From b9a1dfbf8d0dc806594eafa17f327df5d002a337 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Thu, 8 Jun 2023 17:04:59 +0100 Subject: [PATCH 01/27] add graph neural networks --- docs/notebooks.rst | 2 + .../example_graph_neural_network.ipynb | 779 ++++++++++++++++++ src/omlt/neuralnet/layers/__init__.py | 2 +- src/omlt/neuralnet/layers/full_space.py | 177 ++++ src/omlt/neuralnet/nn_formulation.py | 14 +- tests/neuralnet/test_nn_formulation.py | 106 +++ 6 files changed, 1078 insertions(+), 2 deletions(-) create mode 100644 docs/notebooks/neuralnet/example_graph_neural_network.ipynb diff --git a/docs/notebooks.rst b/docs/notebooks.rst index 0a919772..0d3f4f14 100644 --- a/docs/notebooks.rst +++ b/docs/notebooks.rst @@ -14,6 +14,8 @@ github `page `_. * `mnist_example_convolutional.ipynb `_ trains a convolutional neural network on MNIST and uses OMLT to find adversarial examples. +* `example_graph_neural_network.ipynb `_ transforms graph neural networks into dense neural networks and use OMLT to solve optimization problems. + * `auto-thermal-reformer.ipynb `_ develops a neural network surrogate (using sigmoid activations) with data from a process model built using `IDAES-PSE `_. * `auto-thermal-reformer-relu.ipynb `_ develops a neural network surrogate (using ReLU activations) with data from a process model built using `IDAES-PSE `_. diff --git a/docs/notebooks/neuralnet/example_graph_neural_network.ipynb b/docs/notebooks/neuralnet/example_graph_neural_network.ipynb new file mode 100644 index 00000000..aaaadc9a --- /dev/null +++ b/docs/notebooks/neuralnet/example_graph_neural_network.ipynb @@ -0,0 +1,779 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Example: Optimizing over trained graph neural networks\n", + "\n", + "This notebook gives examples where OMLT is used to optimize over trained graph neural networks (GNNs). We follow the below steps:\n", + "\n", + "1.) A general definition of GNNs is provided. For any GNN that fits our definition, it could be transformed into a Dense NN and then exported into OMLT.\n", + "\n", + "2.) We give an example to show how to transform a GNN into a Dense NN. For simplicity, we skip the training process and just use random parameters.\n", + "\n", + "3.) OMLT is used to generate a mixed-interger encoding of the trained GNN using two formulations (bilinear and big-M). \n", + "\n", + "4.) We consider two cases: one has fixed graph structure, another one has non-fixed graph structure. For each case, the output of the GNN is minimized.\n", + "\n", + "\n", + "## Library Setup\n", + "\n", + "This notebook assumes you have a working PyTorch environment to define a Dense NN. This Dense NN is then formulated in Pyomo using OMLT which therefore requires working Pyomo and OMLT installations.\n", + "\n", + "The required Python libraries used in this notebook are as follows:\n", + "\n", + "- `numpy`: used for transformation of parameters\n", + "\n", + "- `torch`: the machine learning language we use to define our Dense NN\n", + "\n", + "- `pyomo`: the algebraic modeling language for Python, it is used to define the optimization model passed to the solver\n", + "\n", + "- `onnx`: used to express trained neural network models\n", + "\n", + "- `omlt`: the package this notebook demonstates. OMLT can formulate machine learning (such as neural networks) within Pyomo\n", + "\n", + "**NOTE:** This notebbook alse assumes you have a working MIP solver executable to solve optimization problems in Pyomo. The open-source solver CBC is called by default. \n", + "\n", + "\n", + "## Definition of GNNs\n", + "\n", + "We define a GNN with $L$ layers as follows:\n", + "\n", + " \\begin{equation*}\n", + "\t\t\\begin{aligned}\n", + "\t\t\tGNN:\\underbrace{\\mathbb R^{d_0}\\otimes\\cdots\\otimes\\mathbb R^{d_0}}_{n \\rm{times}}\\to\\underbrace{\\mathbb R^{d_L}\\otimes\\cdots\\otimes\\mathbb R^{d_L}}_{n\\ \\rm{times}}\n", + "\t\t\\end{aligned}\n", + "\t\\end{equation*}\n", + " \n", + "where $V$ is the set of nodes of the input graph, $n=|V|$ is the number of nodes. \n", + "\n", + "Let $\\mathbf{x}_v^{(0)} \\in \\mathbb{R}^{d_0}$ be the input features for node $v$. Then, the $l$-th layer ($l=1,2,\\dots,L$) is defined by:\n", + "\t\\begin{equation*}\n", + "\t\t\\begin{aligned}\n", + "\t\t\t\\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in\\mathcal N(v)\\cup\\{v\\}}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right),~\\forall v\\in V\n", + "\t\t\\end{aligned}\n", + "\t\\end{equation*}\n", + "where $\\mathcal N(v)$ is the set of all neighbors of $v$, $\\sigma$ could be identity or any activation function.\n", + "\n", + "*Dimensionality:* $\\mathbf{x}_u^{(l-1)}\\in\\mathbb R^{d_{l-1}}, \\mathbf{x}_v^{(l)},\\mathbf{b}_v^{(l)}\\in\\mathbb R^{d_l}, \\mathbf{w}_{u\\to v}^{(l)}\\in\\mathbb R^{d_l}\\times \\mathbb R^{d_{l-1}}$.\n", + "\n", + "Stack $\\{\\mathbf{x}_v^{(l)}\\}_{v\\in V}$ as a vector $\\mathbf{X}^{(l)}\\in \\mathbb R^{nd_l}$. Rewrite previous definition as:\n", + " \\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{X}^{(l)}=\\sigma\\left(\\mathbf{W}^{(l)}\\mathbf{X}^{(l-1)}+\\mathbf{B}^{(l)}\\right)\n", + " \\end{aligned}\n", + " \\end{equation*}\n", + "where $\\mathbf{W}^{(l)}\\in\\mathbb R^{nd_[\\times nd_{l-1}}$ is a sparse matrix with nonzero sub-matrices $\\{\\mathbf{w}_{u\\to v}^{(l)}\\}_{v\\in V,u\\in\\mathcal N(v)\\cup\\{v\\}}$ and $\\mathbf{B}^{(l)}\\in\\mathbb R^{nd_l}$ is the stack of $\\{\\mathbf{b}_v^{(l)}\\}_{v\\in V}$.\n", + "\n", + "If the input graph structure is fixed, then weights ($\\mathbf{w}_{u\\to v}^{(l)}$), bias ($\\mathbf{b}_{v}^{(l)}$), and links between layers (determined by $\\mathcal N(v)$) are all fixed after the GNN is trained. In this case, the second definition is equivalent to a dense layer. It suffices to define a Dense NN with weights $\\mathbf{W}^{(l)}$ and bias $\\mathbf{B}^{(l)}$. \n", + "\n", + "\n", + "## Formulating Trained GNNs with OMLT: Fixed Graph Structure\n", + "\n", + "\n", + "### Import Requisite Packages " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9e687e95", + "metadata": {}, + "outputs": [], + "source": [ + "# parameters manipulation\n", + "import numpy as np\n", + "import tempfile\n", + "\n", + "# pytorch for defining Dense NN\n", + "import torch \n", + "import torch.nn as nn\n", + "\n", + "# pyomo for optimization\n", + "import pyomo.environ as pyo\n", + "\n", + "# omlt for interfacing our neural network with pyomo\n", + "from omlt import OmltBlock\n", + "from omlt.neuralnet import ReluBigMFormulation\n", + "from omlt.io.onnx import write_onnx_model_with_bounds, load_onnx_neural_network_with_bounds" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "797f068a", + "metadata": {}, + "source": [ + "### Constrcut a GNN with Random Parameters\n", + "\n", + "We use a simple GNN as an example, which consists of a GraphSAGE layer, an add pooling layer, and a dense layer with single output. Let the input and output features of the GraphSAGE layer are 2 and 3, respectively. \n", + "\n", + "The GraphSAGE layer is defined by:\n", + " \\begin{equation*}\n", + " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\mathbf{w_1}^{(l)}\\mathbf{x}_v^{(l-1)}+\\mathbf{w_2}^{(l)}\\sum\\limits_{u\\in\\mathcal N(v)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}^{(l)}\\right)\n", + " \\end{equation*}\n", + "where a sum aggregation is used.\n", + "\n", + "For the fixed graph structure, assume that it is a line graph with $N=3$ nodes, i.e., the adjacency matrix $A=\\begin{pmatrix}1 & 1 & 0\\\\1 & 1 & 1\\\\ 0 & 1 & 1\\end{pmatrix}$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a3e6f5a5", + "metadata": {}, + "outputs": [], + "source": [ + "# graph structure\n", + "# number of nodes\n", + "N = 3\n", + "# adjacency matrix\n", + "A = np.array([[1,1,0],[1,1,1],[0,1,1]])\n", + "\n", + "# in/out features\n", + "in_features = 2\n", + "out_features = 3\n", + "\n", + "# architecture of GNN\n", + "# sage: in_features to out_features for each node, with ReLU as activation\n", + "# add_pool: read out, sum out_features of each node\n", + "# dense: out_features to 1\n", + "gnn_layers = ['sage', 'add_pool', 'dense']\n", + "activations = [True, False, False]\n", + "\n", + "# randomly generate GNN parameters from (-1,1)\n", + "# in practice, these paprameters should be extracted from the trained GNN\n", + "np.random.seed(123)\n", + "sage_w1 = 2.* np.random.rand(out_features, in_features) -1.\n", + "sage_w2 = 2.* np.random.rand(out_features, in_features) -1.\n", + "sage_b = 2. * np.random.rand(out_features) - 1.\n", + "\n", + "dense_w = 2.* np.random.rand(1, out_features) - 1.\n", + "dense_b = 2.* np.random.rand(1) - 1." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "90289287", + "metadata": {}, + "source": [ + "### Transforming a GNN into a Dense NN\n", + "\n", + "The GraphSAGE layer could be rewritten as a dense layer with parameters:\n", + "\n", + " \\begin{equation*}\n", + " \\mathbf{W}=\\begin{pmatrix}\n", + " \\mathbf{w_1} & \\mathbf{w_2} & \\mathbf{0} \\\\\n", + " \\mathbf{w_2} & \\mathbf{w_1} & \\mathbf{w_2} \\\\\n", + " \\mathbf{0} & \\mathbf{w_2} & \\mathbf{w_1} \\\\\n", + " \\end{pmatrix},\n", + " \\mathbf{B}=\\begin{pmatrix}\n", + " \\mathbf{b}\\\\\\mathbf{b}\\\\\\mathbf{b}\n", + " \\end{pmatrix}\n", + " \\end{equation*}\n", + " \n", + "It is straightforward to rewritte the add pooling layer into a dense layer. See the following code for details.\n", + "\n", + "See below as a mapping between a GNN and a Dense NN with format \"layer (in_channel, out_channel)\":\n", + "\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\text{GraphSAGE(2, 3)} &\\Rightarrow \\text{dense(6, 9)}\\\\\n", + " \\text{add pooling(9, 3)} &\\Rightarrow \\text{dense(9, 3)}\\\\\n", + " \\text{dense(3, 1)} &\\Rightarrow \\text{dense(3, 1)}\n", + " \\end{aligned}\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "e4d5fa7f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "PyTorchModel(\n", + " (layer): Sequential(\n", + " (0): Linear(\n", + " in_features=6, out_features=9, bias=True\n", + " (relu): ReLU()\n", + " )\n", + " (1): Linear(in_features=9, out_features=3, bias=True)\n", + " (2): Linear(in_features=3, out_features=1, bias=True)\n", + " )\n", + ")\n" + ] + } + ], + "source": [ + "# transform a sage layer to dense layer\n", + "# N is the number of nodes\n", + "# w1,w2,b are parameters in a sage layer\n", + "def SAGE_to_Dense(N, A, w1, w2, b):\n", + " out_channel, in_channel = w1.shape\n", + " weight = np.zeros((N*out_channel, N*in_channel))\n", + " bias = np.zeros(N*out_channel)\n", + " for u in range(N):\n", + " for v in range(N):\n", + " if u == v:\n", + " weight[u*out_channel:(u+1)*out_channel, v*in_channel:(v+1)*in_channel] = w2\n", + " else:\n", + " weight[u*out_channel:(u+1)*out_channel, v*in_channel:(v+1)*in_channel] = w1 * A[u,v]\n", + " bias[u*out_channel:(u+1)*out_channel] = b\n", + " return weight, bias\n", + "\n", + "params = []\n", + "channels = []\n", + "channels.append(N * in_features)\n", + "\n", + "for layer in gnn_layers:\n", + " if layer == 'sage':\n", + " params.append(SAGE_to_Dense(N,A,sage_w1,sage_w2,sage_b))\n", + " channels.append(sage_w1.shape[0] * N)\n", + " elif layer == 'dense':\n", + " params.append((dense_w,dense_b))\n", + " channels.append(w.shape[0])\n", + " elif layer == 'add_pool':\n", + " channels.append(channels[-1] // N)\n", + " w = np.zeros((channels[-1],channels[-2]))\n", + " for i in range(channels[-1]):\n", + " for j in range(N):\n", + " w[i, i+j*channels[-1]] = 1.\n", + " b = np.zeros(channels[-1])\n", + " params.append((w,b))\n", + "\n", + "class PyTorchModel(nn.Module):\n", + " def __init__(self, L, params, activations):\n", + " super().__init__()\n", + " layers = []\n", + " for l in range(L):\n", + " layers.append(nn.Linear(params[l][0].shape[1], params[l][0].shape[0]))\n", + " layers[-1].weight = nn.Parameter(torch.tensor(params[l][0], dtype=torch.float64))\n", + " layers[-1].bias = nn.Parameter(torch.tensor(params[l][1], dtype=torch.float64))\n", + " if activations[l]:\n", + " layers[-1].relu = nn.ReLU()\n", + " self.layer = nn.Sequential(*layers)\n", + " \n", + " def forward(self, x):\n", + " x = self.layer(x)\n", + " return x\n", + "\n", + "model_dense = PyTorchModel(len(channels)-1, params, activations)\n", + "print(model_dense)\n", + "# for param in model_dense.parameters():\n", + "# print(param)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "8554dd1e", + "metadata": {}, + "source": [ + "### Build a MIP Formulation and Solve the Optimization Problem\n", + "\n", + "We can now export the PyTorch model as an ONNX model and use `load_onnx_neural_network_with_bounds` to load it into OMLT." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "2afb1bc9", + "metadata": {}, + "outputs": [], + "source": [ + "dummy_input = torch.zeros(channels[0], dtype=torch.float64)\n", + "dummy_input.requires_grad=True\n", + "input_bounds = [(-1., 1.) for _ in range(channels[0])]\n", + "\n", + "with tempfile.NamedTemporaryFile(suffix='.onnx', delete=False) as f:\n", + " #export neural network to ONNX\n", + " torch.onnx.export(\n", + " model_dense,\n", + " dummy_input,\n", + " f,\n", + " input_names=['input'],\n", + " output_names=['output'],\n", + " )\n", + " #write ONNX model and its bounds using OMLT\n", + " write_onnx_model_with_bounds(f.name, None, input_bounds)\n", + " #load the network definition from the ONNX model\n", + " network_definition = load_onnx_neural_network_with_bounds(f.name)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "4dee6a2c", + "metadata": {}, + "source": [ + "As a sanity check before creating the optimization model, we can print the properties of the neural network layers from `network_definition`. This allows us to check input/output sizes, as well as activation functions." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "35b6a53b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\tInputLayer(input_size=[6], output_size=[6])\tlinear\n", + "1\tDenseLayer(input_size=[6], output_size=[9])\tlinear\n", + "2\tDenseLayer(input_size=[9], output_size=[3])\tlinear\n", + "3\tDenseLayer(input_size=[3], output_size=[1])\tlinear\n" + ] + } + ], + "source": [ + "for layer_id, layer in enumerate(network_definition.layers):\n", + " print(f\"{layer_id}\\t{layer}\\t{layer.activation}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "dbf59025", + "metadata": {}, + "source": [ + "Finally, we can load `network_definition` as a full-space `ReluBigMFormulation` object." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "14b82060", + "metadata": {}, + "outputs": [], + "source": [ + "formulation = ReluBigMFormulation(network_definition)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "8d2c17a6", + "metadata": {}, + "source": [ + "We now encode the Dense NN in a Pyomo model from the `ReluBigMFormulation` object." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "30a42a58", + "metadata": {}, + "outputs": [], + "source": [ + "# create pyomo model\n", + "m = pyo.ConcreteModel()\n", + "\n", + "# create an OMLT block for the neural network and build its formulation\n", + "m.nn = OmltBlock()\n", + "m.nn.build_formulation(formulation)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b2dde6f5", + "metadata": {}, + "source": [ + "Next, we define the objective function as the single output of the Dense NN and solve the minimization problem using a mixed integer solver." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "0c0e1dd4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Welcome to the CBC MILP Solver \n", + "Version: 2.10.5 \n", + "Build Date: Dec 8 2020 \n", + "\n", + "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT/bin/cbc -printingOptions all -import /var/tmp/pbs.7715724.pbs/tmp9gxn1x7c.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.7715724.pbs/tmp9gxn1x7c.pyomo.soln (default strategy 1)\n", + "Option for printingOptions changed from normal to all\n", + "Presolve 1 (-39) rows, 7 (-39) columns and 7 (-114) elements\n", + "Statistics for presolved model\n", + "\n", + "\n", + "Problem has 1 rows, 7 columns (7 with objective) and 7 elements\n", + "There are 7 singletons with objective \n", + "Column breakdown:\n", + "0 of type 0.0->inf, 0 of type 0.0->up, 0 of type lo->inf, \n", + "7 of type lo->up, 0 of type free, 0 of type fixed, \n", + "0 of type -inf->0.0, 0 of type -inf->up, 0 of type 0.0->1.0 \n", + "Row breakdown:\n", + "0 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, \n", + "1 of type E other, 0 of type G 0.0, 0 of type G 1.0, \n", + "0 of type G other, 0 of type L 0.0, 0 of type L 1.0, \n", + "0 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", + "0 of type Free \n", + "Presolve 1 (-39) rows, 7 (-39) columns and 7 (-114) elements\n", + "0 Obj 0.34521997 Primal inf 1.2424353 (1) Dual inf 3.9956189 (4)\n", + "1 Obj -1.7190541\n", + "Optimal - objective value -1.7190541\n", + "After Postsolve, objective -1.7190541, infeasibilities - dual 0 (0), primal 0 (0)\n", + "Optimal objective -1.719054146 - 1 iterations time 0.002, Presolve 0.00\n", + "Total time (CPU seconds): 0.00 (Wallclock seconds): 0.00\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "{'Problem': [{'Name': 'unknown', 'Lower bound': -1.719054146, 'Upper bound': -1.719054146, 'Number of objectives': 1, 'Number of constraints': 40, 'Number of variables': 46, 'Number of nonzeros': 7, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'User time': -1.0, 'System time': 0.0, 'Wallclock time': 0.0, 'Termination condition': 'optimal', 'Termination message': 'Model was solved to optimality (subject to tolerances), and an optimal solution is available.', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': None, 'Number of created subproblems': None}, 'Black box': {'Number of iterations': 1}}, 'Error rc': 0, 'Time': 0.1509706974029541}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m.obj = pyo.Objective(expr=(m.nn.outputs[0]))\n", + "pyo.SolverFactory('cbc').solve(m, tee=True)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "5a3d2108", + "metadata": {}, + "source": [ + "## Formulating Trained GNNs with OMLT: Non-fixed Graph Structure\n", + "\n", + "When the input graph structure is not fixed, elements in the adjacency matrix $A$ are decision variables. In this case, $\\mathcal N(v)$ is not given anymore. Additionally, $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ may contain the graph information, which makes them be variables.\n", + "\n", + "Assume that $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ are fixed. Then we have two formulations to handle $A$.\n", + "\n", + "\n", + "### Bilinear Formulation\n", + "\n", + "This formulation comes from the observation that the existence of edge $u\\to v$ determines the contribution link from $\\mathbf{x}_u^{(l-1)}$ to $\\mathbf{x}_v^{(l)}$. Adding binary variables $A_{u,v}$ for all $u,v\\in V$, we can formulate GNNs in a bilinear way:\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}A_{u,v}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "\n", + "**NOTE:** The bilinear formulation involves quadratic constraints and therefore needs a working MINLP solver such as Gurobi. We do not use bilinear formulation in this notebook since 1) a license is required to use Gurobi, and 2) the big-M formulation usually outperforms bilinear formulation based on our tests.\n", + "\n", + "### Big-M Formulation\n", + "\n", + "Instead of using binary variables to directly control the existence of contributions between nodes, the second formulation introduces auxiliary variables $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ to represent the contribution from node $u$ to node $v$ in $l$th layer:\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{\\bar x}_{u\\to v}^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "where\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{\\bar x}_{u\\to v}^{(l-1)}=\\begin{cases}\n", + " 0, & A_{u,v}=0\\\\\n", + " \\mathbf{x}_u^{(l-1)}, & A_{u,v}=1\n", + " \\end{cases}\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "Assume that each feature is bounded, then the definition of $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ could be reformulated using big-M:\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{x}_{u}^{(l-1)}-\\mathbf{M}_{u}^{(l-1)}(1-A_{u,v})\\le &\\mathbf{\\bar x}_{u\\to v}^{(l-1)}\\le \\mathbf{x}_{u}^{(l-1)}+\\mathbf{M}_{u}^{(l-1)}(1-A_{u,v})\\\\\n", + " -\\mathbf{M}_{u}^{(l-1)}A_{u,v}\\le &\\mathbf{\\bar x}_{u\\to v}^{(l-1)}\\le \\mathbf{M}_u^{(l-1)}A_{u,v}\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "where $|\\mathbf{x}_u^{(l-1)}|\\le \\mathbf{M}_u^{(l-1)}, A_{u,v}\\in\\{0,1\\}$. By adding extra continuous variables and constraints, as well as utilizing the bounds for all features, the big-M formulation replaces the bi-linear constraints by linear constraints.\n", + "\n", + "\n", + "\n", + "### Transforming a GNN with Non-fixed Graph Structure into a Dense NN\n", + "\n", + "Since the graph structure is unknown, all $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ should be provided. We reuse the previous example but this time the parameters in the Dense NN become:\n", + "\n", + "\\begin{equation*}\n", + " \\mathbf{W}=\\begin{pmatrix}\n", + " \\mathbf{w_1} & \\mathbf{w_2} & \\mathbf{w_2} \\\\\n", + " \\mathbf{w_2} & \\mathbf{w_1} & \\mathbf{w_2} \\\\\n", + " \\mathbf{w_2} & \\mathbf{w_2} & \\mathbf{w_1} \\\\\n", + " \\end{pmatrix},\n", + " \\mathbf{B}=\\begin{pmatrix}\n", + " \\mathbf{b}\\\\\\mathbf{b}\\\\\\mathbf{b}\n", + " \\end{pmatrix}\n", + " \\end{equation*}\n", + " \n", + "Repeat all process before building formulation for the Dense NN." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "45a6c2b3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\tInputLayer(input_size=[6], output_size=[6])\tlinear\n", + "1\tDenseLayer(input_size=[6], output_size=[9])\tlinear\n", + "2\tDenseLayer(input_size=[9], output_size=[3])\tlinear\n", + "3\tDenseLayer(input_size=[3], output_size=[1])\tlinear\n" + ] + } + ], + "source": [ + "# graph structure\n", + "# number of nodes\n", + "N = 3\n", + "# adjacency matrix\n", + "A = np.array([[1,1,1],[1,1,1],[1,1,1]])\n", + "\n", + "# in/out features\n", + "in_features = 2\n", + "out_features = 3\n", + "\n", + "# architecture of GNN\n", + "# sage: in_features to out_features for each node, with ReLU as activation\n", + "# add_pool: read out, sum out_features of each node\n", + "# dense: out_features to 1\n", + "gnn_layers = ['sage', 'add_pool', 'dense']\n", + "activations = [True, False, False]\n", + "\n", + "# randomly generate GNN parameters from (-1,1)\n", + "# in practice, these paprameters should be extracted from the trained GNN\n", + "np.random.seed(123)\n", + "sage_w1 = 2.* np.random.rand(out_features, in_features) -1.\n", + "sage_w2 = 2.* np.random.rand(out_features, in_features) -1.\n", + "sage_b = 2. * np.random.rand(out_features) - 1.\n", + "\n", + "dense_w = 2.* np.random.rand(1, out_features) - 1.\n", + "dense_b = 2.* np.random.rand(1) - 1.\n", + "\n", + "params = []\n", + "channels = []\n", + "channels.append(N * in_features)\n", + "\n", + "for layer in gnn_layers:\n", + " if layer == 'sage':\n", + " params.append(SAGE_to_Dense(N,A,sage_w1,sage_w2,sage_b))\n", + " channels.append(sage_w1.shape[0] * N)\n", + " elif layer == 'dense':\n", + " params.append((dense_w,dense_b))\n", + " channels.append(w.shape[0])\n", + " elif layer == 'add_pool':\n", + " channels.append(channels[-1] // N)\n", + " w = np.zeros((channels[-1],channels[-2]))\n", + " for i in range(channels[-1]):\n", + " for j in range(N):\n", + " w[i, i+j*channels[-1]] = 1.\n", + " b = np.zeros(channels[-1])\n", + " params.append((w,b))\n", + " \n", + "model_dense = PyTorchModel(len(channels)-1, params, activations)\n", + "# print(model_dense)\n", + "\n", + "# for param in model_dense.parameters():\n", + "# print(param)\n", + "\n", + "dummy_input = torch.zeros(channels[0], dtype=torch.float64)\n", + "dummy_input.requires_grad=True\n", + "input_bounds = [(-1., 1.) for _ in range(channels[0])]\n", + "\n", + "with tempfile.NamedTemporaryFile(suffix='.onnx', delete=False) as f:\n", + " #export neural network to ONNX\n", + " torch.onnx.export(\n", + " model_dense,\n", + " dummy_input,\n", + " f,\n", + " input_names=['input'],\n", + " output_names=['output'],\n", + " )\n", + " #write ONNX model and its bounds using OMLT\n", + " write_onnx_model_with_bounds(f.name, None, input_bounds)\n", + " #load the network definition from the ONNX model\n", + " network_definition = load_onnx_neural_network_with_bounds(f.name)\n", + " \n", + "for layer_id, layer in enumerate(network_definition.layers):\n", + " print(f\"{layer_id}\\t{layer}\\t{layer.activation}\")\n", + " \n", + "formulation = ReluBigMFormulation(network_definition)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Build a MIP Formulation and Solve the Optimization Problem\n", + "\n", + "Note that all types of layers are represented as dense layers in OMLT now. To identify a GNN layer, before building formulation, we need to add the following information:\n", + "\n", + "- `m.nn.N`: number of nodes in the graph.