximum Independent Set (MIS). In the MIS, you are given a graph $G = (V, E)$ and your goal is to find a set of vertices such that no two vertices in the set are connected by an edge. This set is called an independent set. You want to find the independent set with the maximum number of vertices.\n",
    "\n",
    "The QUBO formulation for the MIS is:\n",
    "\n",
    "$$\n",
    "H = \\sum_{v \\in V} x_{v} - P \\sum_{(u, v) \\in E} x_{u}x_{v}\n",
    "$$\n",
    "\n",
    "Because QUBOs don't have constraints, P is a penalty we added to the formulation such that the MIS solution is valid. We set $P = 2$ as in the paper.\n",
    "\n",
    "Now that we discussed the formulations, let's implement them using PyQUBO. We have three functions: one for the Max-Cut formulation; one for the MIS formulation; and one for obtaining the $Q$ matrix defined earlier. Also, keep in mind again that all signs of the hamiltonian are swapped because the solvers find minimums (not maximums)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "def create_max_cut_model(graph):\n",
    "    N = graph.number_of_nodes()\n",
    "    X = Array.create(\"X\", shape=(N,), vartype=\"BINARY\")\n",
    "\n",
    "    hamiltonian = 0\n",
    "    for u, v in graph.edges:\n",
    "        hamiltonian -= (X[u] - X[v]) ** 2\n",
    "\n",
    "    return hamiltonian.compile()\n",
    "\n",
    "\n",
    "def create_mis_model(graph, penalty=2):\n",
    "    N = graph.number_of_nodes()\n",
    "    X = Array.create(\"X\", shape=(N,), vartype=\"BINARY\")\n",
    "\n",
    "    hamiltonian = -sum(X)\n",
    "    for u, v in graph.edges:\n",
    "        hamiltonian += penalty * (X[u] * X[v])\n",
    "\n",
    "    return hamiltonian.compile()\n",
    "\n",
    "\n",
    "def create_Q_matrix(graph, is_max_cut=True):\n",
    "    if is_max_cut:\n",
    "        model = create_max_cut_model(graph)\n",
    "    else:\n",
    "        model = create_mis_model(graph)\n",
    "\n",
    "    N = graph.number_of_nodes()\n",
    "    extract_val = lambda x: int(x[2:-1])\n",
    "    Q_matrix = np.zeros((N, N))\n",
    "\n",
    "    qubo_dict, _ = model.to_qubo()\n",
    "\n",
    "    for (a, b), quv in qubo_dict.items():\n",
    "        u = min(extract_val(a), extract_val(b))\n",
    "        v = max(extract_val(a), extract_val(b))\n",
    "        Q_matrix[u, v] = quv\n",
    "\n",
    "    return jnp.array(Q_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two functions below implement a cost inspired by the hamiltonian using the QUBO matrix discussed earlier:\n",
    "\n",
    "$$\n",
    "H = x^\\intercal Q x\n",
    "$$\n",
    "\n",
    "Notice that in the paper, as we will discussed later, we transition to a relaxed version of the Hamiltonian cost:\n",
    "\n",
    "$$\n",
    "\\mathcal{L}_{QUBO} = p_{\\Theta}^\\intercal Q p_{\\Theta} \n",
    "$$\n",
    "\n",
    "Where $p_{\\Theta}$ is a vector of probabilities. Instead of assigning 0 or 1 to the variables, the authors chose a continuous version which makes sense for training the GNN."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "def qubo_approx_cost(probs, Q):\n",
    "    cost = jnp.sum(jnp.matmul(jnp.matmul(jnp.transpose(probs), Q), probs))\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "def compute_metrics(*, probs, q_matrix):\n",
    "    energy = qubo_approx_cost(probs=probs, Q=q_matrix)\n",
    "    metrics = {\n",
    "        \"energy\": energy,\n",
    "    }\n",
    "    return metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Graph Convolution\n",
    "\n",
    "We enter now the Neural Network section of the paper where we defined the architecture of the Graph Neural Network.\n",
    "\n",
    "The core idea is using message passing. Each vertex $i$ in the graph contains a node feature vector $\\textbf{x}_{i}$. The Graph Convolution learns to aggregate the messages of the vertex and its neighbours using $W_{1}$ and $W_{2}$:\n",
    "\n",
    "$$\n",
    "\\textbf{x}_{i}^{\\prime} = W_{1} \\textbf{x}_{i} + W_{2} \\sum_{j \\in \\mathcal{N}_{i}} e_{j, i} \\textbf{x}_{j}\n",
    "$$\n",
    "\n",
    "\n",
    "We implement the Graph Convolution below using Flax + JAX. To calcualte $\\sum_{j \\in \\mathcal{N}_{i}} e_{j, i} x_{j}$, we use the adjacency matrix of the graph. Notice that our implementation is focused on smaller graphs, hence we did not use sparse matrices which would allow our code to scale to graphs with millions of vertices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "class GraphConvLayer(nn.Module):\n",
    "    c_out: int  # Output feature size\n",
    "\n",
    "    @nn.compact\n",
    "    def __call__(self, node_feats, adj_matrix):\n",
    "        node_feats_w1 = nn.Dense(features=self.c_out, use_bias=False)(node_feats)\n",
    "        node_feats_w2 = jax.lax.batch_matmul(adj_matrix, node_feats)\n",
    "        node_feats_w2 = nn.Dense(features=self.c_out)(node_feats_w2)\n",
    "        return node_feats_w1 + node_feats_w2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unsupervised Learning and the Graph Neural Network \n",
    "\n",
    "\n",
    "After explaining the Graph Convolution layer, we can talk about the GNN architecture and its goals.\n",
    "\n",
    "The idea proposed is to apply unsupervised learning to learn the node labels of the optimal solution just by using $\\mathcal{L}_{QUBO}$. Let's say that the optimal solution is:\n",
    "\n",
    "$$\n",
    "x^\\intercal  = \\begin{bmatrix} 1, 0, 1, 0, 1 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Then, our neural network is trying to predict probabilities that the label is 0 or 1. So $p_{\\Theta}$ would look something like this:\n",
    "\n",
    "$$\n",
    "p_{\\Theta}^\\intercal  = \\begin{bmatrix} 0.9, 0.05, 0.87, 0.13, 0.99 \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "$\\mathcal{L}_{QUBO}$ would give us an approximate cost of the QUBO (as if $p_{\\Theta}$ were a superposition of many $x$). So overall, this is a pretty clever idea.\n",
    "\n",
    "To find $p_{\\Theta}$, they propose the following architecture for the GNN:\n",
    "* Initialize the feature vectors $\\textbf{x}_{i}$ for each vertex at random\n",
    "* $k$ layers consisting of:\n",
    "    * Applying the Graph Convolution\n",
    "    * Applying an activation function which in the case is ReLU\n",
    "    * Applying Dropout regularization to reduce overfitting\n",
    "\n",
    "On the last of the $k$ layers, no ReLU or Regularization is applied. Instead, a Softmax to predict the probabilities takes place.\n",
    "\n",
    "For the paper, the authors use $k = 2$ or $k = 3$ layers. For our Flax implementation. we use $k = 2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "class CombGNN(nn.Module):\n",
    "    hidden_size: int\n",
    "    num_classes: int\n",
    "    dropout_frac: float\n",
    "\n",
    "    @nn.compact\n",
    "    def __call__(self, node_feats, adj_matrix, train=False):\n",
    "        # First convolution\n",
    "        h = GraphConvLayer(c_out=self.hidden_size)(\n",
    "            node_feats=node_feats, adj_matrix=adj_matrix\n",
    "        )\n",
    "        h = nn.relu(h)\n",
    "        h = nn.Dropout(rate=self.dropout_frac, deterministic=not train)(h)\n",
    "        # Second convolution\n",
    "        h = GraphConvLayer(c_out=self.num_classes)(node_feats=h, adj_matrix=adj_matrix)\n",
    "        probs = nn.sigmoid(h)\n",
    "\n",
    "        return probs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training neural networks with Flax\n",
    "\n",
    "Now that we defined our architecture, it is time to write code to train the neural network!\n",
    "\n",
    "Flax provides a TrainState dataclass that is very convenient to keep track of the paramters. Hence the code below does:\n",
    "* Initiates the parameters for GNNComb using random values\n",
    "* Assigns the Adam optimizer with the given learning rate (using optax, the optimizer for JAX)\n",
    "* Returns a TrainState keeping track of our net, the current parameters, and all other hyperparameters we chose"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "def create_train_state(\n",
    "    n_vertices, embedding_size, hidden_size, rng, learning_rate, dropout_frac=0.0\n",
    "):\n",
    "    gnn = CombGNN(hidden_size=hidden_size, num_classes=1, dropout_frac=dropout_frac)\n",