\n", + "- `m.nn.A`: adjacency matrix consists of $(m.nn.N)^2$ binary variables.\n", + "- `m.nn.gnn_layers`: a list consists of the indexes for GNN layers (begins with $1$).\n", + "- `m.nn.gnn_formulation`: type of formulation for GNN layers. Two options are supported (`\"bilinear\"`, `\"bigM\"`). `\"bigM\"` is recommended.\n", + "\n", + "**NOTE:** One can fix different elements in $A$ based on different problems. For example, fix most elements in $A$ and only optimize over a subset of edges. The extrame case is that fixing all elements, which is equivalent to the case with fixed graph structure." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Welcome to the CBC MILP Solver \n", + "Version: 2.10.5 \n", + "Build Date: Dec 8 2020 \n", + "\n", + "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT/bin/cbc -printingOptions all -import /var/tmp/pbs.7715724.pbs/tmpuh1uwdgm.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.7715724.pbs/tmpuh1uwdgm.pyomo.soln (default strategy 1)\n", + "Option for printingOptions changed from normal to all\n", + "Presolve 63 (-49) rows, 33 (-37) columns and 185 (-104) elements\n", + "Statistics for presolved model\n", + "Original problem has 6 integers (6 of which binary)\n", + "Presolved problem has 6 integers (6 of which binary)\n", + "==== 16 zero objective 8 different\n", + "3 variables have objective of -0.649096\n", + "1 variables have objective of -0.635017\n", + "4 variables have objective of -0.268763\n", + "16 variables have objective of 0\n", + "2 variables have objective of 0.312969\n", + "1 variables have objective of 0.475991\n", + "2 variables have objective of 0.481896\n", + "4 variables have objective of 0.533943\n", + "==== absolute objective values 8 different\n", + "16 variables have objective of 0\n", + "4 variables have objective of 0.268763\n", + "2 variables have objective of 0.312969\n", + "1 variables have objective of 0.475991\n", + "2 variables have objective of 0.481896\n", + "4 variables have objective of 0.533943\n", + "1 variables have objective of 0.635017\n", + "3 variables have objective of 0.649096\n", + "==== for integers 6 zero objective 1 different\n", + "6 variables have objective of 0\n", + "==== for integers absolute objective values 1 different\n", + "6 variables have objective of 0\n", + "===== end objective counts\n", + "\n", + "\n", + "Problem has 63 rows, 33 columns (17 with objective) and 185 elements\n", + "There are 3 singletons with objective \n", + "Column breakdown:\n", + "0 of type 0.0->inf, 0 of type 0.0->up, 0 of type lo->inf, \n", + "27 of type lo->up, 0 of type free, 0 of type fixed, \n", + "0 of type -inf->0.0, 0 of type -inf->up, 6 of type 0.0->1.0 \n", + "Row breakdown:\n", + "0 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, \n", + "3 of type E other, 0 of type G 0.0, 0 of type G 1.0, \n", + "0 of type G other, 32 of type L 0.0, 24 of type L 1.0, \n", + "4 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", + "0 of type Free \n", + "Continuous objective value is -2.55499 - 0.00 seconds\n", + "Cgl0004I processed model has 64 rows, 34 columns (6 integer (6 of which binary)) and 184 elements\n", + "Cbc0038I Initial state - 0 integers unsatisfied sum - 0\n", + "Cbc0038I Solution found of -2.55499\n", + "Cbc0038I Relaxing continuous gives -2.55499\n", + "Cbc0038I Before mini branch and bound, 6 integers at bound fixed and 24 continuous\n", + "Cbc0038I Mini branch and bound did not improve solution (0.00 seconds)\n", + "Cbc0038I After 0.00 seconds - Feasibility pump exiting with objective of -2.55499 - took 0.00 seconds\n", + "Cbc0012I Integer solution of -2.5549939 found by feasibility pump after 0 iterations and 0 nodes (0.00 seconds)\n", + "Cbc0001I Search completed - best objective -2.554993930144489, took 0 iterations and 0 nodes (0.00 seconds)\n", + "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", + "Cuts at root node changed objective from -2.55499 to -2.55499\n", + "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "\n", + "Result - Optimal solution found\n", + "\n", + "Objective value: -2.55499393\n", + "Enumerated nodes: 0\n", + "Total iterations: 0\n", + "Time (CPU seconds): 0.00\n", + "Time (Wallclock seconds): 0.00\n", + "\n", + "Total time (CPU seconds): 0.00 (Wallclock seconds): 0.00\n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "{'Problem': [{'Name': 'unknown', 'Lower bound': -2.55499393, 'Upper bound': -2.55499393, 'Number of objectives': 1, 'Number of constraints': 63, 'Number of variables': 33, 'Number of binary variables': 6, 'Number of integer variables': 6, 'Number of nonzeros': 17, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'User time': -1.0, 'System time': 0.0, 'Wallclock time': 0.0, 'Termination condition': 'optimal', 'Termination message': 'Model was solved to optimality (subject to tolerances), and an optimal solution is available.', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': 0, 'Number of created subproblems': 0}, 'Black box': {'Number of iterations': 0}}, 'Error rc': 0, 'Time': 0.03762245178222656}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# create pyomo model\n", + "m = pyo.ConcreteModel()\n", + "\n", + "# create an OMLT block for the neural network and build its formulation\n", + "m.nn = OmltBlock()\n", + "\n", + "# initialize graph information\n", + "m.nn.N = N\n", + "m.nn.A = pyo.Var(pyo.Set(initialize=range(m.nn.N)), pyo.Set(initialize=range(m.nn.N)), within=pyo.Binary)\n", + "# usually, the contribution from node v to itself exists\n", + "for i in range(N):\n", + " m.nn.A[i,i].fix(1)\n", + "\n", + "# specify the indexes for GNN layers and the formulation\n", + "m.nn.gnn_layers = [1]\n", + "m.nn.gnn_formulation = 'bigM'\n", + "\n", + "m.nn.build_formulation(formulation)\n", + "\n", + "m.obj = pyo.Objective(expr=(m.nn.outputs[0]))\n", + "pyo.SolverFactory('cbc').solve(m, tee=True)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [conda env:OMLT]", + "language": "python", + "name": "conda-env-OMLT-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/src/omlt/neuralnet/layers/__init__.py b/src/omlt/neuralnet/layers/__init__.py index a37c5c87..d98d22dc 100644 --- a/src/omlt/neuralnet/layers/__init__.py +++ b/src/omlt/neuralnet/layers/__init__.py @@ -1,2 +1,2 @@ -from .full_space import full_space_conv2d_layer, full_space_dense_layer +from .full_space import full_space_conv2d_layer, full_space_dense_layer, full_space_gnn_layer_bilinear, full_space_gnn_layer_bigm from .reduced_space import reduced_space_dense_layer diff --git a/src/omlt/neuralnet/layers/full_space.py b/src/omlt/neuralnet/layers/full_space.py index e0923656..ed8a445f 100644 --- a/src/omlt/neuralnet/layers/full_space.py +++ b/src/omlt/neuralnet/layers/full_space.py @@ -39,6 +39,183 @@ def dense_layer(b, *output_index): return layer_block.zhat[output_index] == expr +def full_space_gnn_layer_bilinear(net_block, net, layer_block, layer): + r""" + Add full-space formulation of the gnn layer to the block + + .. math:: + + \begin{align*} + & \hat z_i = \sum_{j{=}1}^{M_i} A_{v_i,v_j} w_{ij} z_j + b_i && \forall i \in N \\ + & A_{v_i,v_j}\in\{0,1\} + \end{align*} + + where :math:`v_i` is the graph indexing of the i-th node. + + """ + + input_layer, input_layer_block = _input_layer_and_block(net_block, net, layer) + + input_channel = layer.input_size[0] // net_block.N + output_channel = layer.output_size[0] // net_block.N + + @layer_block.Constraint(layer.output_indexes) + def gnn_layer_bilinear_formulation(b, *output_index): + # dense layers multiply only the last dimension of + # their inputs + expr = 0.0 + for local_index, input_index in layer.input_indexes_with_input_layer_indexes: + w = layer.weights[input_index[-1], output_index[-1]] + + input_node_index = input_index[-1] // input_channel + output_node_index = output_index[-1] // output_channel + + expr += ( + input_layer_block.z[input_index] + * w + * net_block.A[input_node_index, output_node_index] + ) + # move this at the end to avoid numpy/pyomo var bug + output_node_index = output_index[-1] // output_channel + expr += layer.biases[output_index[-1]] + + lb, ub = compute_bounds_on_expr(expr) + layer_block.zhat[output_index].setlb(lb) + layer_block.zhat[output_index].setub(ub) + + return layer_block.zhat[output_index] == expr + + +from omlt.neuralnet.layer import InputLayer + + +def full_space_gnn_layer_bigm(net_block, net, layer_block, layer): + r""" + Add full-space formulation of the gnn layer to the block + + .. math:: + + \begin{align*} + \hat z_i &= \sum_{j{=}1}^{M_i} w_{ij} \bar z_{ij} + b_i && \forall i \in N \\ + \bar z_{ij} &= A_{v_i,v_j} z_{j} + \end{align*} + + The big-M formulation for :math:`\bar z_{ij}` is given by: + + .. math:: + + \begin{align*} + z_{j} - M_{j}(1-A_{v_i,v_j}) &\le \bar z_{ij} \le z_{j} + M_{j}(1-A_{v_i,v_j})\\ + - M_{j}A_{v_i,v_j} &\le \bar z_{ij} \le M_{j}A_{v_i,v_j}\\ + A_{v_i,v_j}&\in \{0,1\} + \end{align*} + + where :math:`M_{j}` is upper bound of :math:`|z_{j}|`. + """ + + input_layer, input_layer_block = _input_layer_and_block(net_block, net, layer) + input_channel = layer.input_size[0] // net_block.N + output_channel = layer.output_size[0] // net_block.N + + input_layer_block.zbar = pyo.Var( + pyo.Set(initialize=range(layer.input_size[0])), + pyo.Set(initialize=range(net_block.N)), + initialize=0, + ) + + input_layer_block._zbar_lower_bound_z_big_m = pyo.Constraint( + pyo.Set(initialize=range(layer.input_size[0] * net_block.N)) + ) + input_layer_block._zbar_upper_bound_z_big_m = pyo.Constraint( + pyo.Set(initialize=range(layer.input_size[0] * net_block.N)) + ) + input_layer_block._zbar_lower_bound_big_m = pyo.Constraint( + pyo.Set(initialize=range(layer.input_size[0] * net_block.N)) + ) + input_layer_block._zbar_upper_bound_big_m = pyo.Constraint( + pyo.Set(initialize=range(layer.input_size[0] * net_block.N)) + ) + + # set dummy parameters here to avoid warning message from Pyomo + input_layer_block._abs_bound_big_m = pyo.Param( + input_layer.output_indexes, default=1e6, mutable=True + ) + + for input_index in layer.input_indexes: + lb, ub = input_layer_block.z[input_index].bounds + input_layer_block._abs_bound_big_m[input_index] = max(abs(lb), abs(ub)) + + for output_node_index in range(net_block.N): + input_layer_block.zbar[input_index, output_node_index].setlb(min(0, lb)) + input_layer_block.zbar[input_index, output_node_index].setub(max(0, ub)) + + input_node_index = input_index[-1] // input_channel + + constraint_index = input_index[-1] * net_block.N + output_node_index + input_layer_block._zbar_lower_bound_z_big_m[ + constraint_index + ] = input_layer_block.zbar[ + input_index, output_node_index + ] >= input_layer_block.z[ + input_index + ] - input_layer_block._abs_bound_big_m[ + input_index + ] * ( + 1.0 - net_block.A[input_node_index, output_node_index] + ) + + input_layer_block._zbar_upper_bound_z_big_m[ + constraint_index + ] = input_layer_block.zbar[ + input_index, output_node_index + ] <= input_layer_block.z[ + input_index + ] + input_layer_block._abs_bound_big_m[ + input_index + ] * ( + 1.0 - net_block.A[input_node_index, output_node_index] + ) + + input_layer_block._zbar_lower_bound_big_m[constraint_index] = ( + input_layer_block.zbar[input_index, output_node_index] + >= -input_layer_block._abs_bound_big_m[input_index] + * net_block.A[input_node_index, output_node_index] + ) + + input_layer_block._zbar_upper_bound_big_m[constraint_index] = ( + input_layer_block.zbar[input_index, output_node_index] + <= input_layer_block._abs_bound_big_m[input_index] + * net_block.A[input_node_index, output_node_index] + ) + + # input_layer_block._zbar_lower_bound_z_big_m.pprint() + # input_layer_block._zbar_upper_bound_z_big_m.pprint() + # input_layer_block._zbar_lower_bound_big_m.pprint() + # input_layer_block._zbar_upper_bound_big_m.pprint() + + @layer_block.Constraint(layer.output_indexes) + def dense_layer(b, *output_index): + # dense layers multiply only the last dimension of + # their inputs + expr = 0.0 + for local_index, input_index in layer.input_indexes_with_input_layer_indexes: + w = layer.weights[input_index[-1], output_index[-1]] + + input_node_index = input_index[-1] // input_channel + output_node_index = output_index[-1] // output_channel + + expr += input_layer_block.zbar[input_index, output_node_index] * w + # move this at the end to avoid numpy/pyomo var bug + output_node_index = output_index[-1] // output_channel + expr += layer.biases[output_index[-1]] + + lb, ub = compute_bounds_on_expr(expr) + layer_block.zhat[output_index].setlb(lb) + layer_block.zhat[output_index].setub(ub) + # print(layer_block.zhat[output_index] == expr) + return layer_block.zhat[output_index] == expr + + def full_space_conv2d_layer(net_block, net, layer_block, layer): r""" Add full-space formulation of the 2-D convolutional layer to the block diff --git a/src/omlt/neuralnet/nn_formulation.py b/src/omlt/neuralnet/nn_formulation.py index 068abd6b..f3a0578d 100644 --- a/src/omlt/neuralnet/nn_formulation.py +++ b/src/omlt/neuralnet/nn_formulation.py @@ -22,6 +22,8 @@ full_space_conv2d_layer, full_space_dense_layer, full_space_maxpool2d_layer, + full_space_gnn_layer_bilinear, + full_space_gnn_layer_bigm, ) from omlt.neuralnet.layers.partition_based import ( default_partition_split_func, @@ -172,13 +174,23 @@ def layer(b, layer_id): return b - for layer in layers: + for layer_index, layer in enumerate(layers): if isinstance(layer, InputLayer): continue layer_id = id(layer) layer_block = block.layer[layer_id] layer_constraints_func = layer_constraints.get(type(layer), None) + + if "gnn_layers" in dir( + block + ): # if the block has GNN layers, then apply one of these two formulations + if layer_index in block.gnn_layers: + if block.gnn_formulation == "bilinear": + layer_constraints_func = full_space_gnn_layer_bilinear + elif block.gnn_formulation == "bigM": + layer_constraints_func = full_space_gnn_layer_bigm + if layer_constraints_func is None: raise ValueError( "Layer type {} is not supported by this formulation.".format( diff --git a/tests/neuralnet/test_nn_formulation.py b/tests/neuralnet/test_nn_formulation.py index c566add4..636c8c6e 100644 --- a/tests/neuralnet/test_nn_formulation.py +++ b/tests/neuralnet/test_nn_formulation.py @@ -323,3 +323,109 @@ def test_maxpool_FullSpaceNNFormulation(): m.obj1 = pyo.Objective(expr=0) status = pyo.SolverFactory("cbc").solve(m, tee=False) assert abs(pyo.value(m.neural_net_block.outputs[0, 0, 0]) - y[0, 0, 0]) < 1e-6 + + +def three_node_graph_neural_network(activation): + input_size = [6] + input_bounds = [(-10.0, 10.0) for i in range(6)] + + net = NetworkDefinition(scaled_input_bounds=input_bounds) + + input_layer = InputLayer(input_size) + net.add_layer(input_layer) + + dense_layer_0 = DenseLayer( + input_layer.output_size, + [9], + activation=activation, + weights=np.array( + [ + [1.0, 0.0, 1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0], + [0.0, 1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0], + [1.0, -1.0, 1.0, 1.0, 0.0, 1.0, 1.0, -1.0, 1.0], + [-1.0, 1.0, 1.0, 0.0, 1.0, 1.0, -1.0, 1.0, 1.0], + [1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 0.0, 1.0], + [-1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 0.0, 1.0, 1.0], + ] + ), + biases=np.array([-1.0, 0.0, 1.0, -1.0, 0.0, 1.0, -1.0, 0.0, 1.0]), + ) + net.add_layer(dense_layer_0) + net.add_edge(input_layer, dense_layer_0) + + return net + + +def examples_of_graphs(graph_type): + # complete graph + if graph_type == "complete": + A = np.ones([3, 3], dtype=int) + y = np.array([-11.0, 9.0, 1.0, -12.0, 11.0, 1.0, -10.0, 10.0, 1.0]) + # edgeless graph + elif graph_type == "edgeless": + A = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) + y = np.array([-4.0, 2.0, 0.0, -2.0, 1.0, 1.0, -3.0, 3.0, 2.0]) + # line graph, i.e., 0-1-2 + elif graph_type == "line": + A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]]) + y = np.array([-6.0, 4.0, 0.0, -12.0, 11.0, 1.0, -5.0, 5.0, 2.0]) + return A, y + + +def _test_three_node_graph_neural_network(gnn_formulation, graph_type): + m = pyo.ConcreteModel() + m.nn = OmltBlock() + inputs = np.array([-3.0, 2.0, -1.0, 1.0, -2.0, 3.0]) + net = three_node_graph_neural_network("linear") + + # add graph information + m.nn.N = 3 + m.nn.A = pyo.Var( + pyo.Set(initialize=range(m.nn.N)), + pyo.Set(initialize=range(m.nn.N)), + within=pyo.Binary, + ) + # specify the indexes of GNN layers and the type of formulation + m.nn.gnn_layers = [1] + m.nn.gnn_formulation = gnn_formulation + + m.nn.build_formulation(FullSpaceNNFormulation(net)) + + A, y = examples_of_graphs(graph_type) + for i in range(m.nn.N): + for j in range(m.nn.N): + m.nn.A[i, j].fix(A[i, j]) + for i in range(6): + m.nn.inputs[i].fix(inputs[i]) + + if gnn_formulation == "bilinear": + assert m.nvariables() == 63 + assert m.nconstraints() == 48 + elif gnn_formulation == "bigM": + assert m.nvariables() == 81 + assert m.nconstraints() == 120 + m.obj = pyo.Objective(expr=0) + + status = pyo.SolverFactory("cbc").solve(m, tee=False) + + for i in range(9): + assert abs(pyo.value(m.nn.outputs[i]) - y[i]) < 1e-6 + + if gnn_formulation == "bigM": + for i in range(6): + for j in range(3): + assert ( + abs( + pyo.value(m.nn.layer[m.nn.layers.at(1)].zbar[i, j]) + - pyo.value(m.nn.A[i // 2, j]) * inputs[i] + ) + < 1e-6 + ) + + +def test_three_node_graph_neural_network(): + gnn_formulations = ["bilinear", "bigM"] + graph_types = ["complete", "edgeless", "line"] + for gnn_formulation in gnn_formulations: + for graph_type in graph_types: + _test_three_node_graph_neural_network(gnn_formulation, graph_type) From 703f05817c121bc95e71a60c3ae5bc82adedbf73 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Tue, 13 Jun 2023 10:32:29 +0100 Subject: [PATCH 02/27] fix input issue for max pooling --- tests/neuralnet/test_nn_formulation.py | 36 ++++++++++++++------------ 1 file changed, 19 insertions(+), 17 deletions(-) diff --git a/tests/neuralnet/test_nn_formulation.py b/tests/neuralnet/test_nn_formulation.py index 636c8c6e..346fc659 100644 --- a/tests/neuralnet/test_nn_formulation.py +++ b/tests/neuralnet/test_nn_formulation.py @@ -219,8 +219,10 @@ def test_invalid_layer_type(): def _maxpool_conv_network(inputs): input_size = [1, 8, 6] - input_bounds = np.empty(input_size, dtype="i,i") - input_bounds.fill((-10, 10)) + input_bounds = {} + for i in range(input_size[1]): + for j in range(input_size[2]): + input_bounds[(0, i, j)] = (-10.0, 10.0) net = NetworkDefinition(scaled_input_bounds=input_bounds) input_layer = InputLayer(input_size) @@ -327,8 +329,9 @@ def test_maxpool_FullSpaceNNFormulation(): def three_node_graph_neural_network(activation): input_size = [6] - input_bounds = [(-10.0, 10.0) for i in range(6)] - + input_bounds = {} + for i in range(input_size[0]): + input_bounds[(i)] = (-10.0, 10.0) net = NetworkDefinition(scaled_input_bounds=input_bounds) input_layer = InputLayer(input_size) @@ -340,15 +343,15 @@ def three_node_graph_neural_network(activation): activation=activation, weights=np.array( [ - [1.0, 0.0, 1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0], - [0.0, 1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0], - [1.0, -1.0, 1.0, 1.0, 0.0, 1.0, 1.0, -1.0, 1.0], - [-1.0, 1.0, 1.0, 0.0, 1.0, 1.0, -1.0, 1.0, 1.0], - [1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 0.0, 1.0], - [-1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 0.0, 1.0, 1.0], + [1, 0, 1, 1, -1, 1, 1, -1, 1], + [0, 1, 1, -1, 1, 1, -1, 1, 1], + [1, -1, 1, 1, 0, 1, 1, -1, 1], + [-1, 1, 1, 0, 1, 1, -1, 1, 1], + [1, -1, 1, 1, -1, 1, 1, 0, 1], + [-1, 1, 1, -1, 1, 1, 0, 1, 1], ] ), - biases=np.array([-1.0, 0.0, 1.0, -1.0, 0.0, 1.0, -1.0, 0.0, 1.0]), + biases=np.array([-1, 0, 1, -1, 0, 1, -1, 0, 1]), ) net.add_layer(dense_layer_0) net.add_edge(input_layer, dense_layer_0) @@ -360,32 +363,31 @@ def examples_of_graphs(graph_type): # complete graph if graph_type == "complete": A = np.ones([3, 3], dtype=int) - y = np.array([-11.0, 9.0, 1.0, -12.0, 11.0, 1.0, -10.0, 10.0, 1.0]) + y = np.array([-11, 9, 1, -12, 11, 1, -10, 10, 1]) # edgeless graph elif graph_type == "edgeless": A = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) - y = np.array([-4.0, 2.0, 0.0, -2.0, 1.0, 1.0, -3.0, 3.0, 2.0]) + y = np.array([-4, 2, 0, -2, 1, 1, -3, 3, 2]) # line graph, i.e., 0-1-2 elif graph_type == "line": A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]]) - y = np.array([-6.0, 4.0, 0.0, -12.0, 11.0, 1.0, -5.0, 5.0, 2.0]) + y = np.array([-6, 4, 0, -12, 11, 1, -5, 5, 2]) return A, y def _test_three_node_graph_neural_network(gnn_formulation, graph_type): m = pyo.ConcreteModel() m.nn = OmltBlock() - inputs = np.array([-3.0, 2.0, -1.0, 1.0, -2.0, 3.0]) + inputs = np.array([-3, 2, -1, 1, -2, 3]) net = three_node_graph_neural_network("linear") - # add graph information m.nn.N = 3 m.nn.A = pyo.Var( pyo.Set(initialize=range(m.nn.N)), pyo.Set(initialize=range(m.nn.N)), within=pyo.Binary, ) - # specify the indexes of GNN layers and the type of formulation + m.nn.gnn_layers = [1] m.nn.gnn_formulation = gnn_formulation From 0592729d8a1da3f54850096c1ca779205aacd80f Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 21 Jun 2023 15:25:46 +0100 Subject: [PATCH 03/27] update formulation for GNN --- .../example_graph_neural_network.ipynb | 162 ++++++++++-------- src/omlt/neuralnet/layer.py | 91 +++++++++- src/omlt/neuralnet/layers/__init__.py | 6 +- src/omlt/neuralnet/layers/full_space.py | 141 +++++---------- src/omlt/neuralnet/network_definition.py | 57 +++++- src/omlt/neuralnet/nn_formulation.py | 24 ++- tests/neuralnet/test_layer.py | 38 ++++ tests/neuralnet/test_nn_formulation.py | 97 +++++------ 8 files changed, 374 insertions(+), 242 deletions(-) diff --git a/docs/notebooks/neuralnet/example_graph_neural_network.ipynb b/docs/notebooks/neuralnet/example_graph_neural_network.ipynb index aaaadc9a..2290043f 100644 --- a/docs/notebooks/neuralnet/example_graph_neural_network.ipynb +++ b/docs/notebooks/neuralnet/example_graph_neural_network.ipynb @@ -13,7 +13,7 @@ "\n", "2.) We give an example to show how to transform a GNN into a Dense NN. For simplicity, we skip the training process and just use random parameters.\n", "\n", - "3.) OMLT is used to generate a mixed-interger encoding of the trained GNN using two formulations (bilinear and big-M). \n", + "3.) OMLT is used to generate a mixed-interger encoding of the trained GNN. \n", "\n", "4.) We consider two cases: one has fixed graph structure, another one has non-fixed graph structure. For each case, the output of the GNN is minimized.\n", "\n", @@ -78,8 +78,7 @@ }, { "cell_type": "code", - "execution_count": null, - "id": "9e687e95", + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -97,13 +96,13 @@ "# omlt for interfacing our neural network with pyomo\n", "from omlt import OmltBlock\n", "from omlt.neuralnet import ReluBigMFormulation\n", + "from omlt.neuralnet.network_definition import gnn_layer_definition\n", "from omlt.io.onnx import write_onnx_model_with_bounds, load_onnx_neural_network_with_bounds" ] }, { "attachments": {}, "cell_type": "markdown", - "id": "797f068a", "metadata": {}, "source": [ "### Constrcut a GNN with Random Parameters\n", @@ -121,8 +120,7 @@ }, { "cell_type": "code", - "execution_count": 2, - "id": "a3e6f5a5", + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -157,7 +155,6 @@ { "attachments": {}, "cell_type": "markdown", - "id": "90289287", "metadata": {}, "source": [ "### Transforming a GNN into a Dense NN\n", @@ -190,8 +187,7 @@ }, { "cell_type": "code", - "execution_count": 3, - "id": "e4d5fa7f", + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -273,7 +269,6 @@ { "attachments": {}, "cell_type": "markdown", - "id": "8554dd1e", "metadata": {}, "source": [ "### Build a MIP Formulation and Solve the Optimization Problem\n", @@ -283,8 +278,7 @@ }, { "cell_type": "code", - "execution_count": 4, - "id": "2afb1bc9", + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -310,7 +304,6 @@ { "attachments": {}, "cell_type": "markdown", - "id": "4dee6a2c", "metadata": {}, "source": [ "As a sanity check before creating the optimization model, we can print the properties of the neural network layers from `network_definition`. This allows us to check input/output sizes, as well as activation functions." @@ -318,8 +311,7 @@ }, { "cell_type": "code", - "execution_count": 5, - "id": "35b6a53b", + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -341,7 +333,6 @@ { "attachments": {}, "cell_type": "markdown", - "id": "dbf59025", "metadata": {}, "source": [ "Finally, we can load `network_definition` as a full-space `ReluBigMFormulation` object." @@ -349,8 +340,7 @@ }, { "cell_type": "code", - "execution_count": 6, - "id": "14b82060", + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ @@ -360,7 +350,6 @@ { "attachments": {}, "cell_type": "markdown", - "id": "8d2c17a6", "metadata": {}, "source": [ "We now encode the Dense NN in a Pyomo model from the `ReluBigMFormulation` object." @@ -368,8 +357,7 @@ }, { "cell_type": "code", - "execution_count": 7, - "id": "30a42a58", + "execution_count": 18, "metadata": {}, "outputs": [], "source": [ @@ -384,7 +372,6 @@ { "attachments": {}, "cell_type": "markdown", - "id": "b2dde6f5", "metadata": {}, "source": [ "Next, we define the objective function as the single output of the Dense NN and solve the minimization problem using a mixed integer solver." @@ -392,8 +379,7 @@ }, { "cell_type": "code", - "execution_count": 8, - "id": "0c0e1dd4", + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -404,7 +390,7 @@ "Version: 2.10.5 \n", "Build Date: Dec 8 2020 \n", "\n", - "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT/bin/cbc -printingOptions all -import /var/tmp/pbs.7715724.pbs/tmp9gxn1x7c.