    "    dropout_rng = jax.random.PRNGKey(0)\n",
    "    params = gnn.init(\n",
    "        rngs={\"params\": rng, \"dropout\": dropout_rng},\n",
    "        node_feats=jnp.ones([n_vertices, embedding_size]),\n",
    "        adj_matrix=jnp.ones([n_vertices, n_vertices]),\n",
    "        train=True,\n",
    "    )[\"params\"]\n",
    "    tx = optax.adam(learning_rate)\n",
    "    return train_state.TrainState.create(apply_fn=gnn.apply, params=params, tx=tx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After we have our convenient TrainState class, we are going to perform training steps on them. One of the true magics of JAX is it just-in-time compilation. We apply the `@jax.jit` decorator to compile the code and make things super fast!\n",
    "\n",
    "To train the neural network, we:\n",
    "* Evaluate the GNN using the current parameters\n",
    "* Calcualte the cost $\\mathcal{L}_{QUBO}$\n",
    "* Calcualte the gradients using JAX, which does all the backpropagation for us\n",
    "* Let the optimizer handle the gradients and update the parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "@jax.jit\n",
    "def train_step(state, node_embeddings, adj_matrix, q_matrix, dropout_rng):\n",
    "    \"\"\"Train for a single step.\"\"\"\n",
    "\n",
    "    def cost_fn(params):\n",
    "        probs = state.apply_fn(\n",
    "            {\"params\": params},\n",
    "            node_embeddings,\n",
    "            adj_matrix,\n",
    "            rngs={\"dropout\": dropout_rng},\n",
    "            train=True,\n",
    "        )\n",
    "        cost = qubo_approx_cost(probs=probs, Q=q_matrix)\n",
    "        return cost, probs\n",
    "\n",
    "    grad_fn = jax.grad(cost_fn, has_aux=True)\n",
    "    grads, probs = grad_fn(state.params)\n",
    "    state = state.apply_gradients(grads=grads)\n",
    "    metrics = compute_metrics(probs=probs, q_matrix=q_matrix)\n",
    "    return state, metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Last but not least on our training steps, is an utility method to recover the classifications. We are not interested in probabilities at the end. We want zeroes or ones!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# | export\n",
    "def get_classification(apply_fn, params, node_embeddings, adj_matrix):\n",
    "    pred_probs = apply_fn({\"params\": params}, node_embeddings, adj_matrix)\n",
    "    classification = jnp.where(pred_probs >= 0.5, 1, 0)\n",
    "    return np.ravel(classification)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Max-Cut On Example Graph\n",
    "\n",
    "After all this introduction, it is time to check if our implementation works, right? We will start with the Max-Cut case.\n",
    "\n",
    "We check our implementation against the small example present in the paper. So let's first define and visualize our graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "edgelist = [(0, 1), (1, 2), (2, 3), (3, 0), (1, 4), (2, 4)]\n",
    "G = nx.from_edgelist(edgelist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, pos=nx.spring_layout(G, seed=2023))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright, our graph looks ready. Time to calculate two very important matrices for our training steps: the adjacency matrix $A$ and the QUBO matrix $Q$. $A$ is used in the graph convolutions and $Q$ is used for the cost. We take a peek at $A$ and $Q$ to check if they are correct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = jnp.array(nx.to_numpy_array(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([[0., 1., 0., 1., 0.],\n",
       "             [1., 0., 1., 0., 1.],\n",
       "             [0., 1., 0., 1., 1.],\n",
       "             [1., 0., 1., 0., 0.],\n",
       "             [0., 1., 1., 0., 0.]], dtype=float32)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = create_Q_matrix(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([[-2.,  2.,  0.,  2.,  0.],\n",
       "             [ 0., -3.,  2.,  0.,  2.],\n",
       "             [ 0.,  0., -3.,  2.,  2.],\n",
       "             [ 0.,  0.,  0., -2.,  0.],\n",