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.7715724.pbs/tmp9gxn1x7c.pyomo.soln (default strategy 1)\n", + "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT/bin/cbc -printingOptions all -import /var/tmp/pbs.7796016.pbs/tmpazbklmrp.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.7796016.pbs/tmpazbklmrp.pyomo.soln (default strategy 1)\n", "Option for printingOptions changed from normal to all\n", "Presolve 1 (-39) rows, 7 (-39) columns and 7 (-114) elements\n", "Statistics for presolved model\n", @@ -435,10 +421,10 @@ { "data": { "text/plain": [ - "{'Problem': [{'Name': 'unknown', 'Lower bound': -1.719054146, 'Upper bound': -1.719054146, 'Number of objectives': 1, 'Number of constraints': 40, 'Number of variables': 46, 'Number of nonzeros': 7, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'User time': -1.0, 'System time': 0.0, 'Wallclock time': 0.0, 'Termination condition': 'optimal', 'Termination message': 'Model was solved to optimality (subject to tolerances), and an optimal solution is available.', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': None, 'Number of created subproblems': None}, 'Black box': {'Number of iterations': 1}}, 'Error rc': 0, 'Time': 0.1509706974029541}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}" + "{'Problem': [{'Name': 'unknown', 'Lower bound': -1.719054146, 'Upper bound': -1.719054146, 'Number of objectives': 1, 'Number of constraints': 40, 'Number of variables': 46, 'Number of nonzeros': 7, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'User time': -1.0, 'System time': 0.0, 'Wallclock time': 0.0, 'Termination condition': 'optimal', 'Termination message': 'Model was solved to optimality (subject to tolerances), and an optimal solution is available.', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': None, 'Number of created subproblems': None}, 'Black box': {'Number of iterations': 1}}, 'Error rc': 0, 'Time': 0.033590078353881836}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}" ] }, - "execution_count": 8, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -451,30 +437,22 @@ { "attachments": {}, "cell_type": "markdown", - "id": "5a3d2108", "metadata": {}, "source": [ "## Formulating Trained GNNs with OMLT: Non-fixed Graph Structure\n", "\n", "When the input graph structure is not fixed, elements in the adjacency matrix $A$ are decision variables. In this case, $\\mathcal N(v)$ is not given anymore. Additionally, $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ may contain the graph information, which makes them be variables.\n", "\n", - "Assume that $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ are fixed. Then we have two formulations to handle $A$.\n", - "\n", - "\n", - "### Bilinear Formulation\n", + "Assume that $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ are fixed. Then we can derive a big-M formulation to handle GNN layers with non-fixed graph structure.\n", "\n", - "This formulation comes from the observation that the existence of edge $u\\to v$ determines the contribution link from $\\mathbf{x}_u^{(l-1)}$ to $\\mathbf{x}_v^{(l)}$. Adding binary variables $A_{u,v}$ for all $u,v\\in V$, we can formulate GNNs in a bilinear way:\n", + "Observe that the existence of edge $u\\to v$ determines the contribution link from $\\mathbf{x}_u^{(l-1)}$ to $\\mathbf{x}_v^{(l)}$. Adding binary variables $A_{u,v}$ for all $u,v\\in V$, we can formulate GNNs in a bilinear way:\n", "\\begin{equation*}\n", " \\begin{aligned}\n", " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}A_{u,v}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", " \\end{aligned}\n", "\\end{equation*}\n", "\n", - "**NOTE:** The bilinear formulation involves quadratic constraints and therefore needs a working MINLP solver such as Gurobi. We do not use bilinear formulation in this notebook since 1) a license is required to use Gurobi, and 2) the big-M formulation usually outperforms bilinear formulation based on our tests.\n", - "\n", - "### Big-M Formulation\n", - "\n", - "Instead of using binary variables to directly control the existence of contributions between nodes, the second formulation introduces auxiliary variables $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ to represent the contribution from node $u$ to node $v$ in $l$th layer:\n", + "This bilinear formulation involves quadratic constraints. Instead of using binary variables to directly control the existence of contributions between nodes, we introduce auxiliary variables $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ to represent the contribution from node $u$ to node $v$ in $l$th layer:\n", "\\begin{equation*}\n", " \\begin{aligned}\n", " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{\\bar x}_{u\\to v}^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", @@ -520,21 +498,9 @@ }, { "cell_type": "code", - "execution_count": 9, - "id": "45a6c2b3", + "execution_count": 20, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0\tInputLayer(input_size=[6], output_size=[6])\tlinear\n", - "1\tDenseLayer(input_size=[6], output_size=[9])\tlinear\n", - "2\tDenseLayer(input_size=[9], output_size=[3])\tlinear\n", - "3\tDenseLayer(input_size=[3], output_size=[1])\tlinear\n" - ] - } - ], + "outputs": [], "source": [ "# graph structure\n", "# number of nodes\n", @@ -605,12 +571,43 @@ " #write ONNX model and its bounds using OMLT\n", " write_onnx_model_with_bounds(f.name, None, input_bounds)\n", " #load the network definition from the ONNX model\n", - " network_definition = load_onnx_neural_network_with_bounds(f.name)\n", + " network_definition = load_onnx_neural_network_with_bounds(f.name)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Build a MIP Formulation and Solve the Optimization Problem\n", + "\n", + "Note that all types of layers are represented as dense layers in OMLT now. Using `gnn_layer_definition` to retrieve GNN layers. The number of nodes `N` and the list of indexes for GNN layers `gnn_layers` should be provided here." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\tInputLayer(input_size=[6], output_size=[6])\tlinear\n", + "1\tGNNLayer(input_size=[6], output_size=[9])\tlinear\n", + "2\tDenseLayer(input_size=[9], output_size=[3])\tlinear\n", + "3\tDenseLayer(input_size=[3], output_size=[1])\tlinear\n" + ] + } + ], + "source": [ + "# replace dense layers with GNN layers\n", + "gnn_net = gnn_layer_definition(network_definition, N=N, gnn_layers=[1])\n", " \n", - "for layer_id, layer in enumerate(network_definition.layers):\n", + "for layer_id, layer in enumerate(gnn_net.layers):\n", " print(f\"{layer_id}\\t{layer}\\t{layer.activation}\")\n", " \n", - "formulation = ReluBigMFormulation(network_definition)" + "formulation = ReluBigMFormulation(gnn_net)" ] }, { @@ -618,21 +615,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Build a MIP Formulation and Solve the Optimization Problem\n", - "\n", - "Note that all types of layers are represented as dense layers in OMLT now. To identify a GNN layer, before building formulation, we need to add the following information:\n", + "Before building formulation for GNN layers, one needs to define binary variables for adjacency matrix $A$, which is required when using `build_formulation` to encode GNN layers. \n", "\n", - "- `m.nn.N`: number of nodes in the graph.\n", - "- `m.nn.A`: adjacency matrix consists of $(m.nn.N)^2$ binary variables.\n", - "- `m.nn.gnn_layers`: a list consists of the indexes for GNN layers (begins with $1$).\n", - "- `m.nn.gnn_formulation`: type of formulation for GNN layers. Two options are supported (`\"bilinear\"`, `\"bigM\"`). `\"bigM\"` is recommended.\n", - "\n", - "**NOTE:** One can fix different elements in $A$ based on different problems. For example, fix most elements in $A$ and only optimize over a subset of edges. The extrame case is that fixing all elements, which is equivalent to the case with fixed graph structure." + "Here we set the diagonal elements of $A$ be $1$ to guarantee the self contribution of each node. However, one can fix different elements in $A$ based on different problems. For example, fix most elements in $A$ and only optimize over a subset of edges. The extrame case is that fixing all elements, which is equivalent to the case with fixed graph structure." ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -643,7 +633,7 @@ "Version: 2.10.5 \n", "Build Date: Dec 8 2020 \n", "\n", - "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT/bin/cbc -printingOptions all -import /var/tmp/pbs.7715724.pbs/tmpuh1uwdgm.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.7715724.pbs/tmpuh1uwdgm.pyomo.soln (default strategy 1)\n", + "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT/bin/cbc -printingOptions all -import /var/tmp/pbs.7796016.pbs/tmp4_rnxuex.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.7796016.pbs/tmp4_rnxuex.pyomo.soln (default strategy 1)\n", "Option for printingOptions changed from normal to all\n", "Presolve 63 (-49) rows, 33 (-37) columns and 185 (-104) elements\n", "Statistics for presolved model\n", @@ -722,10 +712,10 @@ { "data": { "text/plain": [ - "{'Problem': [{'Name': 'unknown', 'Lower bound': -2.55499393, 'Upper bound': -2.55499393, 'Number of objectives': 1, 'Number of constraints': 63, 'Number of variables': 33, 'Number of binary variables': 6, 'Number of integer variables': 6, 'Number of nonzeros': 17, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'User time': -1.0, 'System time': 0.0, 'Wallclock time': 0.0, 'Termination condition': 'optimal', 'Termination message': 'Model was solved to optimality (subject to tolerances), and an optimal solution is available.', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': 0, 'Number of created subproblems': 0}, 'Black box': {'Number of iterations': 0}}, 'Error rc': 0, 'Time': 0.03762245178222656}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}" + "{'Problem': [{'Name': 'unknown', 'Lower bound': -2.55499393, 'Upper bound': -2.55499393, 'Number of objectives': 1, 'Number of constraints': 63, 'Number of variables': 33, 'Number of binary variables': 6, 'Number of integer variables': 6, 'Number of nonzeros': 17, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'User time': -1.0, 'System time': 0.0, 'Wallclock time': 0.0, 'Termination condition': 'optimal', 'Termination message': 'Model was solved to optimality (subject to tolerances), and an optimal solution is available.', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': 0, 'Number of created subproblems': 0}, 'Black box': {'Number of iterations': 0}}, 'Error rc': 0, 'Time': 0.03782343864440918}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}" ] }, - "execution_count": 10, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -738,21 +728,41 @@ "m.nn = OmltBlock()\n", "\n", "# initialize graph information\n", - "m.nn.N = N\n", - "m.nn.A = pyo.Var(pyo.Set(initialize=range(m.nn.N)), pyo.Set(initialize=range(m.nn.N)), within=pyo.Binary)\n", + "m.nn.A = pyo.Var(\n", + " pyo.Set(initialize=range(N)), pyo.Set(initialize=range(N)), within=pyo.Binary\n", + ")\n", "# usually, the contribution from node v to itself exists\n", "for i in range(N):\n", - " m.nn.A[i,i].fix(1)\n", - "\n", - "# specify the indexes for GNN layers and the formulation\n", - "m.nn.gnn_layers = [1]\n", - "m.nn.gnn_formulation = 'bigM'\n", + " m.nn.A[i, i].fix(1)\n", "\n", "m.nn.build_formulation(formulation)\n", "\n", "m.obj = pyo.Objective(expr=(m.nn.outputs[0]))\n", - "pyo.SolverFactory('cbc').solve(m, tee=True)" + "pyo.SolverFactory(\"cbc\").solve(m, tee=True)" ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion\n", + "\n", + "For cases with fixed graph structure, one needs to transform the trained GNN into a Dense NN before using OMLT. After the transformation step, optimizing over a trained GNN is equivalent to optimizing over the corresponding Dense NN. No extra action is needed when using OMLT to encode the Dense NN.\n", + "\n", + "For cases with non-fixed graph structure, the following actions are required:\n", + "\n", + "- providing all $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ in transformation step since any of them could be used.\n", + "- using `gnn_layer_definition` to retrieve GNN layers after loading ONNX model. The number of nodes in graph `N` and the list of indexes for GNN layers `gnn_layers` should be provided here.\n", + "- defining binary variables for adjacency matrix $A$ before using `build_formulation` since these variables are used to formulate GNN layers." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/src/omlt/neuralnet/layer.py b/src/omlt/neuralnet/layer.py index f226336f..b852fc3e 100644 --- a/src/omlt/neuralnet/layer.py +++ b/src/omlt/neuralnet/layer.py @@ -205,6 +205,95 @@ def _eval(self, x): return y +class GNNLayer(DenseLayer): + """ + GNN layer implementing `output = activation(dot(input, weights, edge) + biases)`. + + Parameters + ---------- + input_size : tuple + the size of the input. + output_size : tuple + the size of the output. + weight : matrix-like + the weight matrix. + biases : array-like + the biases. + N : int + number of nodes in the graph + activation : str or None + activation function name + input_index_mapper : IndexMapper or None + map indexes from this layer index to the input layer index size + """ + + def __init__( + self, + input_size, + output_size, + weights, + biases, + N, + *, + activation=None, + input_index_mapper=None, + ): + super().__init__( + input_size, + output_size, + weights=weights, + biases=biases, + activation=activation, + input_index_mapper=input_index_mapper, + ) + assert input_size[-1] % N == 0 + assert output_size[-1] % N == 0 + self.__N = N + self.__gnn_input_size = input_size[-1] // N + self.__gnn_output_size = output_size[-1] // N + + @property + def N(self): + """Return the number of nodes in the graphs""" + return self.__N + + @property + def gnn_input_size(self): + """Return the size of the input tensor in original GNN""" + return self.__gnn_input_size + + @property + def gnn_output_size(self): + """Return the size of the output tensor in original GNN""" + return self.__gnn_output_size + + def __str__(self): + return f"GNNLayer(input_size={self.input_size}, output_size={self.output_size})" + + def _eval_with_adjacency(self, x, A): + x_reshaped = ( + np.reshape(x, self.input_index_mapper.output_size) + if self.input_index_mapper is not None + else x[:] + ) + assert x_reshaped.shape == tuple(self.input_size) + y = np.zeros(shape=self.output_size) + for output_index in self.output_indexes: + for input_index in self.input_indexes: + if input_index[:-1] == output_index[:-1]: + y[output_index] += ( + x_reshaped[input_index] + * self.weights[input_index[-1], output_index[-1]] + * A[ + input_index[-1] // self.gnn_input_size, + output_index[-1] // self.gnn_output_size, + ] + ) + y[output_index] += self.biases[output_index[-1]] + + return y + + class Layer2D(Layer): """ Abstract two-dimensional layer that downsamples values in a kernel to a single value. @@ -471,7 +560,7 @@ def __str__(self): def _eval_at_index(self, x, out_d, out_r, out_c): acc = 0.0 - for (k, index) in self.kernel_with_input_indexes(out_d, out_r, out_c): + for k, index in self.kernel_with_input_indexes(out_d, out_r, out_c): acc += k * x[index] return acc diff --git a/src/omlt/neuralnet/layers/__init__.py b/src/omlt/neuralnet/layers/__init__.py index d98d22dc..776ab8ec 100644 --- a/src/omlt/neuralnet/layers/__init__.py +++ b/src/omlt/neuralnet/layers/__init__.py @@ -1,2 +1,6 @@ -from .full_space import full_space_conv2d_layer, full_space_dense_layer, full_space_gnn_layer_bilinear, full_space_gnn_layer_bigm +from .full_space import ( + full_space_conv2d_layer, + full_space_dense_layer, + full_space_gnn_layer, +) from .reduced_space import reduced_space_dense_layer diff --git a/src/omlt/neuralnet/layers/full_space.py b/src/omlt/neuralnet/layers/full_space.py index ed8a445f..9c13fb44 100644 --- a/src/omlt/neuralnet/layers/full_space.py +++ b/src/omlt/neuralnet/layers/full_space.py @@ -39,57 +39,7 @@ def dense_layer(b, *output_index): return layer_block.zhat[output_index] == expr -def full_space_gnn_layer_bilinear(net_block, net, layer_block, layer): - r""" - Add full-space formulation of the gnn layer to the block - - .. math:: - - \begin{align*} - & \hat z_i = \sum_{j{=}1}^{M_i} A_{v_i,v_j} w_{ij} z_j + b_i && \forall i \in N \\ - & A_{v_i,v_j}\in\{0,1\} - \end{align*} - - where :math:`v_i` is the graph indexing of the i-th node. - - """ - - input_layer, input_layer_block = _input_layer_and_block(net_block, net, layer) - - input_channel = layer.input_size[0] // net_block.N - output_channel = layer.output_size[0] // net_block.N - - @layer_block.Constraint(layer.output_indexes) - def gnn_layer_bilinear_formulation(b, *output_index): - # dense layers multiply only the last dimension of - # their inputs - expr = 0.0 - for local_index, input_index in layer.input_indexes_with_input_layer_indexes: - w = layer.weights[input_index[-1], output_index[-1]] - - input_node_index = input_index[-1] // input_channel - output_node_index = output_index[-1] // output_channel - - expr += ( - input_layer_block.z[input_index] - * w - * net_block.A[input_node_index, output_node_index] - ) - # move this at the end to avoid numpy/pyomo var bug - output_node_index = output_index[-1] // output_channel - expr += layer.biases[output_index[-1]] - - lb, ub = compute_bounds_on_expr(expr) - layer_block.zhat[output_index].setlb(lb) - layer_block.zhat[output_index].setub(ub) - - return layer_block.zhat[output_index] == expr - - -from omlt.neuralnet.layer import InputLayer - - -def full_space_gnn_layer_bigm(net_block, net, layer_block, layer): +def full_space_gnn_layer(net_block, net, layer_block, layer): r""" Add full-space formulation of the gnn layer to the block @@ -100,6 +50,8 @@ def full_space_gnn_layer_bigm(net_block, net, layer_block, layer): \bar z_{ij} &= A_{v_i,v_j} z_{j} \end{align*} + where :math:`A_{v_i,v_j}` is the binary variable controlling the edge between node :math:`v_i` and :math:`v_j`. + The big-M formulation for :math:`\bar z_{ij}` is given by: .. math:: @@ -114,105 +66,100 @@ def full_space_gnn_layer_bigm(net_block, net, layer_block, layer): """ input_layer, input_layer_block = _input_layer_and_block(net_block, net, layer) - input_channel = layer.input_size[0] // net_block.N - output_channel = layer.output_size[0] // net_block.N input_layer_block.zbar = pyo.Var( - pyo.Set(initialize=range(layer.input_size[0])), - pyo.Set(initialize=range(net_block.N)), + pyo.Set(initialize=layer.input_indexes), + pyo.Set(initialize=range(layer.N)), initialize=0, ) - input_layer_block._zbar_lower_bound_z_big_m = pyo.Constraint( - pyo.Set(initialize=range(layer.input_size[0] * net_block.N)) + pyo.Set(initialize=layer.input_indexes), + pyo.Set(initialize=range(layer.N)), ) input_layer_block._zbar_upper_bound_z_big_m = pyo.Constraint( - pyo.Set(initialize=range(layer.input_size[0] * net_block.N)) + pyo.Set(initialize=layer.input_indexes), + pyo.Set(initialize=range(layer.N)), ) input_layer_block._zbar_lower_bound_big_m = pyo.Constraint( - pyo.Set(initialize=range(layer.input_size[0] * net_block.N)) + pyo.Set(initialize=layer.input_indexes), + pyo.Set(initialize=range(layer.N)), ) input_layer_block._zbar_upper_bound_big_m = pyo.Constraint( - pyo.Set(initialize=range(layer.input_size[0] * net_block.N)) + pyo.Set(initialize=layer.input_indexes), + pyo.Set(initialize=range(layer.N)), ) - # set dummy parameters here to avoid warning message from Pyomo input_layer_block._abs_bound_big_m = pyo.Param( - input_layer.output_indexes, default=1e6, mutable=True + layer.input_indexes, default=1e6, mutable=True ) - for input_index in layer.input_indexes: + for local_index, input_index in layer.input_indexes_with_input_layer_indexes: lb, ub = input_layer_block.z[input_index].bounds - input_layer_block._abs_bound_big_m[input_index] = max(abs(lb), abs(ub)) + input_layer_block._abs_bound_big_m[local_index] = max(abs(lb), abs(ub)) - for output_node_index in range(net_block.N): - input_layer_block.zbar[input_index, output_node_index].setlb(min(0, lb)) - input_layer_block.zbar[input_index, output_node_index].setub(max(0, ub)) + input_node_index = local_index[-1] // layer.gnn_input_size - input_node_index = input_index[-1] // input_channel + for output_node_index in range(layer.N): + input_layer_block.zbar[local_index, output_node_index].setlb(min(0, lb)) + input_layer_block.zbar[local_index, output_node_index].setub(max(0, ub)) - constraint_index = input_index[-1] * net_block.N + output_node_index input_layer_block._zbar_lower_bound_z_big_m[ - constraint_index + local_index, output_node_index ] = input_layer_block.zbar[ - input_index, output_node_index + local_index, output_node_index ] >= input_layer_block.z[ input_index ] - input_layer_block._abs_bound_big_m[ - input_index + local_index ] * ( 1.0 - net_block.A[input_node_index, output_node_index] ) input_layer_block._zbar_upper_bound_z_big_m[ - constraint_index + local_index, output_node_index ] = input_layer_block.zbar[ - input_index, output_node_index + local_index, output_node_index ] <= input_layer_block.z[ input_index ] + input_layer_block._abs_bound_big_m[ - input_index + local_index ] * ( 1.0 - net_block.A[input_node_index, output_node_index] ) - input_layer_block._zbar_lower_bound_big_m[constraint_index] = ( - input_layer_block.zbar[input_index, output_node_index] - >= -input_layer_block._abs_bound_big_m[input_index] + input_layer_block._zbar_lower_bound_big_m[ + local_index, output_node_index + ] = ( + input_layer_block.zbar[local_index, output_node_index] + >= -input_layer_block._abs_bound_big_m[local_index] * net_block.A[input_node_index, output_node_index] ) - input_layer_block._zbar_upper_bound_big_m[constraint_index] = ( - input_layer_block.zbar[input_index, output_node_index] - <= input_layer_block._abs_bound_big_m[input_index] + input_layer_block._zbar_upper_bound_big_m[ + local_index, output_node_index + ] = ( + input_layer_block.zbar[local_index, output_node_index] + <= input_layer_block._abs_bound_big_m[local_index] * net_block.A[input_node_index, output_node_index] ) - # input_layer_block._zbar_lower_bound_z_big_m.pprint() - # input_layer_block._zbar_upper_bound_z_big_m.pprint() - # input_layer_block._zbar_lower_bound_big_m.pprint() - # input_layer_block._zbar_upper_bound_big_m.pprint() - @layer_block.Constraint(layer.output_indexes) - def dense_layer(b, *output_index): - # dense layers multiply only the last dimension of + def gnn_layer(b, *output_index): + # gnn layers multiply only the last dimension of # their inputs expr = 0.0 - for local_index, input_index in layer.input_indexes_with_input_layer_indexes: - w = layer.weights[input_index[-1], output_index[-1]] - - input_node_index = input_index[-1] // input_channel - output_node_index = output_index[-1] // output_channel - - expr += input_layer_block.zbar[input_index, output_node_index] * w + for local_index in layer.input_indexes: + w = layer.weights[local_index[-1], output_index[-1]] + output_node_index = output_index[-1] // layer.gnn_output_size + expr += input_layer_block.zbar[local_index, output_node_index] * w # move this at the end to avoid numpy/pyomo var bug - output_node_index = output_index[-1] // output_channel + output_node_index = output_index[-1] // layer.gnn_output_size expr += layer.biases[output_index[-1]] lb, ub = compute_bounds_on_expr(expr) layer_block.zhat[output_index].setlb(lb) layer_block.zhat[output_index].setub(ub) - # print(layer_block.zhat[output_index] == expr) + return layer_block.zhat[output_index] == expr diff --git a/src/omlt/neuralnet/network_definition.py b/src/omlt/neuralnet/network_definition.py index 1e84d427..9acc82fe 100644 --- a/src/omlt/neuralnet/network_definition.py +++ b/src/omlt/neuralnet/network_definition.py @@ -1,6 +1,6 @@ import networkx as nx -from omlt.neuralnet.layer import Layer +from omlt.neuralnet.layer import Layer, DenseLayer, GNNLayer class NetworkDefinition: @@ -32,7 +32,6 @@ def __init__( # Process input bounds to insure scaled input bounds exist for formulations if scaled_input_bounds is None: - if unscaled_input_bounds is not None and scaling_object is not None: lbs = scaling_object.get_scaled_input_expressions( {k: t[0] for k, t in unscaled_input_bounds.items()} @@ -147,3 +146,57 @@ def successors(self, layer): def __str__(self): return f"NetworkDefinition(num_layers={len(self.__layers_by_id)})" + + +def gnn_layer_definition(net, N, gnn_layers): + """ + Replace dense layers in a NetworkDefinition class with GNN layers + + Parameters + ---------- + net : NetworkDefinition + the neural network definition + N : int + the number of nodes in the graph structure + gnn_layers : list + the list of indexes for GNN layers + """ + assert isinstance(N, int) + assert N > 0 + assert isinstance(gnn_layers, list) + + # copy unchanged properties from net + gnn_net = NetworkDefinition( + scaling_object=net.scaling_object, + scaled_input_bounds=net.scaled_input_bounds, + unscaled_input_bounds=net.unscaled_input_bounds, + ) + + # map the indexes of layers in net to the indexes of layers in gnn_net + layer_id_mapper = {} + + for layer_id, layer in enumerate(net.layers): + # these layers are not GNN layers and do not need to be changed + if layer_id not in gnn_layers: + new_layer = layer + else: + # only dense layers could be replaced with GNN layers + assert isinstance(layer, DenseLayer) + # define the corresponding GNN layer + new_layer = GNNLayer( + input_size=layer.input_size, + output_size=layer.output_size, + weights=layer.weights, + biases=layer.biases, + N=N, + activation=layer.activation, + input_index_mapper=layer.input_index_mapper, + ) + # add new_layer to gnn_net + gnn_net.add_layer(new_layer) + # map layer (in net) to new_layer (in gnn_net) + layer_id_mapper[id(layer)] = id(new_layer) + # add edges between new_layer and its predecessors, which could be retrieved from the predecessors of layer + for layer_input in net.predecessors(layer): + gnn_net.add_edge(gnn_net.layer(layer_id_mapper[id(layer_input)]), new_layer) + return gnn_net diff --git a/src/omlt/neuralnet/nn_formulation.py b/src/omlt/neuralnet/nn_formulation.py index f3a0578d..89bb3fc3 100644 --- a/src/omlt/neuralnet/nn_formulation.py +++ b/src/omlt/neuralnet/nn_formulation.py @@ -17,13 +17,18 @@ tanh_activation_constraint, tanh_activation_function, ) -from omlt.neuralnet.layer import ConvLayer2D, DenseLayer, InputLayer, PoolingLayer2D +from omlt.neuralnet.layer import ( + ConvLayer2D, + DenseLayer, + InputLayer, + PoolingLayer2D, + GNNLayer, +) from omlt.neuralnet.layers.full_space import ( full_space_conv2d_layer, full_space_dense_layer, full_space_maxpool2d_layer, - full_space_gnn_layer_bilinear, - full_space_gnn_layer_bigm, + full_space_gnn_layer, ) from omlt.neuralnet.layers.partition_based import ( default_partition_split_func, @@ -41,6 +46,7 @@ def _ignore_input_layer(): DenseLayer: full_space_dense_layer, ConvLayer2D: full_space_conv2d_layer, PoolingLayer2D: full_space_maxpool2d_layer, + GNNLayer: full_space_gnn_layer, } _DEFAULT_ACTIVATION_CONSTRAINTS = { @@ -174,23 +180,13 @@ def layer(b, layer_id): return b - for layer_index, layer in enumerate(layers): + for layer in layers: if isinstance(layer, InputLayer): continue layer_id = id(layer) layer_block = block.layer[layer_id] layer_constraints_func = layer_constraints.get(type(layer), None) - - if "gnn_layers" in dir( - block - ): # if the block has GNN layers, then apply one of these two formulations - if layer_index in block.gnn_layers: - if block.gnn_formulation == "bilinear": - layer_constraints_func = full_space_gnn_layer_bilinear - elif block.gnn_formulation == "bigM": - layer_constraints_func = full_space_gnn_layer_bigm - if layer_constraints_func is None: raise ValueError( "Layer type {} is not supported by this formulation.".format( diff --git a/tests/neuralnet/test_layer.py b/tests/neuralnet/test_layer.py index 7cb966c0..f58b8ba3 100644 --- a/tests/neuralnet/test_layer.py +++ b/tests/neuralnet/test_layer.py @@ -7,6 +7,7 @@ IndexMapper, InputLayer, PoolingLayer2D, + GNNLayer, ) @@ -94,3 +95,40 @@ def test_maxpool_layer(): layer = PoolingLayer2D([1, 4, 4], [1, 2, 2], [2, 2], "max", [3, 3], 1) y = layer.eval_single_layer(x) assert np.array_equal(y, [[[11, 12], [15, 16]]]) + + +def test_gnn_layer_with_input_index_mapper(): + weights = np.array( + [ + [1, 0, 1, 1, -1, 1, 1, -1, 1], + [0, 1, 1, -1, 1, 1, -1, 1, 1], + [1, -1, 1, 1, 0, 1, 1, -1, 1], + [-1, 1, 1, 0, 1, 1, -1, 1, 1], + [1, -1, 1, 1, -1, 1, 1, 0, 1], + [-1, 1, 1, -1, 1, 1, 0, 1, 1], + ] + ) + + biases = np.array([-1, 0, 1, -1, 0, 1, -1, 0, 1]) + + # input has size [6], but the previous node output is [3, 2] + # use mapper to map between the two + t = IndexMapper([1, 2, 2, 3], [1, 2, 6]) + layer = GNNLayer([1, 2, 6], [1, 2, 9], weights, biases, N=3, input_index_mapper=t) + + inputs = np.array([[[[-3, 2, -1], [1, -2, 3]], [[0, 0, 0], [0, 0, 0]]]]) + + A1 = np.ones([3, 3], dtype=int) + y1 = np.array( + [[[-11, 9, 1, -12, 11, 1, -10, 10, 1], [-1, 0, 1, -1, 0, 1, -1, 0, 1]]] + ) + assert np.array_equal(layer._eval_with_adjacency(inputs, A1), y1) + assert np.array_equal(layer.eval_single_layer(inputs), y1) + + A2 = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) + y2 = np.array([[[-4, 2, 0, -2, 1, 1, -3, 3, 2], [-1, 0, 1, -1, 0, 1, -1, 0, 1]]]) + assert np.array_equal(layer._eval_with_adjacency(inputs, A2), y2) + + A3 = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]]) + y3 = np.array([[[-6, 4, 0, -12, 11, 1, -5, 5, 2], [-1, 0, 1, -1, 0, 1, -1, 0, 1]]]) + assert np.array_equal(layer._eval_with_adjacency(inputs, A3), y3) diff --git a/tests/neuralnet/test_nn_formulation.py b/tests/neuralnet/test_nn_formulation.py index 346fc659..8012baf1 100644 --- a/tests/neuralnet/test_nn_formulation.py +++ b/tests/neuralnet/test_nn_formulation.py @@ -18,6 +18,8 @@ PoolingLayer2D, ) +from omlt.neuralnet.network_definition import gnn_layer_definition + def two_node_network(activation, input_value): """ @@ -327,6 +329,22 @@ def test_maxpool_FullSpaceNNFormulation(): assert abs(pyo.value(m.neural_net_block.outputs[0, 0, 0]) - y[0, 0, 0]) < 1e-6 +def examples_of_graphs(graph_type): + # complete graph + if graph_type == "complete": + A = np.ones([3, 3], dtype=int) + y = np.array([-11, 9, 1, -12, 11, 1, -10, 10, 1]) + # edgeless graph + elif graph_type == "edgeless": + A = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) + y = np.array([-4, 2, 0, -2, 1, 1, -3, 3, 2]) + # line graph, i.e., 0-1-2 + elif graph_type == "line": + A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]]) + y = np.array([-6, 4, 0, -12, 11, 1, -5, 5, 2]) + return A, y + + def three_node_graph_neural_network(activation): input_size = [6] input_bounds = {} @@ -337,8 +355,8 @@ def three_node_graph_neural_network(activation): input_layer = InputLayer(input_size) net.add_layer(input_layer) - dense_layer_0 = DenseLayer( - input_layer.output_size, + dense_layer = DenseLayer( + [6], [9], activation=activation, weights=np.array( @@ -353,59 +371,39 @@ def three_node_graph_neural_network(activation): ), biases=np.array([-1, 0, 1, -1, 0, 1, -1, 0, 1]), ) - net.add_layer(dense_layer_0) - net.add_edge(input_layer, dense_layer_0) + net.add_layer(dense_layer) + net.add_edge(input_layer, dense_layer) - return net + gnn_net = gnn_layer_definition(net, N=3, gnn_layers=[1]) - -def examples_of_graphs(graph_type): - # complete graph - if graph_type == "complete": - A = np.ones([3, 3], dtype=int) - y = np.array([-11, 9, 1, -12, 11, 1, -10, 10, 1]) - # edgeless graph - elif graph_type == "edgeless": - A = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) - y = np.array([-4, 2, 0, -2, 1, 1, -3, 3, 2]) - # line graph, i.e., 0-1-2 - elif graph_type == "line": - A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]]) - y = np.array([-6, 4, 0, -12, 11, 1, -5, 5, 2]) - return A, y + return gnn_net -def _test_three_node_graph_neural_network(gnn_formulation, graph_type): +def _test_three_node_graph_neural_network(graph_type): m = pyo.ConcreteModel() m.nn = OmltBlock() - inputs = np.array([-3, 2, -1, 1, -2, 3]) - net = three_node_graph_neural_network("linear") + gnn_net = three_node_graph_neural_network("linear") - m.nn.N = 3 + N = 3 m.nn.A = pyo.Var( - pyo.Set(initialize=range(m.nn.N)), - pyo.Set(initialize=range(m.nn.N)), + pyo.Set(initialize=range(N)), + pyo.Set(initialize=range(N)), within=pyo.Binary, ) - m.nn.gnn_layers = [1] - m.nn.gnn_formulation = gnn_formulation - - m.nn.build_formulation(FullSpaceNNFormulation(net)) + m.nn.build_formulation(FullSpaceNNFormulation(gnn_net)) + inputs = np.array([-3, 2, -1, 1, -2, 3]) A, y = examples_of_graphs(graph_type) - for i in range(m.nn.N): - for j in range(m.nn.N): + for i in range(N): + for j in range(N): m.nn.A[i, j].fix(A[i, j]) for i in range(6): m.nn.inputs[i].fix(inputs[i]) - if gnn_formulation == "bilinear": - assert m.nvariables() == 63 - assert m.nconstraints() == 48 - elif gnn_formulation == "bigM": - assert m.nvariables() == 81 - assert m.nconstraints() == 120 + assert m.nvariables() == 81 + assert m.nconstraints() == 120 + m.obj = pyo.Objective(expr=0) status = pyo.SolverFactory("cbc").solve(m, tee=False) @@ -413,21 +411,18 @@ def _test_three_node_graph_neural_network(gnn_formulation, graph_type): for i in range(9): assert abs(pyo.value(m.nn.outputs[i]) - y[i]) < 1e-6 - if gnn_formulation == "bigM": - for i in range(6): - for j in range(3): - assert ( - abs( - pyo.value(m.nn.layer[m.nn.layers.at(1)].zbar[i, j]) - - pyo.value(m.nn.A[i // 2, j]) * inputs[i] - ) - < 1e-6 + for i in range(6): + for j in range(3): + assert ( + abs( + pyo.value(m.nn.layer[m.nn.layers.at(1)].zbar[i, j]) + - pyo.value(m.nn.A[i // 2, j]) * inputs[i] ) + < 1e-6 + ) def test_three_node_graph_neural_network(): - gnn_formulations = ["bilinear", "bigM"] graph_types = ["complete", "edgeless", "line"] - for gnn_formulation in gnn_formulations: - for graph_type in graph_types: - _test_three_node_graph_neural_network(gnn_formulation, graph_type) + for graph_type in graph_types: + _test_three_node_graph_neural_network(graph_type) From 78207c1fb2b60a29419f6f07192425220b0bb161 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Mon, 14 Aug 2023 14:52:22 +0100 Subject: [PATCH 04/27] add torch_geometric_reader --- .../example_graph_neural_network.ipynb | 789 ------------------ src/omlt/dependencies.py | 4 + src/omlt/io/__init__.py | 10 +- src/omlt/io/torch_geometric/__init__.py | 3 + .../torch_geometric/torch_geometric_reader.py | 278 ++++++ src/omlt/neuralnet/network_definition.py | 56 +- tests/io/test_keras_reader.py | 2 +- tests/io/test_torch_geometric_reader.py | 110 +++ tests/neuralnet/test_layer.py | 2 +- tests/neuralnet/test_nn_formulation.py | 62 +- 10 files changed, 437 insertions(+), 879 deletions(-) delete mode 100644 docs/notebooks/neuralnet/example_graph_neural_network.ipynb create mode 100644 src/omlt/io/torch_geometric/__init__.py create mode 100644 src/omlt/io/torch_geometric/torch_geometric_reader.py create mode 100644 tests/io/test_torch_geometric_reader.py diff --git a/docs/notebooks/neuralnet/example_graph_neural_network.ipynb b/docs/notebooks/neuralnet/example_graph_neural_network.ipynb deleted file mode 100644 index 2290043f..00000000 --- a/docs/notebooks/neuralnet/example_graph_neural_network.ipynb +++ /dev/null @@ -1,789 +0,0 @@ -{ - "cells": [ - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Example: Optimizing over trained graph neural networks\n", - "\n", - "This notebook gives examples where OMLT is used to optimize over trained graph neural networks (GNNs). We follow the below steps:\n", - "\n", - "1.) A general definition of GNNs is provided. For any GNN that fits our definition, it could be transformed into a Dense NN and then exported into OMLT.\n", - "\n", - "2.) We give an example to show how to transform a GNN into a Dense NN. For simplicity, we skip the training process and just use random parameters.\n", - "\n", - "3.) OMLT is used to generate a mixed-interger encoding of the trained GNN. \n", - "\n", - "4.) We consider two cases: one has fixed graph structure, another one has non-fixed graph structure. For each case, the output of the GNN is minimized.\n", - "\n", - "\n", - "## Library Setup\n", - "\n", - "This notebook assumes you have a working PyTorch environment to define a Dense NN. This Dense NN is then formulated in Pyomo using OMLT which therefore requires working Pyomo and OMLT installations.\n", - "\n", - "The required Python libraries used in this notebook are as follows:\n", - "\n", - "- `numpy`: used for transformation of parameters\n", - "\n", - "- `torch`: the machine learning language we use to define our Dense NN\n", - "\n", - "- `pyomo`: the algebraic modeling language for Python, it is used to define the optimization model passed to the solver\n", - "\n", - "- `onnx`: used to express trained neural network models\n", - "\n", - "- `omlt`: the package this notebook demonstates. OMLT can formulate machine learning (such as neural networks) within Pyomo\n", - "\n", - "**NOTE:** This notebbook alse assumes you have a working MIP solver executable to solve optimization problems in Pyomo. The open-source solver CBC is called by default. \n", - "\n", - "\n", - "## Definition of GNNs\n", - "\n", - "We define a GNN with $L$ layers as follows:\n", - "\n", - " \\begin{equation*}\n", - "\t\t\\begin{aligned}\n", - "\t\t\tGNN:\\underbrace{\\mathbb R^{d_0}\\otimes\\cdots\\otimes\\mathbb R^{d_0}}_{n \\rm{times}}\\to\\underbrace{\\mathbb R^{d_L}\\otimes\\cdots\\otimes\\mathbb R^{d_L}}_{n\\ \\rm{times}}\n", - "\t\t\\end{aligned}\n", - "\t\\end{equation*}\n", - " \n", - "where $V$ is the set of nodes of the input graph, $n=|V|$ is the number of nodes. \n", - "\n", - "Let $\\mathbf{x}_v^{(0)} \\in \\mathbb{R}^{d_0}$ be the input features for node $v$. Then, the $l$-th layer ($l=1,2,\\dots,L$) is defined by:\n", - "\t\\begin{equation*}\n", - "\t\t\\begin{aligned}\n", - "\t\t\t\\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in\\mathcal N(v)\\cup\\{v\\}}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right),~\\forall v\\in V\n", - "\t\t\\end{aligned}\n", - "\t\\end{equation*}\n", - "where $\\mathcal N(v)$ is the set of all neighbors of $v$, $\\sigma$ could be identity or any activation function.\n", - "\n", - "*Dimensionality:* $\\mathbf{x}_u^{(l-1)}\\in\\mathbb R^{d_{l-1}}, \\mathbf{x}_v^{(l)},\\mathbf{b}_v^{(l)}\\in\\mathbb R^{d_l}, \\mathbf{w}_{u\\to v}^{(l)}\\in\\mathbb R^{d_l}\\times \\mathbb R^{d_{l-1}}$.\n", - "\n", - "Stack $\\{\\mathbf{x}_v^{(l)}\\}_{v\\in V}$ as a vector $\\mathbf{X}^{(l)}\\in \\mathbb R^{nd_l}$. Rewrite previous definition as:\n", - " \\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{X}^{(l)}=\\sigma\\left(\\mathbf{W}^{(l)}\\mathbf{X}^{(l-1)}+\\mathbf{B}^{(l)}\\right)\n", - " \\end{aligned}\n", - " \\end{equation*}\n", - "where $\\mathbf{W}^{(l)}\\in\\mathbb R^{nd_[\\times nd_{l-1}}$ is a sparse matrix with nonzero sub-matrices $\\{\\mathbf{w}_{u\\to v}^{(l)}\\}_{v\\in V,u\\in\\mathcal N(v)\\cup\\{v\\}}$ and $\\mathbf{B}^{(l)}\\in\\mathbb R^{nd_l}$ is the stack of $\\{\\mathbf{b}_v^{(l)}\\}_{v\\in V}$.\n", - "\n", - "If the input graph structure is fixed, then weights ($\\mathbf{w}_{u\\to v}^{(l)}$), bias ($\\mathbf{b}_{v}^{(l)}$), and links between layers (determined by $\\mathcal N(v)$) are all fixed after the GNN is trained. In this case, the second definition is equivalent to a dense layer. It suffices to define a Dense NN with weights $\\mathbf{W}^{(l)}$ and bias $\\mathbf{B}^{(l)}$. \n", - "\n", - "\n", - "## Formulating Trained GNNs with OMLT: Fixed Graph Structure\n", - "\n", - "\n", - "### Import Requisite Packages " - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "# parameters manipulation\n", - "import numpy as np\n", - "import tempfile\n", - "\n", - "# pytorch for defining Dense NN\n", - "import torch \n", - "import torch.nn as nn\n", - "\n", - "# pyomo for optimization\n", - "import pyomo.environ as pyo\n", - "\n", - "# omlt for interfacing our neural network with pyomo\n", - "from omlt import OmltBlock\n", - "from omlt.neuralnet import ReluBigMFormulation\n", - "from omlt.neuralnet.network_definition import gnn_layer_definition\n", - "from omlt.io.onnx import write_onnx_model_with_bounds, load_onnx_neural_network_with_bounds" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Constrcut a GNN with Random Parameters\n", - "\n", - "We use a simple GNN as an example, which consists of a GraphSAGE layer, an add pooling layer, and a dense layer with single output. Let the input and output features of the GraphSAGE layer are 2 and 3, respectively. \n", - "\n", - "The GraphSAGE layer is defined by:\n", - " \\begin{equation*}\n", - " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\mathbf{w_1}^{(l)}\\mathbf{x}_v^{(l-1)}+\\mathbf{w_2}^{(l)}\\sum\\limits_{u\\in\\mathcal N(v)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}^{(l)}\\right)\n", - " \\end{equation*}\n", - "where a sum aggregation is used.\n", - "\n", - "For the fixed graph structure, assume that it is a line graph with $N=3$ nodes, i.e., the adjacency matrix $A=\\begin{pmatrix}1 & 1 & 0\\\\1 & 1 & 1\\\\ 0 & 1 & 1\\end{pmatrix}$." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "# graph structure\n", - "# number of nodes\n", - "N = 3\n", - "# adjacency matrix\n", - "A = np.array([[1,1,0],[1,1,1],[0,1,1]])\n", - "\n", - "# in/out features\n", - "in_features = 2\n", - "out_features = 3\n", - "\n", - "# architecture of GNN\n", - "# sage: in_features to out_features for each node, with ReLU as activation\n", - "# add_pool: read out, sum out_features of each node\n", - "# dense: out_features to 1\n", - "gnn_layers = ['sage', 'add_pool', 'dense']\n", - "activations = [True, False, False]\n", - "\n", - "# randomly generate GNN parameters from (-1,1)\n", - "# in practice, these paprameters should be extracted from the trained GNN\n", - "np.random.seed(123)\n", - "sage_w1 = 2.* np.random.rand(out_features, in_features) -1.\n", - "sage_w2 = 2.* np.random.rand(out_features, in_features) -1.\n", - "sage_b = 2. * np.random.rand(out_features) - 1.\n", - "\n", - "dense_w = 2.* np.random.rand(1, out_features) - 1.\n", - "dense_b = 2.* np.random.rand(1) - 1." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Transforming a GNN into a Dense NN\n", - "\n", - "The GraphSAGE layer could be rewritten as a dense layer with parameters:\n", - "\n", - " \\begin{equation*}\n", - " \\mathbf{W}=\\begin{pmatrix}\n", - " \\mathbf{w_1} & \\mathbf{w_2} & \\mathbf{0} \\\\\n", - " \\mathbf{w_2} & \\mathbf{w_1} & \\mathbf{w_2} \\\\\n", - " \\mathbf{0} & \\mathbf{w_2} & \\mathbf{w_1} \\\\\n", - " \\end{pmatrix},\n", - " \\mathbf{B}=\\begin{pmatrix}\n", - " \\mathbf{b}\\\\\\mathbf{b}\\\\\\mathbf{b}\n", - " \\end{pmatrix}\n", - " \\end{equation*}\n", - " \n", - "It is straightforward to rewritte the add pooling layer into a dense layer. See the following code for details.\n", - "\n", - "See below as a mapping between a GNN and a Dense NN with format \"layer (in_channel, out_channel)\":\n", - "\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\text{GraphSAGE(2, 3)} &\\Rightarrow \\text{dense(6, 9)}\\\\\n", - " \\text{add pooling(9, 3)} &\\Rightarrow \\text{dense(9, 3)}\\\\\n", - " \\text{dense(3, 1)} &\\Rightarrow \\text{dense(3, 1)}\n", - " \\end{aligned}\n", - "\\end{equation*}\n" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "PyTorchModel(\n", - " (layer): Sequential(\n", - " (0): Linear(\n", - " in_features=6, out_features=9, bias=True\n", - " (relu): ReLU()\n", - " )\n", - " (1): Linear(in_features=9, out_features=3, bias=True)\n", - " (2): Linear(in_features=3, out_features=1, bias=True)\n", - " )\n", - ")\n" - ] - } - ], - "source": [ - "# transform a sage layer to dense layer\n", - "# N is the number of nodes\n", - "# w1,w2,b are parameters in a sage layer\n", - "def SAGE_to_Dense(N, A, w1, w2, b):\n", - " out_channel, in_channel = w1.shape\n", - " weight = np.zeros((N*out_channel, N*in_channel))\n", - " bias = np.zeros(N*out_channel)\n", - " for u in range(N):\n", - " for v in range(N):\n", - " if u == v:\n", - " weight[u*out_channel:(u+1)*out_channel, v*in_channel:(v+1)*in_channel] = w2\n", - " else:\n", - " weight[u*out_channel:(u+1)*out_channel, v*in_channel:(v+1)*in_channel] = w1 * A[u,v]\n", - " bias[u*out_channel:(u+1)*out_channel] = b\n", - " return weight, bias\n", - "\n", - "params = []\n", - "channels = []\n", - "channels.append(N * in_features)\n", - "\n", - "for layer in gnn_layers:\n", - " if layer == 'sage':\n", - " params.append(SAGE_to_Dense(N,A,sage_w1,sage_w2,sage_b))\n", - " channels.append(sage_w1.shape[0] * N)\n", - " elif layer == 'dense':\n", - " params.append((dense_w,dense_b))\n", - " channels.append(w.shape[0])\n", - " elif layer == 'add_pool':\n", - " channels.append(channels[-1] // N)\n", - " w = np.zeros((channels[-1],channels[-2]))\n", - " for i in range(channels[-1]):\n", - " for j in range(N):\n", - " w[i, i+j*channels[-1]] = 1.\n", - " b = np.zeros(channels[-1])\n", - " params.append((w,b))\n", - "\n", - "class PyTorchModel(nn.Module):\n", - " def __init__(self, L, params, activations):\n", - " super().__init__()\n", - " layers = []\n", - " for l in range(L):\n", - " layers.append(nn.Linear(params[l][0].shape[1], params[l][0].shape[0]))\n", - " layers[-1].weight = nn.Parameter(torch.tensor(params[l][0], dtype=torch.float64))\n", - " layers[-1].bias = nn.Parameter(torch.tensor(params[l][1], dtype=torch.float64))\n", - " if activations[l]:\n", - " layers[-1].relu = nn.ReLU()\n", - " self.layer = nn.Sequential(*layers)\n", - " \n", - " def forward(self, x):\n", - " x = self.layer(x)\n", - " return x\n", - "\n", - "model_dense = PyTorchModel(len(channels)-1, params, activations)\n", - "print(model_dense)\n", - "# for param in model_dense.parameters():\n", - "# print(param)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Build a MIP Formulation and Solve the Optimization Problem\n", - "\n", - "We can now export the PyTorch model as an ONNX model and use `load_onnx_neural_network_with_bounds` to load it into OMLT." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [], - "source": [ - "dummy_input = torch.zeros(channels[0], dtype=torch.float64)\n", - "dummy_input.requires_grad=True\n", - "input_bounds = [(-1., 1.) for _ in range(channels[0])]\n", - "\n", - "with tempfile.NamedTemporaryFile(suffix='.onnx', delete=False) as f:\n", - " #export neural network to ONNX\n", - " torch.onnx.export(\n", - " model_dense,\n", - " dummy_input,\n", - " f,\n", - " input_names=['input'],\n", - " output_names=['output'],\n", - " )\n", - " #write ONNX model and its bounds using OMLT\n", - " write_onnx_model_with_bounds(f.name, None, input_bounds)\n", - " #load the network definition from the ONNX model\n", - " network_definition = load_onnx_neural_network_with_bounds(f.name)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As a sanity check before creating the optimization model, we can print the properties of the neural network layers from `network_definition`. This allows us to check input/output sizes, as well as activation functions." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0\tInputLayer(input_size=[6], output_size=[6])\tlinear\n", - "1\tDenseLayer(input_size=[6], output_size=[9])\tlinear\n", - "2\tDenseLayer(input_size=[9], output_size=[3])\tlinear\n", - "3\tDenseLayer(input_size=[3], output_size=[1])\tlinear\n" - ] - } - ], - "source": [ - "for layer_id, layer in enumerate(network_definition.layers):\n", - " print(f\"{layer_id}\\t{layer}\\t{layer.activation}\")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, we can load `network_definition` as a full-space `ReluBigMFormulation` object." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "formulation = ReluBigMFormulation(network_definition)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We now encode the Dense NN in a Pyomo model from the `ReluBigMFormulation` object." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "# create pyomo model\n", - "m = pyo.ConcreteModel()\n", - "\n", - "# create an OMLT block for the neural network and build its formulation\n", - "m.nn = OmltBlock()\n", - "m.nn.build_formulation(formulation)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next, we define the objective function as the single output of the Dense NN and solve the minimization problem using a mixed integer solver." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.5 \n", - "Build Date: Dec 8 2020 \n", - "\n", - "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT/bin/cbc -printingOptions all -import /var/tmp/pbs.7796016.pbs/tmpazbklmrp.