       "             [ 0.,  0.,  0.,  0., -2.]], dtype=float32)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The matrices look right. Time to train the neural network! The code:\n",
    "* Creates the random number keys we need for initializing the network, embeddings, and training\n",
    "* Defines our learning rate, size of node featurs, and size of the hidden features\n",
    "* Trains the network for 500 epochs\n",
    "\n",
    "note: JAX has a very particular way of working with random numbers; if you are new to JAX, pay attention to that"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = jax.random.PRNGKey(2023)\n",
    "rng, init_rng = jax.random.split(rng)\n",
    "rng, embed_rng = jax.random.split(rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 0.005"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "embedding_d0 = 5\n",
    "embedding_d1 = embedding_d0 // 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "state = create_train_state(\n",
    "    G.number_of_nodes(), embedding_d0, embedding_d1, init_rng, learning_rate\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_embeddings = jax.random.uniform(embed_rng, [G.number_of_nodes(), embedding_d0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([[0.90081596, 0.38583064, 0.02542734, 0.7263125 , 0.77239466],\n",
       "             [0.13210392, 0.2291317 , 0.15860796, 0.39851677, 0.9010197 ],\n",
       "             [0.5372865 , 0.6941434 , 0.948866  , 0.5196214 , 0.97492456],\n",
       "             [0.13318086, 0.49488008, 0.6443068 , 0.95046246, 0.5960568 ],\n",
       "             [0.19223976, 0.44076335, 0.9235079 , 0.26473606, 0.49318063]],            dtype=float32)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "node_embeddings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "69b2e4021db24ff5af8b4fdb92c8cdba",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/500 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train epoch: 25, cost: -0.34\n",
      "train epoch: 50, cost: -2.10\n",
      "train epoch: 75, cost: -3.84\n",
      "train epoch: 100, cost: -4.42\n",
      "train epoch: 125, cost: -4.66\n",
      "train epoch: 150, cost: -4.78\n",
      "train epoch: 175, cost: -4.84\n",
      "train epoch: 200, cost: -4.88\n",
      "train epoch: 225, cost: -4.91\n",
      "train epoch: 250, cost: -4.93\n",
      "train epoch: 275, cost: -4.94\n",
      "train epoch: 300, cost: -4.95\n",
      "train epoch: 325, cost: -4.96\n",
      "train epoch: 350, cost: -4.96\n",
      "train epoch: 375, cost: -4.97\n",
      "train epoch: 400, cost: -4.97\n",
      "train epoch: 425, cost: -4.97\n",
      "train epoch: 450, cost: -4.98\n",
      "train epoch: 475, cost: -4.98\n",
      "train epoch: 500, cost: -4.98\n"
     ]
    }
   ],
   "source": [
    "for epoch in trange(1, num_epochs + 1):\n",
    "    rng, dropout_rng = jax.random.split(rng)\n",
    "    state, metrics = train_step(\n",
    "        state=state,\n",
    "        node_embeddings=node_embeddings,\n",
    "        adj_matrix=A,\n",
    "        q_matrix=Q,\n",
    "        dropout_rng=dropout_rng,\n",
    "    )\n",
    "\n",
    "    if epoch % 25 == 0:\n",
    "        print(\"train epoch: %d, cost: %.2f\" % (epoch, metrics[\"energy\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After finding the optimal parameters, let's examine the solution the network found:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([[9.9998617e-01],\n",
       "             [2.1988944e-04],\n",
       "             [9.9997127e-01],\n",
       "             [2.0501104e-03],\n",
       "             [9.9555635e-01]], dtype=float32)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "state.apply_fn({\"params\": state.params}, node_embeddings, A, train=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probabilities are not very useful, so let's convert them to zeroes and ones and visualize:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "classification = get_classification(state.apply_fn, state.params, node_embeddings, A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(\n",
    "    G,\n",
    "    pos=nx.spring_layout(G, seed=2023),\n",
    "    node_color=[\"yellow\" if c else \"lightblue\" for c in classification],\n",