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.7796016.pbs/tmpazbklmrp.pyomo.soln (default strategy 1)\n", - "Option for printingOptions changed from normal to all\n", - "Presolve 1 (-39) rows, 7 (-39) columns and 7 (-114) elements\n", - "Statistics for presolved model\n", - "\n", - "\n", - "Problem has 1 rows, 7 columns (7 with objective) and 7 elements\n", - "There are 7 singletons with objective \n", - "Column breakdown:\n", - "0 of type 0.0->inf, 0 of type 0.0->up, 0 of type lo->inf, \n", - "7 of type lo->up, 0 of type free, 0 of type fixed, \n", - "0 of type -inf->0.0, 0 of type -inf->up, 0 of type 0.0->1.0 \n", - "Row breakdown:\n", - "0 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, \n", - "1 of type E other, 0 of type G 0.0, 0 of type G 1.0, \n", - "0 of type G other, 0 of type L 0.0, 0 of type L 1.0, \n", - "0 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", - "0 of type Free \n", - "Presolve 1 (-39) rows, 7 (-39) columns and 7 (-114) elements\n", - "0 Obj 0.34521997 Primal inf 1.2424353 (1) Dual inf 3.9956189 (4)\n", - "1 Obj -1.7190541\n", - "Optimal - objective value -1.7190541\n", - "After Postsolve, objective -1.7190541, infeasibilities - dual 0 (0), primal 0 (0)\n", - "Optimal objective -1.719054146 - 1 iterations time 0.002, Presolve 0.00\n", - "Total time (CPU seconds): 0.00 (Wallclock seconds): 0.00\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "{'Problem': [{'Name': 'unknown', 'Lower bound': -1.719054146, 'Upper bound': -1.719054146, 'Number of objectives': 1, 'Number of constraints': 40, 'Number of variables': 46, 'Number of nonzeros': 7, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'User time': -1.0, 'System time': 0.0, 'Wallclock time': 0.0, 'Termination condition': 'optimal', 'Termination message': 'Model was solved to optimality (subject to tolerances), and an optimal solution is available.', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': None, 'Number of created subproblems': None}, 'Black box': {'Number of iterations': 1}}, 'Error rc': 0, 'Time': 0.033590078353881836}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "m.obj = pyo.Objective(expr=(m.nn.outputs[0]))\n", - "pyo.SolverFactory('cbc').solve(m, tee=True)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Formulating Trained GNNs with OMLT: Non-fixed Graph Structure\n", - "\n", - "When the input graph structure is not fixed, elements in the adjacency matrix $A$ are decision variables. In this case, $\\mathcal N(v)$ is not given anymore. Additionally, $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ may contain the graph information, which makes them be variables.\n", - "\n", - "Assume that $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ are fixed. Then we can derive a big-M formulation to handle GNN layers with non-fixed graph structure.\n", - "\n", - "Observe that the existence of edge $u\\to v$ determines the contribution link from $\\mathbf{x}_u^{(l-1)}$ to $\\mathbf{x}_v^{(l)}$. Adding binary variables $A_{u,v}$ for all $u,v\\in V$, we can formulate GNNs in a bilinear way:\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}A_{u,v}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "\n", - "This bilinear formulation involves quadratic constraints. Instead of using binary variables to directly control the existence of contributions between nodes, we introduce auxiliary variables $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ to represent the contribution from node $u$ to node $v$ in $l$th layer:\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{\\bar x}_{u\\to v}^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "where\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{\\bar x}_{u\\to v}^{(l-1)}=\\begin{cases}\n", - " 0, & A_{u,v}=0\\\\\n", - " \\mathbf{x}_u^{(l-1)}, & A_{u,v}=1\n", - " \\end{cases}\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "Assume that each feature is bounded, then the definition of $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ could be reformulated using big-M:\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{x}_{u}^{(l-1)}-\\mathbf{M}_{u}^{(l-1)}(1-A_{u,v})\\le &\\mathbf{\\bar x}_{u\\to v}^{(l-1)}\\le \\mathbf{x}_{u}^{(l-1)}+\\mathbf{M}_{u}^{(l-1)}(1-A_{u,v})\\\\\n", - " -\\mathbf{M}_{u}^{(l-1)}A_{u,v}\\le &\\mathbf{\\bar x}_{u\\to v}^{(l-1)}\\le \\mathbf{M}_u^{(l-1)}A_{u,v}\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "where $|\\mathbf{x}_u^{(l-1)}|\\le \\mathbf{M}_u^{(l-1)}, A_{u,v}\\in\\{0,1\\}$. By adding extra continuous variables and constraints, as well as utilizing the bounds for all features, the big-M formulation replaces the bi-linear constraints by linear constraints.\n", - "\n", - "\n", - "\n", - "### Transforming a GNN with Non-fixed Graph Structure into a Dense NN\n", - "\n", - "Since the graph structure is unknown, all $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ should be provided. We reuse the previous example but this time the parameters in the Dense NN become:\n", - "\n", - "\\begin{equation*}\n", - " \\mathbf{W}=\\begin{pmatrix}\n", - " \\mathbf{w_1} & \\mathbf{w_2} & \\mathbf{w_2} \\\\\n", - " \\mathbf{w_2} & \\mathbf{w_1} & \\mathbf{w_2} \\\\\n", - " \\mathbf{w_2} & \\mathbf{w_2} & \\mathbf{w_1} \\\\\n", - " \\end{pmatrix},\n", - " \\mathbf{B}=\\begin{pmatrix}\n", - " \\mathbf{b}\\\\\\mathbf{b}\\\\\\mathbf{b}\n", - " \\end{pmatrix}\n", - " \\end{equation*}\n", - " \n", - "Repeat all process before building formulation for the Dense NN." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "# graph structure\n", - "# number of nodes\n", - "N = 3\n", - "# adjacency matrix\n", - "A = np.array([[1,1,1],[1,1,1],[1,1,1]])\n", - "\n", - "# in/out features\n", - "in_features = 2\n", - "out_features = 3\n", - "\n", - "# architecture of GNN\n", - "# sage: in_features to out_features for each node, with ReLU as activation\n", - "# add_pool: read out, sum out_features of each node\n", - "# dense: out_features to 1\n", - "gnn_layers = ['sage', 'add_pool', 'dense']\n", - "activations = [True, False, False]\n", - "\n", - "# randomly generate GNN parameters from (-1,1)\n", - "# in practice, these paprameters should be extracted from the trained GNN\n", - "np.random.seed(123)\n", - "sage_w1 = 2.* np.random.rand(out_features, in_features) -1.\n", - "sage_w2 = 2.* np.random.rand(out_features, in_features) -1.\n", - "sage_b = 2. * np.random.rand(out_features) - 1.\n", - "\n", - "dense_w = 2.* np.random.rand(1, out_features) - 1.\n", - "dense_b = 2.* np.random.rand(1) - 1.\n", - "\n", - "params = []\n", - "channels = []\n", - "channels.append(N * in_features)\n", - "\n", - "for layer in gnn_layers:\n", - " if layer == 'sage':\n", - " params.append(SAGE_to_Dense(N,A,sage_w1,sage_w2,sage_b))\n", - " channels.append(sage_w1.shape[0] * N)\n", - " elif layer == 'dense':\n", - " params.append((dense_w,dense_b))\n", - " channels.append(w.shape[0])\n", - " elif layer == 'add_pool':\n", - " channels.append(channels[-1] // N)\n", - " w = np.zeros((channels[-1],channels[-2]))\n", - " for i in range(channels[-1]):\n", - " for j in range(N):\n", - " w[i, i+j*channels[-1]] = 1.\n", - " b = np.zeros(channels[-1])\n", - " params.append((w,b))\n", - " \n", - "model_dense = PyTorchModel(len(channels)-1, params, activations)\n", - "# print(model_dense)\n", - "\n", - "# for param in model_dense.parameters():\n", - "# print(param)\n", - "\n", - "dummy_input = torch.zeros(channels[0], dtype=torch.float64)\n", - "dummy_input.requires_grad=True\n", - "input_bounds = [(-1., 1.) for _ in range(channels[0])]\n", - "\n", - "with tempfile.NamedTemporaryFile(suffix='.onnx', delete=False) as f:\n", - " #export neural network to ONNX\n", - " torch.onnx.export(\n", - " model_dense,\n", - " dummy_input,\n", - " f,\n", - " input_names=['input'],\n", - " output_names=['output'],\n", - " )\n", - " #write ONNX model and its bounds using OMLT\n", - " write_onnx_model_with_bounds(f.name, None, input_bounds)\n", - " #load the network definition from the ONNX model\n", - " network_definition = load_onnx_neural_network_with_bounds(f.name)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Build a MIP Formulation and Solve the Optimization Problem\n", - "\n", - "Note that all types of layers are represented as dense layers in OMLT now. Using `gnn_layer_definition` to retrieve GNN layers. The number of nodes `N` and the list of indexes for GNN layers `gnn_layers` should be provided here." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0\tInputLayer(input_size=[6], output_size=[6])\tlinear\n", - "1\tGNNLayer(input_size=[6], output_size=[9])\tlinear\n", - "2\tDenseLayer(input_size=[9], output_size=[3])\tlinear\n", - "3\tDenseLayer(input_size=[3], output_size=[1])\tlinear\n" - ] - } - ], - "source": [ - "# replace dense layers with GNN layers\n", - "gnn_net = gnn_layer_definition(network_definition, N=N, gnn_layers=[1])\n", - " \n", - "for layer_id, layer in enumerate(gnn_net.layers):\n", - " print(f\"{layer_id}\\t{layer}\\t{layer.activation}\")\n", - " \n", - "formulation = ReluBigMFormulation(gnn_net)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Before building formulation for GNN layers, one needs to define binary variables for adjacency matrix $A$, which is required when using `build_formulation` to encode GNN layers. \n", - "\n", - "Here we set the diagonal elements of $A$ be $1$ to guarantee the self contribution of each node. However, one can fix different elements in $A$ based on different problems. For example, fix most elements in $A$ and only optimize over a subset of edges. The extrame case is that fixing all elements, which is equivalent to the case with fixed graph structure." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Welcome to the CBC MILP Solver \n", - "Version: 2.10.5 \n", - "Build Date: Dec 8 2020 \n", - "\n", - "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT/bin/cbc -printingOptions all -import /var/tmp/pbs.7796016.pbs/tmp4_rnxuex.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.7796016.pbs/tmp4_rnxuex.pyomo.soln (default strategy 1)\n", - "Option for printingOptions changed from normal to all\n", - "Presolve 63 (-49) rows, 33 (-37) columns and 185 (-104) elements\n", - "Statistics for presolved model\n", - "Original problem has 6 integers (6 of which binary)\n", - "Presolved problem has 6 integers (6 of which binary)\n", - "==== 16 zero objective 8 different\n", - "3 variables have objective of -0.649096\n", - "1 variables have objective of -0.635017\n", - "4 variables have objective of -0.268763\n", - "16 variables have objective of 0\n", - "2 variables have objective of 0.312969\n", - "1 variables have objective of 0.475991\n", - "2 variables have objective of 0.481896\n", - "4 variables have objective of 0.533943\n", - "==== absolute objective values 8 different\n", - "16 variables have objective of 0\n", - "4 variables have objective of 0.268763\n", - "2 variables have objective of 0.312969\n", - "1 variables have objective of 0.475991\n", - "2 variables have objective of 0.481896\n", - "4 variables have objective of 0.533943\n", - "1 variables have objective of 0.635017\n", - "3 variables have objective of 0.649096\n", - "==== for integers 6 zero objective 1 different\n", - "6 variables have objective of 0\n", - "==== for integers absolute objective values 1 different\n", - "6 variables have objective of 0\n", - "===== end objective counts\n", - "\n", - "\n", - "Problem has 63 rows, 33 columns (17 with objective) and 185 elements\n", - "There are 3 singletons with objective \n", - "Column breakdown:\n", - "0 of type 0.0->inf, 0 of type 0.0->up, 0 of type lo->inf, \n", - "27 of type lo->up, 0 of type free, 0 of type fixed, \n", - "0 of type -inf->0.0, 0 of type -inf->up, 6 of type 0.0->1.0 \n", - "Row breakdown:\n", - "0 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, \n", - "3 of type E other, 0 of type G 0.0, 0 of type G 1.0, \n", - "0 of type G other, 32 of type L 0.0, 24 of type L 1.0, \n", - "4 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", - "0 of type Free \n", - "Continuous objective value is -2.55499 - 0.00 seconds\n", - "Cgl0004I processed model has 64 rows, 34 columns (6 integer (6 of which binary)) and 184 elements\n", - "Cbc0038I Initial state - 0 integers unsatisfied sum - 0\n", - "Cbc0038I Solution found of -2.55499\n", - "Cbc0038I Relaxing continuous gives -2.55499\n", - "Cbc0038I Before mini branch and bound, 6 integers at bound fixed and 24 continuous\n", - "Cbc0038I Mini branch and bound did not improve solution (0.00 seconds)\n", - "Cbc0038I After 0.00 seconds - Feasibility pump exiting with objective of -2.55499 - took 0.00 seconds\n", - "Cbc0012I Integer solution of -2.5549939 found by feasibility pump after 0 iterations and 0 nodes (0.00 seconds)\n", - "Cbc0001I Search completed - best objective -2.554993930144489, took 0 iterations and 0 nodes (0.00 seconds)\n", - "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", - "Cuts at root node changed objective from -2.55499 to -2.55499\n", - "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "\n", - "Result - Optimal solution found\n", - "\n", - "Objective value: -2.55499393\n", - "Enumerated nodes: 0\n", - "Total iterations: 0\n", - "Time (CPU seconds): 0.00\n", - "Time (Wallclock seconds): 0.00\n", - "\n", - "Total time (CPU seconds): 0.00 (Wallclock seconds): 0.00\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "{'Problem': [{'Name': 'unknown', 'Lower bound': -2.55499393, 'Upper bound': -2.55499393, 'Number of objectives': 1, 'Number of constraints': 63, 'Number of variables': 33, 'Number of binary variables': 6, 'Number of integer variables': 6, 'Number of nonzeros': 17, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'User time': -1.0, 'System time': 0.0, 'Wallclock time': 0.0, 'Termination condition': 'optimal', 'Termination message': 'Model was solved to optimality (subject to tolerances), and an optimal solution is available.', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': 0, 'Number of created subproblems': 0}, 'Black box': {'Number of iterations': 0}}, 'Error rc': 0, 'Time': 0.03782343864440918}], 'Solution': [OrderedDict([('number of solutions', 0), ('number of solutions displayed', 0)])]}" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# create pyomo model\n", - "m = pyo.ConcreteModel()\n", - "\n", - "# create an OMLT block for the neural network and build its formulation\n", - "m.nn = OmltBlock()\n", - "\n", - "# initialize graph information\n", - "m.nn.A = pyo.Var(\n", - " pyo.Set(initialize=range(N)), pyo.Set(initialize=range(N)), within=pyo.Binary\n", - ")\n", - "# usually, the contribution from node v to itself exists\n", - "for i in range(N):\n", - " m.nn.A[i, i].fix(1)\n", - "\n", - "m.nn.build_formulation(formulation)\n", - "\n", - "m.obj = pyo.Objective(expr=(m.nn.outputs[0]))\n", - "pyo.SolverFactory(\"cbc\").solve(m, tee=True)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conclusion\n", - "\n", - "For cases with fixed graph structure, one needs to transform the trained GNN into a Dense NN before using OMLT. After the transformation step, optimizing over a trained GNN is equivalent to optimizing over the corresponding Dense NN. No extra action is needed when using OMLT to encode the Dense NN.\n", - "\n", - "For cases with non-fixed graph structure, the following actions are required:\n", - "\n", - "- providing all $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ in transformation step since any of them could be used.\n", - "- using `gnn_layer_definition` to retrieve GNN layers after loading ONNX model. The number of nodes in graph `N` and the list of indexes for GNN layers `gnn_layers` should be provided here.\n", - "- defining binary variables for adjacency matrix $A$ before using `build_formulation` since these variables are used to formulate GNN layers." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python [conda env:OMLT]", - "language": "python", - "name": "conda-env-OMLT-py" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.16" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/src/omlt/dependencies.py b/src/omlt/dependencies.py index 07e2b481..f930d238 100644 --- a/src/omlt/dependencies.py +++ b/src/omlt/dependencies.py @@ -4,3 +4,7 @@ onnx, onnx_available = attempt_import("onnx") keras, keras_available = attempt_import("tensorflow.keras") + +torch, torch_available = attempt_import("torch") + +torch_geometric, torch_geometric_available = attempt_import("torch_geometric") diff --git a/src/omlt/io/__init__.py b/src/omlt/io/__init__.py index d4cf2bfc..c1e7f852 100644 --- a/src/omlt/io/__init__.py +++ b/src/omlt/io/__init__.py @@ -1,4 +1,9 @@ -from omlt.dependencies import onnx_available, keras_available +from omlt.dependencies import ( + onnx_available, + keras_available, + torch_available, + torch_geometric_available, +) if onnx_available: from omlt.io.onnx import ( @@ -9,3 +14,6 @@ if keras_available: from omlt.io.keras import load_keras_sequential + +if torch_available and torch_geometric_available: + from omlt.io.torch_geometric import load_torch_geometric_sequential diff --git a/src/omlt/io/torch_geometric/__init__.py b/src/omlt/io/torch_geometric/__init__.py new file mode 100644 index 00000000..a626e86f --- /dev/null +++ b/src/omlt/io/torch_geometric/__init__.py @@ -0,0 +1,3 @@ +from omlt.io.torch_geometric.torch_geometric_reader import ( + load_torch_geometric_sequential, +) diff --git a/src/omlt/io/torch_geometric/torch_geometric_reader.py b/src/omlt/io/torch_geometric/torch_geometric_reader.py new file mode 100644 index 00000000..1acbc2e7 --- /dev/null +++ b/src/omlt/io/torch_geometric/torch_geometric_reader.py @@ -0,0 +1,278 @@ +import numpy as np + +from omlt.neuralnet.layer import DenseLayer, InputLayer, GNNLayer +from omlt.neuralnet.network_definition import NetworkDefinition + + +def _compute_gcn_norm(A): + """ + Calculate the norm for a GCN layer + + Parameters + ---------- + A : matrix-like + the adjacency matrix. + """ + N = A.shape[0] + Ahat = A + np.eye(N) + degrees = np.sum(Ahat, axis=0) + gcn_norm = np.zeros(A.shape) + for u in range(N): + for v in range(N): + gcn_norm[u, v] = Ahat[u, v] / np.sqrt(degrees[u] * degrees[v]) + return gcn_norm + + +def _compute_sage_norm(A, aggr): + """ + Calculate the norm for a SAGE layer + + Parameters + ---------- + A : matrix-like + the adjacency matrix. + aggr : str + the aggregation function. + """ + N = A.shape[0] + sage_norm = A + np.eye(N) + if aggr == "mean": + degrees = np.sum(A, axis=0) + for u in range(N): + for v in range(N): + if u != v and degrees[u] > 0: + sage_norm[u, v] = sage_norm[u, v] / degrees[u] + return sage_norm + + +def _process_gnn_parameters(gnn_weights_uv, gnn_weights_vv, gnn_biases, gnn_norm): + """ + Construct the weights and biases for the GNNLayer class + + Parameters + ---------- + gnn_weights_uv : matrix-like + the weights between two different nodes, shape: (out_channels, in_channels). + gnn_weights_vv : matrix-like + the weights between the same node, shape: (out_channels, in_channels). + gnn_biases : array-like + the biases, shape: (out_channels, ) + gnn_norm : matrix-like + the norm for the GNN layer, shape: (N, N) + + Returns + ------- + weights : matrix-like + the weights for the GNNLayer class, shape: (N * in_channels, N * out_channels) + biases: array-like + the biases for the GNNLayer class, shape: (N * out_channels, ) + """ + out_channels, in_channels = gnn_weights_uv.shape + N = gnn_norm.shape[0] + weights = np.zeros((N * in_channels, N * out_channels), dtype=gnn_weights_uv.dtype) + biases = np.zeros(N * out_channels, dtype=gnn_biases.dtype) + for output_index in range(N * out_channels): + biases[output_index] = gnn_biases[output_index % out_channels] + for input_index in range(N * in_channels): + input_node_index = input_index // in_channels + output_node_index = output_index // out_channels + if input_node_index != output_node_index: + weights[input_index, output_index] = ( + gnn_norm[output_node_index, input_node_index] + * gnn_weights_uv[ + output_index % out_channels, input_index % in_channels + ] + ) + else: + weights[input_index, output_index] = ( + gnn_norm[output_node_index, input_node_index] + * gnn_weights_vv[ + output_index % out_channels, input_index % in_channels + ] + ) + return weights, biases + + +_LAYER_OP_TYPES_FIXED_GRAPH = ["Linear", "GCNConv", "SAGEConv"] +_LAYER_OP_TYPES_NON_FIXED_GRAPH = ["Linear", "SAGEConv"] +_ACTIVATION_OP_TYPES = ["ReLU", "Sigmoid", "LogSoftmax", "Softplus", "Tanh"] +_POOLING_OP_TYPES = ["global_mean_pool", "global_add_pool"] +_AGGREGATION_OP_TYPES = ["sum", "mean"] +_OP_TYPES = _LAYER_OP_TYPES_FIXED_GRAPH + _ACTIVATION_OP_TYPES + _POOLING_OP_TYPES + + +def load_torch_geometric_sequential( + nn, + N, + A=None, + scaling_object=None, + scaled_input_bounds=None, + unscaled_input_bounds=None, +): + """ + Load a torch_geometric graph neural network model (built with Sequential) into + an OMLT network definition object. This network definition object + can be used in different formulations. + + Parameters + ---------- + nn : torch_geometric.model + A torch_geometric model that was built with Sequential + N : int + The number of nodes of input graph + A : matrix-like + The adjacency matrix of input graph + scaling_object : instance of ScalingInterface or None + Provide an instance of a scaling object to use to scale iputs --> scaled_inputs + and scaled_outputs --> outputs. If None, no scaling is performed. See scaling.py. + scaled_input_bounds : dict or None + A dict that contains the bounds on the scaled variables (the + direct inputs to the neural network). If None, then no bounds + are specified or they are generated using unscaled bounds. + unscaled_input_bounds : dict or None + A dict that contains the bounds on the unscaled variables (the + direct inputs to the neural network). If specified the scaled_input_bounds + dictionary will be generated using the provided scaling object. + If None, then no bounds are specified. + + Returns + ------- + NetworkDefinition + """ + n_inputs = N * nn[0].in_channels + + net = NetworkDefinition( + scaling_object=scaling_object, + scaled_input_bounds=scaled_input_bounds, + unscaled_input_bounds=unscaled_input_bounds, + ) + + prev_layer = InputLayer([n_inputs]) + net.add_layer(prev_layer) + + operations = [] + for l in nn: + op_name = None + if l.__class__.__name__ == "function": + op_name = l.__name__ + else: + op_name = l.__class__.__name__ + + if op_name not in _OP_TYPES: + raise ValueError("this operation is not supported") + operations.append(op_name) + + if A is None: + # If A is None, then the graph is not fixed. + # Only layers in _LAYER_OP_TYPES_NON_FIXED_GRAPH are supported. + # Only "sum" aggregation is supported. + # Since all weights and biases are possibly needed, A is set to correspond to a complete graph. + for index, l in enumerate(nn): + if ( + operations[index] + in ["Linear"] + _ACTIVATION_OP_TYPES + _POOLING_OP_TYPES + ): + # Linear layers, all activation functions, and all pooling functions are still supported. + continue + if operations[index] not in _LAYER_OP_TYPES_NON_FIXED_GRAPH: + raise ValueError( + "this layer is not supported when the graph is not fixed" + ) + elif l.aggr != "sum": + raise ValueError( + "this aggregation is not supported when the graph is not fixed" + ) + A = np.ones((N, N)) - np.eye(N) + + for index, l in enumerate(nn): + if operations[index] in _ACTIVATION_OP_TYPES: + # Skip activation layers since they are already handled in last layer + continue + + activation = None + if index + 1 < len(nn) and operations[index + 1] in _ACTIVATION_OP_TYPES: + # Check if this layer has an activation function + activation = operations[index + 1].lower() + + if operations[index] == "Linear": + gnn_weights = l.weight.detach().numpy() + gnn_biases = l.bias.detach().numpy() + # A linear layer is either applied on each node's features (i.e., prev_layer.output_size[-1] = N * gnn_weights.shape[1]) + # or the features after pooling (i.e., prev_layer.output_size[-1] = gnn_weights.shape[1]) + gnn_norm = np.eye(prev_layer.output_size[-1] // gnn_weights.shape[1]) + weights, biases = _process_gnn_parameters( + gnn_weights, gnn_weights, gnn_biases, gnn_norm + ) + n_layer_inputs, n_layer_outputs = weights.shape + curr_layer = DenseLayer( + [n_layer_inputs], + [n_layer_outputs], + activation=activation, + weights=weights, + biases=biases, + ) + elif operations[index] == "GCNConv": + assert l.improved == False + assert l.cached == False + assert l.add_self_loops == True + assert l.normalize == True + gnn_weights = l.lin.weight.detach().numpy() + gnn_biases = l.bias.detach().numpy() + gnn_norm = _compute_gcn_norm(A) + weights, biases = _process_gnn_parameters( + gnn_weights, gnn_weights, gnn_biases, gnn_norm + ) + n_layer_inputs, n_layer_outputs = weights.shape + curr_layer = GNNLayer( + [n_layer_inputs], + [n_layer_outputs], + activation=activation, + weights=weights, + biases=biases, + N=N, + ) + elif operations[index] == "SAGEConv": + assert l.normalize == False + assert l.project == False + assert l.aggr in _AGGREGATION_OP_TYPES + gnn_weights_uv = l.lin_l.weight.detach().numpy() + gnn_biases = l.lin_l.bias.detach().numpy() + gnn_weights_vv = np.zeros(shape=gnn_weights_uv.shape) + if l.root_weight: + gnn_weights_vv = l.lin_r.weight.detach().numpy() + gnn_norm = _compute_sage_norm(A, l.aggr) + weights, biases = _process_gnn_parameters( + gnn_weights_uv, gnn_weights_vv, gnn_biases, gnn_norm + ) + n_layer_inputs, n_layer_outputs = weights.shape + curr_layer = GNNLayer( + [n_layer_inputs], + [n_layer_outputs], + activation=activation, + weights=weights, + biases=biases, + N=N, + ) + elif operations[index] in _POOLING_OP_TYPES: + # Both mean and add pooling layers can be transformed into a DenseLayer + n_layer_inputs = prev_layer.output_size[-1] + n_layer_outputs = prev_layer.output_size[-1] // N + weights = np.zeros((n_layer_inputs, n_layer_outputs)) + biases = np.zeros(n_layer_outputs) + for input_index in range(n_layer_inputs): + for output_index in range(n_layer_outputs): + if input_index % n_layer_outputs == output_index: + if operations[index] == "global_mean_pool": + weights[input_index, output_index] = 1.0 / N + elif operations[index] == "global_add_pool": + weights[input_index, output_index] = 1.0 + curr_layer = DenseLayer( + [n_layer_inputs], + [n_layer_outputs], + weights=weights, + biases=biases, + ) + net.add_layer(curr_layer) + net.add_edge(prev_layer, curr_layer) + prev_layer = curr_layer + return net diff --git a/src/omlt/neuralnet/network_definition.py b/src/omlt/neuralnet/network_definition.py index 9acc82fe..ac930baa 100644 --- a/src/omlt/neuralnet/network_definition.py +++ b/src/omlt/neuralnet/network_definition.py @@ -1,6 +1,6 @@ import networkx as nx -from omlt.neuralnet.layer import Layer, DenseLayer, GNNLayer +from omlt.neuralnet.layer import Layer class NetworkDefinition: @@ -146,57 +146,3 @@ def successors(self, layer): def __str__(self): return f"NetworkDefinition(num_layers={len(self.__layers_by_id)})" - - -def gnn_layer_definition(net, N, gnn_layers): - """ - Replace dense layers in a NetworkDefinition class with GNN layers - - Parameters - ---------- - net : NetworkDefinition - the neural network definition - N : int - the number of nodes in the graph structure - gnn_layers : list - the list of indexes for GNN layers - """ - assert isinstance(N, int) - assert N > 0 - assert isinstance(gnn_layers, list) - - # copy unchanged properties from net - gnn_net = NetworkDefinition( - scaling_object=net.scaling_object, - scaled_input_bounds=net.scaled_input_bounds, - unscaled_input_bounds=net.unscaled_input_bounds, - ) - - # map the indexes of layers in net to the indexes of layers in gnn_net - layer_id_mapper = {} - - for layer_id, layer in enumerate(net.layers): - # these layers are not GNN layers and do not need to be changed - if layer_id not in gnn_layers: - new_layer = layer - else: - # only dense layers could be replaced with GNN layers - assert isinstance(layer, DenseLayer) - # define the corresponding GNN layer - new_layer = GNNLayer( - input_size=layer.input_size, - output_size=layer.output_size, - weights=layer.weights, - biases=layer.biases, - N=N, - activation=layer.activation, - input_index_mapper=layer.input_index_mapper, - ) - # add new_layer to gnn_net - gnn_net.add_layer(new_layer) - # map layer (in net) to new_layer (in gnn_net) - layer_id_mapper[id(layer)] = id(new_layer) - # add edges between new_layer and its predecessors, which could be retrieved from the predecessors of layer - for layer_input in net.predecessors(layer): - gnn_net.add_edge(gnn_net.layer(layer_id_mapper[id(layer_input)]), new_layer) - return gnn_net diff --git a/tests/io/test_keras_reader.py b/tests/io/test_keras_reader.py index f5c9668f..d47b0920 100644 --- a/tests/io/test_keras_reader.py +++ b/tests/io/test_keras_reader.py @@ -7,7 +7,7 @@ @pytest.mark.skipif( - not keras_available, reason="Test only valid when keras not available" + not keras_available, reason="Test only valid when keras is available" ) def test_keras_reader(datadir): nn = keras.models.load_model(datadir.file("keras_linear_131"), compile=False) diff --git a/tests/io/test_torch_geometric_reader.py b/tests/io/test_torch_geometric_reader.py new file mode 100644 index 00000000..5e777720 --- /dev/null +++ b/tests/io/test_torch_geometric_reader.py @@ -0,0 +1,110 @@ +import pytest +import numpy as np + +from omlt.dependencies import ( + torch, + torch_available, + torch_geometric, + torch_geometric_available, +) + +if torch_available and torch_geometric_available: + from torch.nn import Linear, ReLU, Sigmoid, Softplus, Tanh + from torch_geometric.nn import Sequential, GCNConv, SAGEConv + from torch_geometric.nn import global_mean_pool, global_add_pool + from torch_geometric.utils import erdos_renyi_graph + from omlt.io.torch_geometric import load_torch_geometric_sequential + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def GCN_Sequential(activation, pooling): + torch.manual_seed(123) + return Sequential( + "x, edge_index", + [ + (GCNConv(2, 4), "x, edge_index -> x"), + activation(), + (GCNConv(4, 4), "x, edge_index -> x"), + activation(), + Linear(4, 4), + (pooling, "x, None -> x"), + Linear(4, 2), + activation(), + Linear(2, 1), + ], + ) + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def SAGE_Sequential(activation, pooling, aggr, root_weight): + torch.manual_seed(123) + return Sequential( + "x, edge_index", + [ + (SAGEConv(2, 4, aggr=aggr, root_weight=root_weight), "x, edge_index -> x"), + activation(), + (SAGEConv(4, 4, aggr=aggr, root_weight=root_weight), "x, edge_index -> x"), + activation(), + Linear(4, 4), + (pooling, "x, None -> x"), + Linear(4, 2), + activation(), + Linear(2, 1), + ], + ) + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def generate_random_inputs(N, F, seed, p): + torch.manual_seed(seed) + edges = erdos_renyi_graph(N, p, directed=False) + A = np.zeros((N, N), dtype=int) + for k in range(edges.shape[1]): + u = edges[0, k].numpy() + v = edges[1, k].numpy() + A[u, v] = 1 + x = 2.0 * torch.rand((N, F)) - 1.0 + return x, edges, np.squeeze(x.numpy().reshape(1, -1)), A + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def _test_torch_geometric_reader(nn): + N = 4 + F = 2 + nn.eval() + for seed in range(10): + for p in range(10): + x, edges, x_np, A = generate_random_inputs(N, F, seed, p / 10.0) + net = load_torch_geometric_sequential(nn, N, A) + y = nn(x, edges).detach().numpy() + y_np = x_np + for layer in net.layers: + y_np = layer.eval_single_layer(y_np) + assert abs(y - y_np) < 1e-6 + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def test_torch_geometric_reader(): + for activation in [ReLU, Sigmoid, Tanh]: + for pooling in [global_mean_pool, global_add_pool]: + nn = GCN_Sequential(activation, pooling) + _test_torch_geometric_reader(nn) + for aggr in ["sum", "mean"]: + for root_weight in [False, True]: + nn = SAGE_Sequential(activation, pooling, aggr, root_weight) + _test_torch_geometric_reader(nn) diff --git a/tests/neuralnet/test_layer.py b/tests/neuralnet/test_layer.py index f58b8ba3..fa0bc085 100644 --- a/tests/neuralnet/test_layer.py +++ b/tests/neuralnet/test_layer.py @@ -111,7 +111,7 @@ def test_gnn_layer_with_input_index_mapper(): biases = np.array([-1, 0, 1, -1, 0, 1, -1, 0, 1]) - # input has size [6], but the previous node output is [3, 2] + # input has size [6], but the previous node output is [2, 3] # use mapper to map between the two t = IndexMapper([1, 2, 2, 3], [1, 2, 6]) layer = GNNLayer([1, 2, 6], [1, 2, 9], weights, biases, N=3, input_index_mapper=t) diff --git a/tests/neuralnet/test_nn_formulation.py b/tests/neuralnet/test_nn_formulation.py index 8012baf1..95d47bfb 100644 --- a/tests/neuralnet/test_nn_formulation.py +++ b/tests/neuralnet/test_nn_formulation.py @@ -16,10 +16,9 @@ IndexMapper, InputLayer, PoolingLayer2D, + GNNLayer, ) -from omlt.neuralnet.network_definition import gnn_layer_definition - def two_node_network(activation, input_value): """ @@ -329,22 +328,6 @@ def test_maxpool_FullSpaceNNFormulation(): assert abs(pyo.value(m.neural_net_block.outputs[0, 0, 0]) - y[0, 0, 0]) < 1e-6 -def examples_of_graphs(graph_type): - # complete graph - if graph_type == "complete": - A = np.ones([3, 3], dtype=int) - y = np.array([-11, 9, 1, -12, 11, 1, -10, 10, 1]) - # edgeless graph - elif graph_type == "edgeless": - A = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) - y = np.array([-4, 2, 0, -2, 1, 1, -3, 3, 2]) - # line graph, i.e., 0-1-2 - elif graph_type == "line": - A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]]) - y = np.array([-6, 4, 0, -12, 11, 1, -5, 5, 2]) - return A, y - - def three_node_graph_neural_network(activation): input_size = [6] input_bounds = {} @@ -355,8 +338,8 @@ def three_node_graph_neural_network(activation): input_layer = InputLayer(input_size) net.add_layer(input_layer) - dense_layer = DenseLayer( - [6], + gnn_layer = GNNLayer( + input_layer.output_size, [9], activation=activation, weights=np.array( @@ -370,33 +353,48 @@ def three_node_graph_neural_network(activation): ] ), biases=np.array([-1, 0, 1, -1, 0, 1, -1, 0, 1]), + N=3, ) - net.add_layer(dense_layer) - net.add_edge(input_layer, dense_layer) + net.add_layer(gnn_layer) + net.add_edge(input_layer, gnn_layer) - gnn_net = gnn_layer_definition(net, N=3, gnn_layers=[1]) + return net - return gnn_net + +def examples_of_graphs(graph_type): + # complete graph + if graph_type == "complete": + A = np.ones([3, 3], dtype=int) + y = np.array([-11, 9, 1, -12, 11, 1, -10, 10, 1]) + # edgeless graph + elif graph_type == "edgeless": + A = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) + y = np.array([-4, 2, 0, -2, 1, 1, -3, 3, 2]) + # line graph, i.e., 0-1-2 + elif graph_type == "line": + A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]]) + y = np.array([-6, 4, 0, -12, 11, 1, -5, 5, 2]) + return A, y def _test_three_node_graph_neural_network(graph_type): m = pyo.ConcreteModel() m.nn = OmltBlock() - gnn_net = three_node_graph_neural_network("linear") + inputs = np.array([-3, 2, -1, 1, -2, 3]) + net = three_node_graph_neural_network("linear") - N = 3 + m.nn.N = 3 m.nn.A = pyo.Var( - pyo.Set(initialize=range(N)), - pyo.Set(initialize=range(N)), + pyo.Set(initialize=range(m.nn.N)), + pyo.Set(initialize=range(m.nn.N)), within=pyo.Binary, ) - m.nn.build_formulation(FullSpaceNNFormulation(gnn_net)) + m.nn.build_formulation(FullSpaceNNFormulation(net)) - inputs = np.array([-3, 2, -1, 1, -2, 3]) A, y = examples_of_graphs(graph_type) - for i in range(N): - for j in range(N): + for i in range(m.nn.N): + for j in range(m.nn.N): m.nn.A[i, j].fix(A[i, j]) for i in range(6): m.nn.inputs[i].fix(inputs[i]) From 52d25fa1953d7e0d95675a3b3b7d0b69adc13808 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Thu, 17 Aug 2023 15:26:37 +0100 Subject: [PATCH 05/27] update torch_geometric --- docs/notebooks.rst | 2 +- .../graph_neural_network_formulation.ipynb | 813 ++++++++++++++++++ src/omlt/io/torch_geometric/__init__.py | 5 + .../torch_geometric/build_gnn_formulation.py | 148 ++++ ...tric_reader.py => test_torch_geometric.py} | 90 +- tests/notebooks/test_run_notebooks.py | 15 +- 6 files changed, 1069 insertions(+), 4 deletions(-) create mode 100644 docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb create mode 100644 src/omlt/io/torch_geometric/build_gnn_formulation.py rename tests/io/{test_torch_geometric_reader.py => test_torch_geometric.py} (52%) diff --git a/docs/notebooks.rst b/docs/notebooks.rst index 0d3f4f14..d03e40de 100644 --- a/docs/notebooks.rst +++ b/docs/notebooks.rst @@ -14,7 +14,7 @@ github `page `_. * `mnist_example_convolutional.ipynb `_ trains a convolutional neural network on MNIST and uses OMLT to find adversarial examples. -* `example_graph_neural_network.ipynb `_ transforms graph neural networks into dense neural networks and use OMLT to solve optimization problems. +* `graph_neural_network_formulation.ipynb `_ transforms graph neural networks into OMLT and builds formulation to solve optimization problems. * `auto-thermal-reformer.ipynb `_ develops a neural network surrogate (using sigmoid activations) with data from a process model built using `IDAES-PSE `_. diff --git a/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb b/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb new file mode 100644 index 00000000..364f9b7c --- /dev/null +++ b/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb @@ -0,0 +1,813 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optimizing over trained graph neural networks\n", + "\n", + "This notebook explains how OMLT is used to optimize over trained graph neural networks (GNNs). We follow the below steps:\n", + "\n", + "1.) A general definition of GNNs is provided. OMLT currently only supports GNN that fits our definition. \n", + "\n", + "2.) Introduce the `GNNLayer` class inside OMLT.\n", + "\n", + "3.) Derive the big-M formulation for GNN layers.\n", + "\n", + "4.) List operations that are implemented inside OMLT. OMLT can automatically encode a given GNN consists of these operations. \n", + "\n", + "5.) For customized GNNs, we give examples to illustrate how to transform it into OMLT. \n", + "\n", + "6.) Examples: one has fixed graph structure, another one has non-fixed graph structure. For each case, the output of the GNN is minimized.\n", + "\n", + "**NOTE:** For simplicity, we skip the training process and just use random parameters for GNNs.\n", + "\n", + "\n", + "## Library Setup\n", + "\n", + "This notebook assumes you have a working PyTorch environment to define a Dense NN. This Dense NN is then formulated in Pyomo using OMLT which therefore requires working Pyomo and OMLT installations.\n", + "\n", + "The required Python libraries used in this notebook are as follows:\n", + "\n", + "- `numpy`: used for transformation of parameters\n", + "\n", + "- `torch`: the machine learning language used for neural networks\n", + "\n", + "- `torch_geometric`: the machine learning language used for graph neural networks\n", + "\n", + "- `pyomo`: the algebraic modeling language for Python, it is used to define the optimization model passed to the solver\n", + "\n", + "- `onnx`: used to express trained neural network models\n", + "\n", + "- `omlt`: the package this notebook demonstrates. OMLT can formulate machine learning (such as neural networks) within Pyomo\n", + "\n", + "**NOTE:** This notebook also assumes you have a working MIP solver executable to solve optimization problems in Pyomo. The open-source solver CBC is called by default. \n", + "\n", + "\n", + "## Definition of GNNs\n", + "\n", + "We define a GNN with $L$ layers as follows:\n", + "\n", + "\\begin{equation*}\n", + "\t\\begin{aligned}\n", + "\t\tGNN:\\underbrace{\\mathbb R^{d_0}\\otimes\\cdots\\otimes\\mathbb R^{d_0}}_{N \\rm{times}}\\to\\underbrace{\\mathbb R^{d_L}\\otimes\\cdots\\otimes\\mathbb R^{d_L}}_{N\\ \\rm{times}}\n", + "\t\\end{aligned}\n", + "\\end{equation*}\n", + " \n", + "where $V$ is the set of nodes of the input graph, $N=|V|$ is the number of nodes. \n", + "\n", + "Let $\\mathbf{x}_v^{(0)} \\in \\mathbb{R}^{d_0}$ be the input features for node $v$. Then, the $l$-th layer ($l=1,2,\\dots,L$) is defined by:\n", + "\n", + "\\begin{equation*}\n", + "\t\\begin{aligned}\n", + "\t\t\\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in\\mathcal N(v)\\cup\\{v\\}}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right),~\\forall v\\in V\n", + "\t\\end{aligned}\n", + "\\end{equation*}\n", + "\n", + "where $\\mathcal N(v)$ is the set of all neighbors of $v$, $\\sigma$ could be identity or any activation function.\n", + "\n", + "*Dimensionality:* $\\mathbf{x}_u^{(l-1)}\\in\\mathbb R^{d_{l-1}}, \\mathbf{x}_v^{(l)},\\mathbf{b}_v^{(l)}\\in\\mathbb R^{d_l}, \\mathbf{w}_{u\\to v}^{(l)}\\in\\mathbb R^{d_l}\\times \\mathbb R^{d_{l-1}}$.\n", + "\n", + "## GNN Layers in OMLT\n", + "\n", + "For optimization purposes, OMLT requires a given number of nodes $N$ in the input graph. Each GNN layer will be expanded as shown in follows.\n", + "\n", + "Stack $\\{\\mathbf{x}_v^{(l)}\\}_{v\\in V}$ as a vector $\\mathbf{X}^{(l)}\\in \\mathbb R^{Nd_l}$. Rewrite previous definition as:\n", + "\\begin{equation*}\n", + "\t\\begin{aligned}\n", + "\t\t\\mathbf{X}^{(l)}=\\sigma\\left(\\mathbf{W}^{(l)}\\mathbf{X}^{(l-1)}+\\mathbf{B}^{(l)}\\right)\n", + "\t\\end{aligned}\n", + "\\end{equation*}\n", + "\n", + "One needs to provide $\\mathbf{W}^{(l)}\\in\\mathbb R^{Nd_l\\times Nd_{l-1}}, \\mathbf{B}^{(l)}\\in\\mathbb R^{Nd_l}, N$ to define a `GNNLayer` in OMLT. \n", + "\n", + "**NOTE:** To keep consistency with other types of layers, all weights are transposed.\n", + "\n", + "If the input graph structure is fixed, then weights $\\mathbf{w}_{u\\to v}^{(l)}$, biases $\\mathbf{b}_{v}^{(l)}$, and links between layers determined by $\\mathcal N(v)$ are all fixed after the GNN is trained. In this case, $\\mathbf{W}^{(l)}$ is a sparse matrix with nonzero sub-matrices $\\{\\mathbf{w}_{u\\to v}^{(l)}\\}_{v\\in V,u\\in\\mathcal N(v)\\cup\\{v\\}}$ and $\\mathbf{B}^{(l)}$ is the stack of $\\{\\mathbf{b}_v^{(l)}\\}_{v\\in V}$. The mixed-integer formulation of `GNNLayer` can be interpreted from two perspectives: (1) the same as a `DenseLayer`; (2) a simplified setting of `GNNLayer` with non-fixed input graph (introduced later). \n", + "\n", + "If the input graph structure is not fixed, then all weights $\\mathbf{w}_{u\\to v}^{(l)}$ and biases $\\mathbf{b}_{v}^{(l)}$ are needed to build mixed-integer formulations. In this case, $\\mathbf{B}^{(l)}$ is still the stack of $\\{\\mathbf{b}_v^{(l)}\\}_{v\\in V}$, while $\\mathbf{W}^{(l)}$ is a dense matrix consists of $\\{\\mathbf{w}_{u\\to v}^{(l)}\\}_{u,v\\in V}$.\n", + "\n", + "## Formulation for GNN Layers\n", + "\n", + "When the input graph structure is not fixed, elements in the adjacency matrix $A$ are decision variables. In this case, $\\mathcal N(v)$ is not given anymore. Additionally, $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ may contain the graph information, which makes them be variables. The formulation for GNN layers is built assuming that $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ are fixed.\n", + "\n", + "First, observe that the existence of edge $u\\to v$ determines the contribution link from $\\mathbf{x}_u^{(l-1)}$ to $\\mathbf{x}_v^{(l)}$. Adding binary variables $A_{u,v}$ for all $u,v\\in V$, we can formulate GNNs in a bilinear way:\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}A_{u,v}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "\n", + "This formulation involves quadratic constraints. To avoid them, instead of using binary variables to directly control the existence of contributions between nodes, we introduce introduces auxiliary variables $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ to represent the contribution from node $u$ to node $v$ in $l$-th layer:\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{\\bar x}_{u\\to v}^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "where\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{\\bar x}_{u\\to v}^{(l-1)}=\\begin{cases}\n", + " 0, & A_{u,v}=0\\\\\n", + " \\mathbf{x}_u^{(l-1)}, & A_{u,v}=1\n", + " \\end{cases}\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "Assume that each feature is bounded, then the definition of $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ could be reformulated using big-M:\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\mathbf{x}_{u}^{(l-1)}-\\mathbf{M}_{u}^{(l-1)}(1-A_{u,v})\\le &~\\mathbf{\\bar x}_{u\\to v}^{(l-1)}\\le \\mathbf{x}_{u}^{(l-1)}+\\mathbf{M}_{u}^{(l-1)}(1-A_{u,v})\\\\\n", + " -\\mathbf{M}_{u}^{(l-1)}A_{u,v}\\le &~\\mathbf{\\bar x}_{u\\to v}^{(l-1)}\\le \\mathbf{M}_u^{(l-1)}A_{u,v}\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "where $|\\mathbf{x}_u^{(l-1)}|\\le \\mathbf{M}_u^{(l-1)}, A_{u,v}\\in\\{0,1\\}$. By adding extra continuous variables and constraints, as well as utilizing the bounds for all features, the big-M formulation replaces the bi-linear constraints by linear constraints. OMLT uses this big-M formulation as the default (and only) formulation for GNN layers.\n", + "\n", + "**NOTE:** When the input graph structure is fixed, we can fix $A$ to reduce the big-M formulation.\n", + "\n", + "## Implemented GNN Operations in OMLT\n", + "\n", + "The following operations from `torch_geometric` are implemented in OMLT:\n", + "\n", + "- Convolutional Layers: `Linear`, `GCNConv`, `SAGEConv`\n", + "- Aggregation Operators: `sum`, `mean`\n", + "- Pooling Layers: `global_mean_pool`, `global_add_pool`\n", + "- Activation Functions: all activations supported in OMLT are compatible with these GNN operations.\n", + "\n", + "**NOTE:** When the input graph is not fixed, there is no graph information. `GCNConv` layer and `mean` aggregation are not supported.\n", + "\n", + "OMLT provides two functions `gnn_with_fixed_graph` and `gnn_with_non_fixed_graph` to encode GNNs with fixed/non-fixed input graph structure. Both functions only require (1) a sequential model from `torch_geometric`, and (2) number of nodes $N$ (and the adjacency matrix $A$ for fixed graph cases). The basic pipeline of both functions are:\n", + "\n", + "1.) Transform each operation, e.g., linear layers and pooling layers will be transformed into `DenseLayer` (which is straightforward), GNN layers will be rewritten into `GNNLayer`, activation functions are identified and absorbed into corresponding layers.\n", + "\n", + "2.) Define binary variables $A_{u,v}$ for adjacency matrix. We always assume $A$ is symmetric (i.e., $A_{u,v}=A_{v,u}$) and has non-zero diagonal elements (i.e., $A_{v,v}=1$). When $A$ is given for fixed graph cases, these variables will then be fixed.\n", + "\n", + "3.) Build formulation. Currently, we only support `FullSpaceNNFormulations`. ReLU activation functions are encoded into linear constraints using a big-M formulation. For smooth activation functions (e.g., Sigmoid, LogSoftmax, Tanh), a smooth optimization solvers (such as Ipopt) is needed to handle nonlinear constraints.\n", + "\n", + "## How to Transform Your Own GNN into OMLT\n", + "\n", + "As mentioned before, any GNN that satisfies our GNN definition could be transformed into OMLT and then encoded using big-M formulation. Here we give two examples to show how to transform an outside GNN into OMLT.\n", + "\n", + "The first example corresponds to fixed graph cases. Given a simple GNN consists of a GraphSAGE layer, an add pooling layer, and a dense layer with single output. Let the input and output features of the GraphSAGE layer are 2 and 3, respectively. \n", + "\n", + "The GraphSAGE layer is defined by:\n", + "\\begin{equation*}\n", + " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\mathbf{w_1}^{(l)}\\mathbf{x}_v^{(l-1)}+\\mathbf{w_2}^{(l)}\\sum\\limits_{u\\in\\mathcal N(v)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}^{(l)}\\right)\n", + "\\end{equation*}\n", + "where a sum aggregation is used.