    "    with_labels=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The GNN found the optimal solution to the problem! The Max-Cut of the graph is 5 because of the edges $\\{ (0, 1), (0, 3), (2, 1), (2, 3), (4, 1)\\}$. Hence the code worked!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maximum Independet Set on Example Graph\n",
    "\n",
    "We also need to check that our MIS implementation works. Most of the training details are the same. The major difference is on the $Q$ matrix below that looks quite different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = jnp.array(nx.to_numpy_array(G))\n",
    "Q = create_Q_matrix(G, is_max_cut=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DeviceArray([[-1.,  2.,  0.,  2.,  0.],\n",
       "             [ 0., -1.,  2.,  0.,  2.],\n",
       "             [ 0.,  0., -1.,  2.,  2.],\n",
       "             [ 0.,  0.,  0., -1.,  0.],\n",
       "             [ 0.,  0.,  0.,  0., -1.]], dtype=float32)"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = jax.random.PRNGKey(666)  # yeah I know\n",
    "rng, init_rng = jax.random.split(rng)\n",
    "rng, embed_rng = jax.random.split(rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "learning_rate = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "embedding_d0 = 5\n",
    "embedding_d1 = embedding_d0 // 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "state = create_train_state(\n",
    "    G.number_of_nodes(), embedding_d0, embedding_d1, init_rng, learning_rate\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_embeddings = jax.random.uniform(embed_rng, [G.number_of_nodes(), embedding_d0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "289bb88260454d41ab720137cd3c83bf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/500 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train epoch: 25, cost: -0.01\n",
      "train epoch: 50, cost: -0.01\n",
      "train epoch: 75, cost: -0.07\n",
      "train epoch: 100, cost: -0.61\n",
      "train epoch: 125, cost: -1.60\n",
      "train epoch: 150, cost: -1.89\n",
      "train epoch: 175, cost: -1.94\n",
      "train epoch: 200, cost: -1.96\n",
      "train epoch: 225, cost: -1.97\n",
      "train epoch: 250, cost: -1.98\n",
      "train epoch: 275, cost: -1.98\n",
      "train epoch: 300, cost: -1.99\n",
      "train epoch: 325, cost: -1.99\n",
      "train epoch: 350, cost: -1.99\n",
      "train epoch: 375, cost: -1.99\n",
      "train epoch: 400, cost: -1.99\n",
      "train epoch: 425, cost: -1.99\n",
      "train epoch: 450, cost: -1.99\n",
      "train epoch: 475, cost: -1.99\n",
      "train epoch: 500, cost: -2.00\n"
     ]
    }
   ],
   "source": [
    "for epoch in trange(1, num_epochs + 1):\n",
    "    state, metrics = train_step(\n",
    "        state=state,\n",
    "        node_embeddings=node_embeddings,\n",
    "        adj_matrix=A,\n",
    "        q_matrix=Q,\n",
    "        dropout_rng=dropout_rng,\n",
    "    )\n",
    "\n",
    "    if epoch % 25 == 0:\n",
    "        print(\"train epoch: %d, cost: %.2f\" % (epoch, metrics[\"energy\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "classification = get_classification(state.apply_fn, state.params, node_embeddings, A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(\n",
    "    G,\n",
    "    pos=nx.spring_layout(G, seed=2023),\n",
    "    node_color=[\"yellow\" if c else \"lightblue\" for c in classification],\n",
    "    with_labels=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The GNN found again the optimal solution! The MIS has size 2 and the GNN found the solution with vertices 0 and 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Max-Cut on a Larger Graph\n",
    "\n",
    "In general, the GNN will not necessarily find the optimal solution but an approximate solution. Despite that, approximate solutions can be useful as solving the exact problem is hard for larger graphs.\n",
    "\n",
    "We test our code against a random graph with 100 vertices. This should be a tougher challenge for the GNN than the previous two cases we analyzed earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.convert_node_labels_to_integers(\n",