\n", + "\n", + "For the fixed graph structure, assume that it is a line graph with $N=3$ nodes, i.e., the adjacency matrix $A=\\begin{pmatrix}1 & 1 & 0\\\\1 & 1 & 1\\\\ 0 & 1 & 1\\end{pmatrix}$. Then the GraphSAGE layer could be rewritten as a `GNNLayer` with parameters:\n", + "\n", + " \\begin{equation*}\n", + " \\mathbf{W}=\\begin{pmatrix}\n", + " \\mathbf{w_1} & \\mathbf{w_2} & \\mathbf{0} \\\\\n", + " \\mathbf{w_2} & \\mathbf{w_1} & \\mathbf{w_2} \\\\\n", + " \\mathbf{0} & \\mathbf{w_2} & \\mathbf{w_1} \\\\\n", + " \\end{pmatrix},\n", + " \\mathbf{B}=\\begin{pmatrix}\n", + " \\mathbf{b}\\\\\\mathbf{b}\\\\\\mathbf{b}\n", + " \\end{pmatrix}\n", + " \\end{equation*}\n", + " \n", + "See below as a mapping between the given outside GNN and its corresponding GNN inside OMLT in form \"layer type (in_channel, out_channel)\":\n", + "\n", + "\\begin{equation*}\n", + " \\begin{aligned}\n", + " \\text{GraphSAGE(2, 3)} &\\Rightarrow \\text{GNNLayer(6, 9)}\\\\\n", + " \\text{add pooling(9, 3)} &\\Rightarrow \\text{DenseLayer(9, 3)}\\\\\n", + " \\text{dense(3, 1)} &\\Rightarrow \\text{DenseLayer(3, 1)}\n", + " \\end{aligned}\n", + "\\end{equation*}\n", + "\n", + "The second example reuses the GNN architecture but no longer fixes the input graph structure. In such setting, all $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ should be provided. Therefore, the `GNNLayer` is defined by:\n", + "\n", + "\\begin{equation*}\n", + " \\mathbf{W}=\\begin{pmatrix}\n", + " \\mathbf{w_1} & \\mathbf{w_2} & \\mathbf{w_2} \\\\\n", + " \\mathbf{w_2} & \\mathbf{w_1} & \\mathbf{w_2} \\\\\n", + " \\mathbf{w_2} & \\mathbf{w_2} & \\mathbf{w_1} \\\\\n", + " \\end{pmatrix},\n", + " \\mathbf{B}=\\begin{pmatrix}\n", + " \\mathbf{b}\\\\\\mathbf{b}\\\\\\mathbf{b}\n", + " \\end{pmatrix}\n", + " \\end{equation*}\n", + "\n", + "## Example 1: Optimizing a GNN with Fixed Graph\n", + "\n", + "Define a GCN in `torch_geometric` as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import torch\n", + "from torch.nn import Linear, ReLU\n", + "from torch_geometric.nn import Sequential, GCNConv\n", + "from torch_geometric.nn import global_mean_pool\n", + "from omlt.io.torch_geometric import gnn_with_fixed_graph\n", + "import pyomo.environ as pyo\n", + "from omlt import OmltBlock\n", + "\n", + "\n", + "def GCN_Sequential(activation, pooling):\n", + " torch.manual_seed(123)\n", + " return Sequential(\n", + " \"x, edge_index\",\n", + " [\n", + " (GCNConv(2, 4), \"x, edge_index -> x\"),\n", + " activation(),\n", + " (GCNConv(4, 4), \"x, edge_index -> x\"),\n", + " activation(),\n", + " Linear(4, 4),\n", + " (pooling, \"x, None -> x\"),\n", + " Linear(4, 2),\n", + " activation(),\n", + " Linear(2, 1),\n", + " ],\n", + " )\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This model has two types of `Linear` layers: the first linear layer maps in-features to out-features for each node, the last two linear layers map features after pooling. For illustration purposes, we use `load_torch_geometric_sequential` to show the transformed model in OMLT (this step is not needed for later formulation):" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\tInputLayer(input_size=[6], output_size=[6])\tlinear\n", + "1\tGNNLayer(input_size=[6], output_size=[12])\trelu\n", + "2\tGNNLayer(input_size=[12], output_size=[12])\trelu\n", + "3\tDenseLayer(input_size=[12], output_size=[12])\tlinear\n", + "4\tDenseLayer(input_size=[12], output_size=[4])\tlinear\n", + "5\tDenseLayer(input_size=[4], output_size=[2])\trelu\n", + "6\tDenseLayer(input_size=[2], output_size=[1])\tlinear\n" + ] + } + ], + "source": [ + "from omlt.io.torch_geometric import load_torch_geometric_sequential\n", + "\n", + "# define a GCN sequential model\n", + "nn = GCN_Sequential(ReLU, global_mean_pool)\n", + "# number of nodes\n", + "N = 3\n", + "# adjacency matrix\n", + "A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]])\n", + "\n", + "# load the model into OMLT\n", + "net = load_torch_geometric_sequential(nn, N, A)\n", + "\n", + "for layer_id, layer in enumerate(net.layers):\n", + " print(f\"{layer_id}\\t{layer}\\t{layer.activation}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Two GCN layers are rewritten into two `GNNLayer` in OMLT given $N$ and $A$. The first linear layer is expanded since it maps features of each node. The pooling layer is equivalently transformed into a `DenseLayer`. The last two linear layers are the same as before since features of each node are pooled.\n", + "\n", + "Besides giving $N$ and $A$, one needs to define bounds for inputs:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# define a GCN sequential model\n", + "nn1 = GCN_Sequential(ReLU, global_mean_pool)\n", + "# number of nodes\n", + "N = 3\n", + "# adjacency matrix\n", + "A = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]])\n", + "\n", + "# size of inputs = number of nodes x number of input features\n", + "input_size = [6]\n", + "# define lower and upper bounds for each input\n", + "input_bounds = {}\n", + "for i in range(input_size[0]):\n", + " input_bounds[(i)] = (-1.0, 1.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After having these information, the last step is to create an `OmltBlock` and build formulation in this block using `gnn_with_fixed_graph`:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Welcome to the CBC MILP Solver \n", + "Version: 2.10.10 \n", + "Build Date: Aug 1 2023 \n", + "\n", + "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT_test/bin/cbc -printingOptions all -import /var/tmp/pbs.8152010.pbs/tmpo87uiyi0.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.8152010.pbs/tmpo87uiyi0.pyomo.soln (default strategy 1)\n", + "Option for printingOptions changed from normal to all\n", + "Presolve 172 (-222) rows, 111 (-75) columns and 608 (-267) elements\n", + "Statistics for presolved model\n", + "Original problem has 26 integers (26 of which binary)\n", + "Presolved problem has 25 integers (25 of which binary)\n", + "==== 110 zero objective 2 different\n", + "1 variables have objective of -0.0421598\n", + "110 variables have objective of 0\n", + "==== absolute objective values 2 different\n", + "110 variables have objective of 0\n", + "1 variables have objective of 0.0421598\n", + "==== for integers 25 zero objective 1 different\n", + "25 variables have objective of 0\n", + "==== for integers absolute objective values 1 different\n", + "25 variables have objective of 0\n", + "===== end objective counts\n", + "\n", + "\n", + "Problem has 172 rows, 111 columns (1 with objective) and 608 elements\n", + "Column breakdown:\n", + "0 of type 0.0->inf, 49 of type 0.0->up, 0 of type lo->inf, \n", + "37 of type lo->up, 0 of type free, 0 of type fixed, \n", + "0 of type -inf->0.0, 0 of type -inf->up, 25 of type 0.0->1.0 \n", + "Row breakdown:\n", + "8 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, \n", + "5 of type E other, 0 of type G 0.0, 0 of type G 1.0, \n", + "0 of type G other, 134 of type L 0.0, 0 of type L 1.0, \n", + "25 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", + "0 of type Free \n", + "Continuous objective value is 0.315152 - 0.00 seconds\n", + "Cgl0003I 0 fixed, 0 tightened bounds, 2 strengthened rows, 0 substitutions\n", + "Cgl0004I processed model has 166 rows, 105 columns (25 integer (25 of which binary)) and 670 elements\n", + "Cbc0038I Initial state - 5 integers unsatisfied sum - 0.124759\n", + "Cbc0038I Pass 1: suminf. 0.00000 (0) obj. 0.317969 iterations 41\n", + "Cbc0038I Solution found of 0.317969\n", + "Cbc0038I Relaxing continuous gives 0.317969\n", + "Cbc0038I Before mini branch and bound, 20 integers at bound fixed and 63 continuous\n", + "Cbc0038I Full problem 166 rows 105 columns, reduced to 17 rows 13 columns\n", + "Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n", + "Cbc0038I Round again with cutoff of 0.317791\n", + "Cbc0038I Pass 2: suminf. 0.00876 (1) obj. 0.317791 iterations 11\n", + "Cbc0038I Pass 3: suminf. 0.18897 (1) obj. 0.317791 iterations 20\n", + "Cbc0038I Pass 4: suminf. 0.00876 (1) obj. 0.317791 iterations 58\n", + "Cbc0038I Pass 5: suminf. 0.18897 (1) obj. 0.317791 iterations 13\n", + "Cbc0038I Pass 6: suminf. 0.00876 (1) obj. 0.317791 iterations 21\n", + "Cbc0038I Pass 7: suminf. 0.00876 (1) obj. 0.317791 iterations 32\n", + "Cbc0038I Pass 8: suminf. 0.18897 (1) obj. 0.317791 iterations 16\n", + "Cbc0038I Pass 9: suminf. 0.00876 (1) obj. 0.317791 iterations 19\n", + "Cbc0038I Pass 10: suminf. 0.00876 (1) obj. 0.317791 iterations 57\n", + "Cbc0038I Pass 11: suminf. 0.18897 (1) obj. 0.317791 iterations 7\n", + "Cbc0038I Pass 12: suminf. 0.00876 (1) obj. 0.317791 iterations 7\n", + "Cbc0038I Pass 13: suminf. 0.00876 (1) obj. 0.317791 iterations 5\n", + "Cbc0038I Pass 14: suminf. 0.18897 (1) obj. 0.317791 iterations 7\n", + "Cbc0038I Pass 15: suminf. 0.00876 (1) obj. 0.317791 iterations 7\n", + "Cbc0038I Pass 16: suminf. 0.00876 (1) obj. 0.317791 iterations 10\n", + "Cbc0038I Pass 17: suminf. 0.18897 (1) obj. 0.317791 iterations 9\n", + "Cbc0038I Pass 18: suminf. 0.00876 (1) obj. 0.317791 iterations 8\n", + "Cbc0038I Pass 19: suminf. 0.00876 (1) obj. 0.317791 iterations 22\n", + "Cbc0038I Pass 20: suminf. 0.18897 (1) obj. 0.317791 iterations 6\n", + "Cbc0038I Pass 21: suminf. 0.00876 (1) obj. 0.317791 iterations 9\n", + "Cbc0038I Pass 22: suminf. 0.00876 (1) obj. 0.317791 iterations 17\n", + "Cbc0038I Pass 23: suminf. 0.18897 (1) obj. 0.317791 iterations 6\n", + "Cbc0038I Pass 24: suminf. 0.00876 (1) obj. 0.317791 iterations 5\n", + "Cbc0038I Pass 25: suminf. 0.00876 (1) obj. 0.317791 iterations 10\n", + "Cbc0038I Pass 26: suminf. 0.18897 (1) obj. 0.317791 iterations 6\n", + "Cbc0038I Pass 27: suminf. 0.00876 (1) obj. 0.317791 iterations 5\n", + "Cbc0038I Pass 28: suminf. 0.00876 (1) obj. 0.317791 iterations 30\n", + "Cbc0038I Pass 29: suminf. 0.18897 (1) obj. 0.317791 iterations 5\n", + "Cbc0038I Pass 30: suminf. 0.00876 (1) obj. 0.317791 iterations 6\n", + "Cbc0038I Pass 31: suminf. 0.00876 (1) obj. 0.317791 iterations 3\n", + "Cbc0038I No solution found this major pass\n", + "Cbc0038I Before mini branch and bound, 1 integers at bound fixed and 47 continuous\n", + "Cbc0038I Full problem 166 rows 105 columns, reduced to 48 rows 27 columns\n", + "Cbc0038I Mini branch and bound did not improve solution (0.02 seconds)\n", + "Cbc0038I After 0.02 seconds - Feasibility pump exiting with objective of 0.317969 - took 0.01 seconds\n", + "Cbc0012I Integer solution of 0.31796885 found by feasibility pump after 0 iterations and 0 nodes (0.02 seconds)\n", + "Cbc0038I Full problem 166 rows 105 columns, reduced to 48 rows 27 columns\n", + "Cbc0031I 3 added rows had average density of 3.3333333\n", + "Cbc0013I At root node, 31 cuts changed objective from 0.31628066 to 0.31796885 in 1 passes\n", + "Cbc0014I Cut generator 0 (Probing) - 19 row cuts average 3.0 elements, 1 column cuts (1 active) in 0.000 seconds - new frequency is 1\n", + "Cbc0014I Cut generator 1 (Gomory) - 3 row cuts average 8.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", + "Cbc0014I Cut generator 2 (Knapsack) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", + "Cbc0014I Cut generator 3 (Clique) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", + "Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 3 row cuts average 3.3 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", + "Cbc0014I Cut generator 5 (FlowCover) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", + "Cbc0014I Cut generator 6 (TwoMirCuts) - 6 row cuts average 6.2 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", + "Cbc0001I Search completed - best objective 0.3179688539269278, took 17 iterations and 0 nodes (0.02 seconds)\n", + "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", + "Cuts at root node changed objective from 0.316281 to 0.317969\n", + "Probing was tried 1 times and created 20 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Gomory was tried 1 times and created 3 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Knapsack was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Clique was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "MixedIntegerRounding2 was tried 1 times and created 3 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "FlowCover was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "TwoMirCuts was tried 1 times and created 6 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "ZeroHalf was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "\n", + "Result - Optimal solution found\n", + "\n", + "Objective value: 0.31796885\n", + "Enumerated nodes: 0\n", + "Total iterations: 17\n", + "Time (CPU seconds): 0.02\n", + "Time (Wallclock seconds): 0.02\n", + "\n", + "Total time (CPU seconds): 0.03 (Wallclock seconds): 0.03\n", + "\n" + ] + } + ], + "source": [ + "# create pyomo model\n", + "m1 = pyo.ConcreteModel()\n", + "\n", + "# create an OMLT block for the neural network and build its formulation\n", + "m1.nn = OmltBlock()\n", + "\n", + "# build formulation in block m.nn\n", + "gnn_with_fixed_graph(m1.nn, nn1, N, A, scaled_input_bounds=input_bounds)\n", + "\n", + "# set the objective as the single output of the model\n", + "m1.obj = pyo.Objective(expr=m1.nn.outputs[0])\n", + "\n", + "# solve the optimization problem\n", + "status = pyo.SolverFactory(\"cbc\").solve(m1, tee=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can evaluate the solution in original model to verify it:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.31796885]]\n" + ] + } + ], + "source": [ + "X = []\n", + "edges = []\n", + "for u in range(N):\n", + " for v in range(N):\n", + " if u != v and pyo.value(m1.nn.A[u, v]):\n", + " edges.append((u, v))\n", + "for i in range(6):\n", + " X.append(pyo.value(m1.nn.inputs[i]))\n", + "X = np.array(X).reshape(3, 2)\n", + "edges = np.transpose(np.array(edges)).reshape(2, -1)\n", + "nn.eval()\n", + "print(nn1(torch.tensor(X).float(), torch.tensor(edges)).detach().numpy())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2: Optimizing a GNN with Non-Fixed Graph\n", + "\n", + "Since GCN is not supported when the input graph is not fixed, we define a SAGE in `torch_geometric` as follows:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import torch\n", + "from torch.nn import Linear, ReLU, Sigmoid\n", + "from torch_geometric.nn import Sequential, SAGEConv\n", + "from torch_geometric.nn import global_add_pool\n", + "from omlt.io.torch_geometric import gnn_with_non_fixed_graph\n", + "\n", + "import pyomo.environ as pyo\n", + "from omlt import OmltBlock\n", + "\n", + "\n", + "def SAGE_Sequential(activation, pooling):\n", + " torch.manual_seed(123)\n", + " return Sequential(\n", + " \"x, edge_index\",\n", + " [\n", + " (SAGEConv(2, 4, aggr=\"sum\"), \"x, edge_index -> x\"),\n", + " activation(),\n", + " (SAGEConv(4, 4, aggr=\"sum\"), \"x, edge_index -> x\"),\n", + " activation(),\n", + " Linear(4, 4),\n", + " (pooling, \"x, None -> x\"),\n", + " Linear(4, 2),\n", + " activation(),\n", + " Linear(2, 1),\n", + " ],\n", + " )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We follow the same procedure as in Example 1 except that $A$ is no longer needed for `gnn_with_non_fixed_graph`:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Welcome to the CBC MILP Solver \n", + "Version: 2.10.10 \n", + "Build Date: Aug 1 2023 \n", + "\n", + "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT_test/bin/cbc -printingOptions all -import /var/tmp/pbs.8152010.pbs/tmpnzmuzmeh.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.8152010.pbs/tmpnzmuzmeh.pyomo.soln (default strategy 1)\n", + "Option for printingOptions changed from normal to all\n", + "Presolve 260 (-137) rows, 141 (-51) columns and 876 (-197) elements\n", + "Statistics for presolved model\n", + "Original problem has 32 integers (32 of which binary)\n", + "Presolved problem has 29 integers (29 of which binary)\n", + "==== 139 zero objective 3 different\n", + "139 variables have objective of 0\n", + "1 variables have objective of 0.203177\n", + "1 variables have objective of 0.686721\n", + "==== absolute objective values 3 different\n", + "139 variables have objective of 0\n", + "1 variables have objective of 0.203177\n", + "1 variables have objective of 0.686721\n", + "==== for integers 29 zero objective 1 different\n", + "29 variables have objective of 0\n", + "==== for integers absolute objective values 1 different\n", + "29 variables have objective of 0\n", + "===== end objective counts\n", + "\n", + "\n", + "Problem has 260 rows, 141 columns (2 with objective) and 876 elements\n", + "Column breakdown:\n", + "0 of type 0.0->inf, 62 of type 0.0->up, 0 of type lo->inf, \n", + "50 of type lo->up, 0 of type free, 0 of type fixed, \n", + "0 of type -inf->0.0, 0 of type -inf->up, 29 of type 0.0->1.0 \n", + "Row breakdown:\n", + "0 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, \n", + "26 of type E other, 0 of type G 0.0, 0 of type G 1.0, \n", + "0 of type G other, 130 of type L 0.0, 24 of type L 1.0, \n", + "80 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", + "0 of type Free \n", + "Continuous objective value is 0.107106 - 0.00 seconds\n", + "Cgl0003I 0 fixed, 0 tightened bounds, 4 strengthened rows, 0 substitutions\n", + "Cgl0004I processed model has 237 rows, 118 columns (29 integer (29 of which binary)) and 989 elements\n", + "Cbc0038I Initial state - 17 integers unsatisfied sum - 3.14435\n", + "Cbc0038I Pass 1: suminf. 1.01765 (9) obj. 0.107106 iterations 71\n", + "Cbc0038I Solution found of 0.107106\n", + "Cbc0038I Relaxing continuous gives 0.107106\n", + "Cbc0038I Before mini branch and bound, 12 integers at bound fixed and 38 continuous\n", + "Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n", + "Cbc0038I After 0.01 seconds - Feasibility pump exiting with objective of 0.107106 - took 0.00 seconds\n", + "Cbc0012I Integer solution of 0.10710584 found by feasibility pump after 0 iterations and 0 nodes (0.01 seconds)\n", + "Cbc0001I Search completed - best objective 0.1071058437228203, took 0 iterations and 0 nodes (0.01 seconds)\n", + "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", + "Cuts at root node changed objective from 0.107106 to 0.107106\n", + "Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "\n", + "Result - Optimal solution found\n", + "\n", + "Objective value: 0.10710584\n", + "Enumerated nodes: 0\n", + "Total iterations: 0\n", + "Time (CPU seconds): 0.01\n", + "Time (Wallclock seconds): 0.01\n", + "\n", + "Total time (CPU seconds): 0.01 (Wallclock seconds): 0.02\n", + "\n" + ] + } + ], + "source": [ + "# define a GAGE sequential model\n", + "nn2 = SAGE_Sequential(ReLU, global_add_pool)\n", + "# number of nodes\n", + "N = 3\n", + "\n", + "# size of inputs = number of nodes x number of input features\n", + "input_size = [6]\n", + "# define lower and upper bounds for each input\n", + "input_bounds = {}\n", + "for i in range(input_size[0]):\n", + " input_bounds[(i)] = (-1.0, 1.0)\n", + "\n", + "# create pyomo model\n", + "m2 = pyo.ConcreteModel()\n", + "\n", + "# create an OMLT block for the neural network and build its formulation\n", + "m2.nn = OmltBlock()\n", + "\n", + "# build formulation in block m.nn\n", + "gnn_with_non_fixed_graph(m2.nn, nn2, N, scaled_input_bounds=input_bounds)\n", + "\n", + "# set the objective as the single output of the model\n", + "m2.obj = pyo.Objective(expr=m2.nn.outputs[0])\n", + "\n", + "# solve the optimization problem\n", + "status = pyo.SolverFactory(\"cbc\").solve(m2, tee=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For smooth activation function like Sigmoid, a smooth optimization solvers (such as Ipopt) is needed:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ipopt 3.14.12: \n", + "==> Warning: Treating 6 binary and 0 integer variables as continuous.\n", + "\n", + "\n", + "******************************************************************************\n", + "This program contains Ipopt, a library for large-scale nonlinear optimization.\n", + " Ipopt is released as open source code under the Eclipse Public License (EPL).\n", + " For more information visit https://github.com/coin-or/Ipopt\n", + "******************************************************************************\n", + "\n", + "This is Ipopt version 3.14.12, running with linear solver MUMPS 5.2.1.\n", + "\n", + "Number of nonzeros in equality constraint Jacobian...: 449\n", + "Number of nonzeros in inequality constraint Jacobian.: 468\n", + "Number of nonzeros in Lagrangian Hessian.............: 26\n", + "\n", + "Total number of variables............................: 166\n", + " variables with only lower bounds: 0\n", + " variables with lower and upper bounds: 164\n", + " variables with only upper bounds: 0\n", + "Total number of equality constraints.................: 103\n", + "Total number of inequality constraints...............: 216\n", + " inequality constraints with only lower bounds: 0\n", + " inequality constraints with lower and upper bounds: 0\n", + " inequality constraints with only upper bounds: 216\n", + "\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 0 0.0000000e+00 6.52e-01 7.52e-04 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0\n", + " 1 1.4746296e-02 6.32e-01 1.39e+00 -1.0 8.66e-01 - 1.28e-02 3.08e-02f 1\n", + " 2 3.1873491e-01 2.12e-01 1.91e+01 -1.0 1.08e+00 - 3.20e-02 6.65e-01f 1\n", + " 3 3.3291931e-01 1.93e-01 1.56e+01 -1.0 3.34e-01 - 7.50e-01 9.04e-02f 1\n", + " 4 4.1605860e-01 8.12e-02 6.77e+00 -1.0 3.72e-01 - 5.03e-01 5.79e-01f 1\n", + " 5 4.4666096e-01 4.00e-02 1.79e+01 -1.0 3.96e-01 - 7.08e-01 5.07e-01h 1\n", + " 6 4.6317765e-01 1.82e-02 8.24e+01 -1.0 2.77e-01 - 1.00e+00 5.44e-01h 1\n", + " 7 4.7137936e-01 7.43e-03 1.79e+02 -1.0 1.71e-01 - 1.00e+00 5.93e-01h 1\n", + " 8 4.7469933e-01 3.08e-03 4.39e+02 -1.0 6.74e-02 - 1.00e+00 5.85e-01h 1\n", + " 9 4.7608122e-01 1.28e-03 1.06e+03 -1.0 2.81e-02 - 1.00e+00 5.86e-01h 1\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 10 4.7665353e-01 5.29e-04 2.55e+03 -1.0 1.16e-02 - 1.00e+00 5.86e-01h 1\n", + " 11 4.7689072e-01 2.19e-04 6.15e+03 -1.0 4.81e-03 - 1.00e+00 5.86e-01h 1\n", + " 12 4.7698895e-01 9.04e-05 1.48e+04 -1.0 1.99e-03 - 1.00e+00 5.87e-01h 1\n", + " 13 4.7702965e-01 3.72e-05 3.54e+04 -1.0 8.22e-04 - 1.00e+00 5.88e-01h 1\n", + " 14 4.7703175e-01 3.44e-05 1.90e+05 -1.0 3.38e-04 - 1.00e+00 7.40e-02f 4\n", + " 15 4.7705226e-01 7.65e-06 8.24e+04 -1.0 3.13e-04 - 1.00e+00 7.78e-01h 1\n", + " 16 4.7705268e-01 7.10e-06 7.71e+05 -1.0 6.96e-05 - 1.00e+00 7.20e-02f 4\n", + " 17 4.7705708e-01 1.35e-06 2.87e+05 -1.0 6.46e-05 - 1.00e+00 8.10e-01h 1\n", + " 18 4.7705717e-01 1.24e-06 2.66e+06 -1.0 1.23e-05 - 1.00e+00 8.39e-02f 4\n", + " 19 4.7705812e-01 1.73e-12 1.00e-06 -1.0 1.13e-05 - 1.00e+00 1.00e+00h 1\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 20 4.7704910e-01 6.57e-09 9.15e+03 -5.7 5.47e-04 - 9.99e-01 1.00e+00f 1\n", + " 21 4.7241100e-01 2.07e-03 4.56e+03 -5.7 2.94e-01 - 5.74e-01 9.31e-01f 1\n", + " 22 4.7107356e-01 1.09e-03 1.39e+03 -5.7 1.83e-01 - 6.98e-01 8.54e-01h 1\n", + " 23 4.7049903e-01 3.12e-03 2.62e+02 -5.7 3.65e-01 - 8.13e-01 8.89e-01f 1\n", + " 24 4.7022019e-01 3.61e-03 3.33e+01 -5.7 5.62e-01 - 8.71e-01 5.90e-01f 1\n", + " 25 4.7016027e-01 4.04e-04 7.29e-01 -5.7 2.34e-01 - 9.79e-01 1.00e+00f 1\n", + " 26 4.7014863e-01 2.24e-05 7.68e-08 -5.7 3.49e-02 - 1.00e+00 1.00e+00h 1\n", + " 27 4.7014848e-01 2.14e-08 1.85e-11 -5.7 8.68e-04 - 1.00e+00 1.00e+00h 1\n", + " 28 4.7004983e-01 2.73e-04 3.48e+00 -8.6 1.95e-01 - 8.70e-01 8.51e-01h 1\n", + " 29 4.7002727e-01 1.61e-04 1.42e-01 -8.6 7.82e-02 - 9.74e-01 9.83e-01h 1\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 30 4.7002699e-01 1.53e-06 2.93e-09 -8.6 7.19e-03 - 1.00e+00 1.00e+00f 1\n", + " 31 4.7002699e-01 1.63e-10 2.98e-13 -8.6 7.38e-05 - 1.00e+00 1.00e+00h 1\n", + "\n", + "Number of Iterations....: 31\n", + "\n", + " (scaled) (unscaled)\n", + "Objective...............: 4.7002698793134651e-01 4.7002698793134651e-01\n", + "Dual infeasibility......: 2.9843906102589463e-13 2.9843906102589463e-13\n", + "Constraint violation....: 1.6278367542810201e-10 1.6278367542810201e-10\n", + "Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00\n", + "Complementarity.........: 2.5060961140067687e-09 2.5060961140067687e-09\n", + "Overall NLP error.......: 2.5060961140067687e-09 2.5060961140067687e-09\n", + "\n", + "\n", + "Number of objective function evaluations = 41\n", + "Number of objective gradient evaluations = 32\n", + "Number of equality constraint evaluations = 41\n", + "Number of inequality constraint evaluations = 41\n", + "Number of equality constraint Jacobian evaluations = 32\n", + "Number of inequality constraint Jacobian evaluations = 32\n", + "Number of Lagrangian Hessian evaluations = 31\n", + "Total seconds in IPOPT = 0.065\n", + "\n", + "EXIT: Optimal Solution Found.