    "    nx.fast_gnp_random_graph(n=100, p=0.05, seed=2023)\n",
    ")\n",
    "A = jnp.array(nx.to_numpy_array(G))\n",
    "Q = create_Q_matrix(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, pos=nx.spring_layout(G, seed=2023), with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "embedding_d0 = int(np.sqrt(G.number_of_nodes()))\n",
    "embedding_d1 = embedding_d0 // 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = jax.random.PRNGKey(2023)\n",
    "rng, init_rng = jax.random.split(rng)\n",
    "rng, embed_rng = jax.random.split(rng)\n",
    "state = create_train_state(\n",
    "    G.number_of_nodes(),\n",
    "    embedding_d0,\n",
    "    embedding_d1,\n",
    "    init_rng,\n",
    "    learning_rate,\n",
    "    dropout_frac=0.01,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_embeddings = jax.random.uniform(embed_rng, [G.number_of_nodes(), embedding_d0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bef4345cde034b1da8cb4bded8065e21",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/1000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train epoch: 25, cost: -119.44\n",
      "train epoch: 50, cost: -143.59\n",
      "train epoch: 75, cost: -168.37\n",
      "train epoch: 100, cost: -176.33\n",
      "train epoch: 125, cost: -177.63\n",
      "train epoch: 150, cost: -181.75\n",
      "train epoch: 175, cost: -174.95\n",
      "train epoch: 200, cost: -185.43\n",
      "train epoch: 225, cost: -185.26\n",
      "train epoch: 250, cost: -184.12\n",
      "train epoch: 275, cost: -192.22\n",
      "train epoch: 300, cost: -190.46\n",
      "train epoch: 325, cost: -190.28\n",
      "train epoch: 350, cost: -194.29\n",
      "train epoch: 375, cost: -194.64\n",
      "train epoch: 400, cost: -187.61\n",
      "train epoch: 425, cost: -190.77\n",
      "train epoch: 450, cost: -195.63\n",
      "train epoch: 475, cost: -195.76\n",
      "train epoch: 500, cost: -193.19\n",
      "train epoch: 525, cost: -196.21\n",
      "train epoch: 550, cost: -196.09\n",
      "train epoch: 575, cost: -195.81\n",
      "train epoch: 600, cost: -196.26\n",
      "train epoch: 625, cost: -196.10\n",
      "train epoch: 650, cost: -190.07\n",
      "train epoch: 675, cost: -194.42\n",
      "train epoch: 700, cost: -197.08\n",
      "train epoch: 725, cost: -197.10\n",
      "train epoch: 750, cost: -193.38\n",
      "train epoch: 775, cost: -193.56\n",
      "train epoch: 800, cost: -197.20\n",
      "train epoch: 825, cost: -197.22\n",
      "train epoch: 850, cost: -197.35\n",
      "train epoch: 875, cost: -196.61\n",
      "train epoch: 900, cost: -195.16\n",
      "train epoch: 925, cost: -197.41\n",
      "train epoch: 950, cost: -195.31\n",
      "train epoch: 975, cost: -197.55\n",
      "train epoch: 1000, cost: -197.45\n"
     ]
    }
   ],
   "source": [
    "for epoch in trange(1, num_epochs + 1):\n",
    "    rng, dropout_rng = jax.random.split(rng)\n",
    "    state, metrics = train_step(\n",
    "        state=state,\n",
    "        node_embeddings=node_embeddings,\n",
    "        adj_matrix=A,\n",
    "        q_matrix=Q,\n",
    "        dropout_rng=dropout_rng,\n",
    "    )\n",
    "\n",
    "    if epoch % 25 == 0:\n",
    "        print(\"train epoch: %d, cost: %.2f\" % (epoch, metrics[\"energy\"]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "classification = get_classification(state.apply_fn, state.params, node_embeddings, A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(\n",
    "    G,\n",
    "    pos=nx.spring_layout(G, seed=2023),\n",
    "    node_color=[\"yellow\" if c else \"lightblue\" for c in classification],\n",
    "    with_labels=True,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overall, our GNN seems to be working!\n",
    "\n",
    "Now, let's jump onto the next notebook where we will compare the GNN against Simulated Annealing. The results will surprise you!\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/IvanIsCoding/GNN-for-Combinatorial-Optimization/blob/main/01_GNN_vs_SA_for_Max_Cut.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  }
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