\n", + "\b" + ] + } + ], + "source": [ + "# define a GAGE sequential model\n", + "nn3 = SAGE_Sequential(Sigmoid, global_add_pool)\n", + "# number of nodes\n", + "N = 3\n", + "\n", + "# size of inputs = number of nodes x number of input features\n", + "input_size = [6]\n", + "# define lower and upper bounds for each input\n", + "input_bounds = {}\n", + "for i in range(input_size[0]):\n", + " input_bounds[(i)] = (-1.0, 1.0)\n", + "\n", + "# create pyomo model\n", + "m3 = pyo.ConcreteModel()\n", + "\n", + "# create an OMLT block for the neural network and build its formulation\n", + "m3.nn = OmltBlock()\n", + "\n", + "# build formulation in block m.nn\n", + "gnn_with_non_fixed_graph(m3.nn, nn3, N, scaled_input_bounds=input_bounds)\n", + "\n", + "# set the objective as the single output of the model\n", + "m3.obj = pyo.Objective(expr=m3.nn.outputs[0])\n", + "\n", + "# solve the optimization problem\n", + "status = pyo.SolverFactory(\"ipopt\").solve(m3, tee=True)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [conda env:OMLT_test]", + "language": "python", + "name": "conda-env-OMLT_test-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.17" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/src/omlt/io/torch_geometric/__init__.py b/src/omlt/io/torch_geometric/__init__.py index a626e86f..50dc3555 100644 --- a/src/omlt/io/torch_geometric/__init__.py +++ b/src/omlt/io/torch_geometric/__init__.py @@ -1,3 +1,8 @@ from omlt.io.torch_geometric.torch_geometric_reader import ( load_torch_geometric_sequential, ) + +from omlt.io.torch_geometric.build_gnn_formulation import ( + gnn_with_fixed_graph, + gnn_with_non_fixed_graph, +) diff --git a/src/omlt/io/torch_geometric/build_gnn_formulation.py b/src/omlt/io/torch_geometric/build_gnn_formulation.py new file mode 100644 index 00000000..f63af267 --- /dev/null +++ b/src/omlt/io/torch_geometric/build_gnn_formulation.py @@ -0,0 +1,148 @@ +import numpy as np +import pyomo.environ as pyo +from omlt.neuralnet import FullSpaceNNFormulation +from omlt.io.torch_geometric import load_torch_geometric_sequential + + +def gnn_with_non_fixed_graph( + block, + nn, + N, + scaling_object=None, + scaled_input_bounds=None, + unscaled_input_bounds=None, +): + """ + Build formulation for a torch_geometric graph neural network model (built with Sequential). + Since the input graph is not fixed, the elements in adjacency matrix are decision variables. + + Parameters + ---------- + block : Block + the Pyomo block + nn : torch_geometric.model + A torch_geometric model that was built with Sequential + N : int + The number of nodes of input graph + scaling_object : instance of ScalingInterface or None + Provide an instance of a scaling object to use to scale iputs --> scaled_inputs + and scaled_outputs --> outputs. If None, no scaling is performed. See scaling.py. + scaled_input_bounds : dict or None + A dict that contains the bounds on the scaled variables (the + direct inputs to the neural network). If None, then no bounds + are specified or they are generated using unscaled bounds. + unscaled_input_bounds : dict or None + A dict that contains the bounds on the unscaled variables (the + direct inputs to the neural network). If specified the scaled_input_bounds + dictionary will be generated using the provided scaling object. + If None, then no bounds are specified. + + Returns + ------- + OmltBlock (formulated) + """ + + # build NetworkDefinition for nn + net = load_torch_geometric_sequential( + nn=nn, + N=N, + A=None, + scaling_object=scaling_object, + scaled_input_bounds=scaled_input_bounds, + unscaled_input_bounds=unscaled_input_bounds, + ) + + # define binary variables for adjacency matrix + block.A = pyo.Var( + pyo.Set(initialize=range(N)), + pyo.Set(initialize=range(N)), + within=pyo.Binary, + ) + # assume that the self contribution always exists + for u in range(N): + block.A[u, u].fix(1) + # assume the adjacency matrix is always symmetric + block.symmetric_adjacency = pyo.ConstraintList() + for u in range(N): + for v in range(u + 1, N): + block.symmetric_adjacency.add((block.A[u, v] == block.A[v, u])) + + # build formulation for GNN + block.build_formulation(FullSpaceNNFormulation(net)) + + return block + + +def gnn_with_fixed_graph( + block, + nn, + N, + A, + scaling_object=None, + scaled_input_bounds=None, + unscaled_input_bounds=None, +): + """ + Build formulation for a torch_geometric graph neural network model (built with Sequential). + Given the adjacency matrix, the input graph structure is fixed. + + Parameters + ---------- + block : Block + the Pyomo block + nn : torch_geometric.model + A torch_geometric model that was built with Sequential + N : int + The number of nodes of input graph + A : matrix-like + The adjacency matrix of input graph + scaling_object : instance of ScalingInterface or None + Provide an instance of a scaling object to use to scale iputs --> scaled_inputs + and scaled_outputs --> outputs. If None, no scaling is performed. See scaling.py. + scaled_input_bounds : dict or None + A dict that contains the bounds on the scaled variables (the + direct inputs to the neural network). If None, then no bounds + are specified or they are generated using unscaled bounds. + unscaled_input_bounds : dict or None + A dict that contains the bounds on the unscaled variables (the + direct inputs to the neural network). If specified the scaled_input_bounds + dictionary will be generated using the provided scaling object. + If None, then no bounds are specified. + + Returns + ------- + OmltBlock (formulated) + """ + + # assume the adjacency matrix is always symmetric + assert np.array_equal(A, np.transpose(A)) + + # build NetworkDefinition for nn + net = load_torch_geometric_sequential( + nn=nn, + N=N, + A=A, + scaling_object=scaling_object, + scaled_input_bounds=scaled_input_bounds, + unscaled_input_bounds=unscaled_input_bounds, + ) + + # define binary variables for adjacency matrix + block.A = pyo.Var( + pyo.Set(initialize=range(N)), + pyo.Set(initialize=range(N)), + within=pyo.Binary, + ) + # fix A using given values + for u in range(N): + for v in range(N): + block.A[u, v].fix(A[u, v]) + + # assume that the self contribution always exists + for u in range(N): + block.A[u, u].fix(1) + + # build formulation for GNN + block.build_formulation(FullSpaceNNFormulation(net)) + + return block diff --git a/tests/io/test_torch_geometric_reader.py b/tests/io/test_torch_geometric.py similarity index 52% rename from tests/io/test_torch_geometric_reader.py rename to tests/io/test_torch_geometric.py index 5e777720..076dccde 100644 --- a/tests/io/test_torch_geometric_reader.py +++ b/tests/io/test_torch_geometric.py @@ -1,5 +1,7 @@ import pytest import numpy as np +import pyomo.environ as pyo +from omlt import OmltBlock from omlt.dependencies import ( torch, @@ -13,7 +15,11 @@ from torch_geometric.nn import Sequential, GCNConv, SAGEConv from torch_geometric.nn import global_mean_pool, global_add_pool from torch_geometric.utils import erdos_renyi_graph - from omlt.io.torch_geometric import load_torch_geometric_sequential + from omlt.io.torch_geometric import ( + load_torch_geometric_sequential, + gnn_with_fixed_graph, + gnn_with_non_fixed_graph, + ) @pytest.mark.skipif( @@ -72,7 +78,7 @@ def generate_random_inputs(N, F, seed, p): u = edges[0, k].numpy() v = edges[1, k].numpy() A[u, v] = 1 - x = 2.0 * torch.rand((N, F)) - 1.0 + x = 1.0 * torch.randint(1, (N, F)) return x, edges, np.squeeze(x.numpy().reshape(1, -1)), A @@ -95,6 +101,60 @@ def _test_torch_geometric_reader(nn): assert abs(y - y_np) < 1e-6 +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def _test_gnn_with_fixed_graph(nn): + N = 4 + F = 2 + nn.eval() + for p in range(10): + x, edges, x_np, A = generate_random_inputs(N, F, 0, p / 10.0) + y = nn(x, edges).detach().numpy() + input_size = [N * F] + input_bounds = {} + for i in range(input_size[0]): + input_bounds[(i)] = (0.0, 1.0) + m = pyo.ConcreteModel() + m.nn = OmltBlock() + gnn_with_fixed_graph(m.nn, nn, N, A, scaled_input_bounds=input_bounds) + for i in range(N * F): + m.nn.inputs[i].fix(x_np[i]) + m.obj = pyo.Objective(expr=m.nn.outputs[0]) + status = pyo.SolverFactory("cbc").solve(m, tee=False) + assert abs(pyo.value(m.nn.outputs[0]) - y) < 1e-6 + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def _test_gnn_with_non_fixed_graph(nn): + N = 4 + F = 2 + nn.eval() + for p in range(10): + x, edges, x_np, A = generate_random_inputs(N, F, 0, p / 10.0) + y = nn(x, edges).detach().numpy() + input_size = [N * F] + input_bounds = {} + for i in range(input_size[0]): + input_bounds[(i)] = (-1.0, 1.0) + m = pyo.ConcreteModel() + m.nn = OmltBlock() + gnn_with_non_fixed_graph(m.nn, nn, N, scaled_input_bounds=input_bounds) + for i in range(N * F): + m.nn.inputs[i].fix(x_np[i]) + for u in range(N): + for v in range(N): + if u != v: + m.nn.A[u, v].fix(A[u, v]) + m.obj = pyo.Objective(expr=m.nn.outputs[0]) + status = pyo.SolverFactory("cbc").solve(m, tee=False) + assert abs(pyo.value(m.nn.outputs[0]) - y) < 1e-6 + + @pytest.mark.skipif( not (torch_available and torch_geometric_available), reason="Test only valid when torch and torch_geometric are available", @@ -108,3 +168,29 @@ def test_torch_geometric_reader(): for root_weight in [False, True]: nn = SAGE_Sequential(activation, pooling, aggr, root_weight) _test_torch_geometric_reader(nn) + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def test_gnn_with_fixed_graph(): + for pooling in [global_mean_pool, global_add_pool]: + nn = GCN_Sequential(ReLU, pooling) + _test_gnn_with_fixed_graph(nn) + for aggr in ["sum", "mean"]: + for root_weight in [False, True]: + nn = SAGE_Sequential(ReLU, pooling, aggr, root_weight) + _test_gnn_with_fixed_graph(nn) + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def test_gnn_with_non_fixed_graph(): + for pooling in [global_mean_pool, global_add_pool]: + for aggr in ["sum"]: + for root_weight in [False, True]: + nn = SAGE_Sequential(ReLU, pooling, aggr, root_weight) + _test_gnn_with_non_fixed_graph(nn) diff --git a/tests/notebooks/test_run_notebooks.py b/tests/notebooks/test_run_notebooks.py index 10083768..85c3d304 100644 --- a/tests/notebooks/test_run_notebooks.py +++ b/tests/notebooks/test_run_notebooks.py @@ -4,7 +4,12 @@ from pyomo.common.fileutils import this_file_dir from testbook import testbook -from omlt.dependencies import keras_available, onnx_available +from omlt.dependencies import ( + keras_available, + onnx_available, + torch_available, + torch_geometric_available, +) # TODO: These will be replaced with stronger tests using testbook soon @@ -52,3 +57,11 @@ def test_mnist_example_dense(): @pytest.mark.skipif(not keras_available, reason="keras needed for this notebook") def test_neural_network_formulations(): _test_run_notebook("neuralnet", "neural_network_formulations.ipynb", 21) + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="torch and torch_geometric needed for this notebook", +) +def test_graph_neural_network_formulation(): + _test_run_notebook("neuralnet", "graph_neural_network_formulation.ipynb", 8) From 6ef1aa83d04bf342d9c0f6b8d09a6e7c54771ece Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Mon, 28 Aug 2023 16:45:16 +0100 Subject: [PATCH 06/27] fix format issue --- .vscode/extensions.json | 5 +++++ src/omlt/neuralnet/layers/full_space.py | 2 +- 2 files changed, 6 insertions(+), 1 deletion(-) create mode 100644 .vscode/extensions.json diff --git a/.vscode/extensions.json b/.vscode/extensions.json new file mode 100644 index 00000000..9f30a5e4 --- /dev/null +++ b/.vscode/extensions.json @@ -0,0 +1,5 @@ +{ + "recommendations": [ + "ms-python.flake8" + ] +} \ No newline at end of file diff --git a/src/omlt/neuralnet/layers/full_space.py b/src/omlt/neuralnet/layers/full_space.py index 9c13fb44..8d4530b3 100644 --- a/src/omlt/neuralnet/layers/full_space.py +++ b/src/omlt/neuralnet/layers/full_space.py @@ -62,7 +62,7 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): A_{v_i,v_j}&\in \{0,1\} \end{align*} - where :math:`M_{j}` is upper bound of :math:`|z_{j}|`. + where :math:`M_{j}` is upper bound of :math:`|z_{j}|`. """ input_layer, input_layer_block = _input_layer_and_block(net_block, net, layer) From 67446c784a2e77fab7d4bd87fda18727af1e7b4d Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Mon, 28 Aug 2023 17:04:35 +0100 Subject: [PATCH 07/27] fix formate issue --- .vscode/extensions.json | 5 ----- 1 file changed, 5 deletions(-) delete mode 100644 .vscode/extensions.json diff --git a/.vscode/extensions.json b/.vscode/extensions.json deleted file mode 100644 index 9f30a5e4..00000000 --- a/.vscode/extensions.json +++ /dev/null @@ -1,5 +0,0 @@ -{ - "recommendations": [ - "ms-python.flake8" - ] -} \ No newline at end of file From 27175bdaebcbe7396b1f377a6db0b640a7d66128 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Tue, 29 Aug 2023 10:04:49 +0100 Subject: [PATCH 08/27] add test dependencies --- setup.cfg | 2 ++ 1 file changed, 2 insertions(+) diff --git a/setup.cfg b/setup.cfg index ff8eb614..aa1ae5e4 100644 --- a/setup.cfg +++ b/setup.cfg @@ -87,6 +87,7 @@ testing = torchvision tqdm protobuf==3.20.3 + torch_geometric testing_lean = setuptools @@ -104,6 +105,7 @@ testing_lean = torch torchvision tqdm + torch_geometric [options.entry_points] # Add here console scripts like: From 8cc976108ae6c4cdae260d830b3b60cb6b8a74b6 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Tue, 29 Aug 2023 11:08:40 +0100 Subject: [PATCH 09/27] update GNN formulation --- src/omlt/neuralnet/layers/full_space.py | 40 ++++++++++++------------- 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/src/omlt/neuralnet/layers/full_space.py b/src/omlt/neuralnet/layers/full_space.py index 8d4530b3..9eb36de3 100644 --- a/src/omlt/neuralnet/layers/full_space.py +++ b/src/omlt/neuralnet/layers/full_space.py @@ -57,12 +57,12 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): .. math:: \begin{align*} - z_{j} - M_{j}(1-A_{v_i,v_j}) &\le \bar z_{ij} \le z_{j} + M_{j}(1-A_{v_i,v_j})\\ - - M_{j}A_{v_i,v_j} &\le \bar z_{ij} \le M_{j}A_{v_i,v_j}\\ + z_{j} - (U_{j}-L_{j})(1-A_{v_i,v_j}) &\le \bar z_{ij} \le z_{j} + (U_{j}-L_{j})(1-A_{v_i,v_j})\\ + L_{j}A_{v_i,v_j} &\le \bar z_{ij} \le U_{j}A_{v_i,v_j}\\ A_{v_i,v_j}&\in \{0,1\} \end{align*} - where :math:`M_{j}` is upper bound of :math:`|z_{j}|`. + where :math:`L_{j}` and :math:`U_{j}` are the lower and upper bound of :math:`z_{j}`, respectively. """ input_layer, input_layer_block = _input_layer_and_block(net_block, net, layer) @@ -88,20 +88,22 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): pyo.Set(initialize=layer.input_indexes), pyo.Set(initialize=range(layer.N)), ) - # set dummy parameters here to avoid warning message from Pyomo - input_layer_block._abs_bound_big_m = pyo.Param( - layer.input_indexes, default=1e6, mutable=True - ) for local_index, input_index in layer.input_indexes_with_input_layer_indexes: lb, ub = input_layer_block.z[input_index].bounds - input_layer_block._abs_bound_big_m[local_index] = max(abs(lb), abs(ub)) input_node_index = local_index[-1] // layer.gnn_input_size for output_node_index in range(layer.N): - input_layer_block.zbar[local_index, output_node_index].setlb(min(0, lb)) - input_layer_block.zbar[local_index, output_node_index].setub(max(0, ub)) + if not net_block.A[input_node_index, output_node_index].fixed: + input_layer_block.zbar[input_index, output_node_index].setlb(min(0, lb)) + input_layer_block.zbar[input_index, output_node_index].setub(max(0, ub)) + elif pyo.value(net_block.A[input_node_index, output_node_index]) == 1: + input_layer_block.zbar[input_index, output_node_index].setlb(lb) + input_layer_block.zbar[input_index, output_node_index].setub(ub) + elif pyo.value(net_block.A[input_node_index, output_node_index]) == 0: + input_layer_block.zbar[input_index, output_node_index].setlb(0) + input_layer_block.zbar[input_index, output_node_index].setub(0) input_layer_block._zbar_lower_bound_z_big_m[ local_index, output_node_index @@ -109,9 +111,9 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): local_index, output_node_index ] >= input_layer_block.z[ input_index - ] - input_layer_block._abs_bound_big_m[ - local_index - ] * ( + ] - ( + ub - lb + ) * ( 1.0 - net_block.A[input_node_index, output_node_index] ) @@ -121,9 +123,9 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): local_index, output_node_index ] <= input_layer_block.z[ input_index - ] + input_layer_block._abs_bound_big_m[ - local_index - ] * ( + ] + ( + ub - lb + ) * ( 1.0 - net_block.A[input_node_index, output_node_index] ) @@ -131,16 +133,14 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): local_index, output_node_index ] = ( input_layer_block.zbar[local_index, output_node_index] - >= -input_layer_block._abs_bound_big_m[local_index] - * net_block.A[input_node_index, output_node_index] + >= lb * net_block.A[input_node_index, output_node_index] ) input_layer_block._zbar_upper_bound_big_m[ local_index, output_node_index ] = ( input_layer_block.zbar[local_index, output_node_index] - <= input_layer_block._abs_bound_big_m[local_index] - * net_block.A[input_node_index, output_node_index] + <= ub * net_block.A[input_node_index, output_node_index] ) @layer_block.Constraint(layer.output_indexes) From b75b99134ccf8316a682998a4c54a5db60ad5aff Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Tue, 29 Aug 2023 11:47:21 +0100 Subject: [PATCH 10/27] update GNN formulation --- src/omlt/io/__init__.py | 6 +++++- tests/io/test_torch_geometric.py | 2 +- 2 files changed, 6 insertions(+), 2 deletions(-) diff --git a/src/omlt/io/__init__.py b/src/omlt/io/__init__.py index c1e7f852..1cee46ad 100644 --- a/src/omlt/io/__init__.py +++ b/src/omlt/io/__init__.py @@ -16,4 +16,8 @@ from omlt.io.keras import load_keras_sequential if torch_available and torch_geometric_available: - from omlt.io.torch_geometric import load_torch_geometric_sequential + from omlt.io.torch_geometric import ( + load_torch_geometric_sequential, + gnn_with_fixed_graph, + gnn_with_non_fixed_graph, + ) diff --git a/tests/io/test_torch_geometric.py b/tests/io/test_torch_geometric.py index 076dccde..6f9c48f9 100644 --- a/tests/io/test_torch_geometric.py +++ b/tests/io/test_torch_geometric.py @@ -15,7 +15,7 @@ from torch_geometric.nn import Sequential, GCNConv, SAGEConv from torch_geometric.nn import global_mean_pool, global_add_pool from torch_geometric.utils import erdos_renyi_graph - from omlt.io.torch_geometric import ( + from omlt.io import ( load_torch_geometric_sequential, gnn_with_fixed_graph, gnn_with_non_fixed_graph, From 13261386e398576d2e60b1ebac5f1b3c549476af Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Tue, 29 Aug 2023 12:37:59 +0100 Subject: [PATCH 11/27] update GNN formulation --- src/omlt/io/__init__.py | 7 ------- tests/io/test_torch_geometric.py | 2 +- 2 files changed, 1 insertion(+), 8 deletions(-) diff --git a/src/omlt/io/__init__.py b/src/omlt/io/__init__.py index 1cee46ad..13b40c8c 100644 --- a/src/omlt/io/__init__.py +++ b/src/omlt/io/__init__.py @@ -14,10 +14,3 @@ if keras_available: from omlt.io.keras import load_keras_sequential - -if torch_available and torch_geometric_available: - from omlt.io.torch_geometric import ( - load_torch_geometric_sequential, - gnn_with_fixed_graph, - gnn_with_non_fixed_graph, - ) diff --git a/tests/io/test_torch_geometric.py b/tests/io/test_torch_geometric.py index 6f9c48f9..076dccde 100644 --- a/tests/io/test_torch_geometric.py +++ b/tests/io/test_torch_geometric.py @@ -15,7 +15,7 @@ from torch_geometric.nn import Sequential, GCNConv, SAGEConv from torch_geometric.nn import global_mean_pool, global_add_pool from torch_geometric.utils import erdos_renyi_graph - from omlt.io import ( + from omlt.io.torch_geometric import ( load_torch_geometric_sequential, gnn_with_fixed_graph, gnn_with_non_fixed_graph, From af61bb6c61219739c8365a066fffe9e9a1133b97 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 13 Sep 2023 11:34:41 +0100 Subject: [PATCH 12/27] update GNN notebook and comments --- .../graph_neural_network_formulation.ipynb | 161 +----------------- src/omlt/neuralnet/layer.py | 48 +++++- src/omlt/neuralnet/layers/full_space.py | 20 ++- 3 files changed, 59 insertions(+), 170 deletions(-) diff --git a/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb b/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb index 364f9b7c..d73e8ea1 100644 --- a/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb +++ b/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb @@ -6,19 +6,7 @@ "source": [ "# Optimizing over trained graph neural networks\n", "\n", - "This notebook explains how OMLT is used to optimize over trained graph neural networks (GNNs). We follow the below steps:\n", - "\n", - "1.) A general definition of GNNs is provided. OMLT currently only supports GNN that fits our definition. \n", - "\n", - "2.) Introduce the `GNNLayer` class inside OMLT.\n", - "\n", - "3.) Derive the big-M formulation for GNN layers.\n", - "\n", - "4.) List operations that are implemented inside OMLT. OMLT can automatically encode a given GNN consists of these operations. \n", - "\n", - "5.) For customized GNNs, we give examples to illustrate how to transform it into OMLT. \n", - "\n", - "6.) Examples: one has fixed graph structure, another one has non-fixed graph structure. For each case, the output of the GNN is minimized.\n", + "This notebook explains how OMLT is used to optimize over trained graph neural networks (GNNs).\n", "\n", "**NOTE:** For simplicity, we skip the training process and just use random parameters for GNNs.\n", "\n", @@ -44,153 +32,6 @@ "**NOTE:** This notebook also assumes you have a working MIP solver executable to solve optimization problems in Pyomo. The open-source solver CBC is called by default. \n", "\n", "\n", - "## Definition of GNNs\n", - "\n", - "We define a GNN with $L$ layers as follows:\n", - "\n", - "\\begin{equation*}\n", - "\t\\begin{aligned}\n", - "\t\tGNN:\\underbrace{\\mathbb R^{d_0}\\otimes\\cdots\\otimes\\mathbb R^{d_0}}_{N \\rm{times}}\\to\\underbrace{\\mathbb R^{d_L}\\otimes\\cdots\\otimes\\mathbb R^{d_L}}_{N\\ \\rm{times}}\n", - "\t\\end{aligned}\n", - "\\end{equation*}\n", - " \n", - "where $V$ is the set of nodes of the input graph, $N=|V|$ is the number of nodes. \n", - "\n", - "Let $\\mathbf{x}_v^{(0)} \\in \\mathbb{R}^{d_0}$ be the input features for node $v$. Then, the $l$-th layer ($l=1,2,\\dots,L$) is defined by:\n", - "\n", - "\\begin{equation*}\n", - "\t\\begin{aligned}\n", - "\t\t\\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in\\mathcal N(v)\\cup\\{v\\}}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right),~\\forall v\\in V\n", - "\t\\end{aligned}\n", - "\\end{equation*}\n", - "\n", - "where $\\mathcal N(v)$ is the set of all neighbors of $v$, $\\sigma$ could be identity or any activation function.\n", - "\n", - "*Dimensionality:* $\\mathbf{x}_u^{(l-1)}\\in\\mathbb R^{d_{l-1}}, \\mathbf{x}_v^{(l)},\\mathbf{b}_v^{(l)}\\in\\mathbb R^{d_l}, \\mathbf{w}_{u\\to v}^{(l)}\\in\\mathbb R^{d_l}\\times \\mathbb R^{d_{l-1}}$.\n", - "\n", - "## GNN Layers in OMLT\n", - "\n", - "For optimization purposes, OMLT requires a given number of nodes $N$ in the input graph. Each GNN layer will be expanded as shown in follows.\n", - "\n", - "Stack $\\{\\mathbf{x}_v^{(l)}\\}_{v\\in V}$ as a vector $\\mathbf{X}^{(l)}\\in \\mathbb R^{Nd_l}$. Rewrite previous definition as:\n", - "\\begin{equation*}\n", - "\t\\begin{aligned}\n", - "\t\t\\mathbf{X}^{(l)}=\\sigma\\left(\\mathbf{W}^{(l)}\\mathbf{X}^{(l-1)}+\\mathbf{B}^{(l)}\\right)\n", - "\t\\end{aligned}\n", - "\\end{equation*}\n", - "\n", - "One needs to provide $\\mathbf{W}^{(l)}\\in\\mathbb R^{Nd_l\\times Nd_{l-1}}, \\mathbf{B}^{(l)}\\in\\mathbb R^{Nd_l}, N$ to define a `GNNLayer` in OMLT. \n", - "\n", - "**NOTE:** To keep consistency with other types of layers, all weights are transposed.\n", - "\n", - "If the input graph structure is fixed, then weights $\\mathbf{w}_{u\\to v}^{(l)}$, biases $\\mathbf{b}_{v}^{(l)}$, and links between layers determined by $\\mathcal N(v)$ are all fixed after the GNN is trained. In this case, $\\mathbf{W}^{(l)}$ is a sparse matrix with nonzero sub-matrices $\\{\\mathbf{w}_{u\\to v}^{(l)}\\}_{v\\in V,u\\in\\mathcal N(v)\\cup\\{v\\}}$ and $\\mathbf{B}^{(l)}$ is the stack of $\\{\\mathbf{b}_v^{(l)}\\}_{v\\in V}$. The mixed-integer formulation of `GNNLayer` can be interpreted from two perspectives: (1) the same as a `DenseLayer`; (2) a simplified setting of `GNNLayer` with non-fixed input graph (introduced later). \n", - "\n", - "If the input graph structure is not fixed, then all weights $\\mathbf{w}_{u\\to v}^{(l)}$ and biases $\\mathbf{b}_{v}^{(l)}$ are needed to build mixed-integer formulations. In this case, $\\mathbf{B}^{(l)}$ is still the stack of $\\{\\mathbf{b}_v^{(l)}\\}_{v\\in V}$, while $\\mathbf{W}^{(l)}$ is a dense matrix consists of $\\{\\mathbf{w}_{u\\to v}^{(l)}\\}_{u,v\\in V}$.\n", - "\n", - "## Formulation for GNN Layers\n", - "\n", - "When the input graph structure is not fixed, elements in the adjacency matrix $A$ are decision variables. In this case, $\\mathcal N(v)$ is not given anymore. Additionally, $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ may contain the graph information, which makes them be variables. The formulation for GNN layers is built assuming that $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ are fixed.\n", - "\n", - "First, observe that the existence of edge $u\\to v$ determines the contribution link from $\\mathbf{x}_u^{(l-1)}$ to $\\mathbf{x}_v^{(l)}$. Adding binary variables $A_{u,v}$ for all $u,v\\in V$, we can formulate GNNs in a bilinear way:\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}A_{u,v}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "\n", - "This formulation involves quadratic constraints. To avoid them, instead of using binary variables to directly control the existence of contributions between nodes, we introduce introduces auxiliary variables $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ to represent the contribution from node $u$ to node $v$ in $l$-th layer:\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\sum\\limits_{u\\in V}\\mathbf{w}_{u\\to v}^{(l)}\\mathbf{\\bar x}_{u\\to v}^{(l-1)}+\\mathbf{b}_{v}^{(l)}\\right), \\forall v\\in V\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "where\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{\\bar x}_{u\\to v}^{(l-1)}=\\begin{cases}\n", - " 0, & A_{u,v}=0\\\\\n", - " \\mathbf{x}_u^{(l-1)}, & A_{u,v}=1\n", - " \\end{cases}\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "Assume that each feature is bounded, then the definition of $\\mathbf{\\bar x}_{u\\to v}^{(l-1)}$ could be reformulated using big-M:\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\mathbf{x}_{u}^{(l-1)}-\\mathbf{M}_{u}^{(l-1)}(1-A_{u,v})\\le &~\\mathbf{\\bar x}_{u\\to v}^{(l-1)}\\le \\mathbf{x}_{u}^{(l-1)}+\\mathbf{M}_{u}^{(l-1)}(1-A_{u,v})\\\\\n", - " -\\mathbf{M}_{u}^{(l-1)}A_{u,v}\\le &~\\mathbf{\\bar x}_{u\\to v}^{(l-1)}\\le \\mathbf{M}_u^{(l-1)}A_{u,v}\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "where $|\\mathbf{x}_u^{(l-1)}|\\le \\mathbf{M}_u^{(l-1)}, A_{u,v}\\in\\{0,1\\}$. By adding extra continuous variables and constraints, as well as utilizing the bounds for all features, the big-M formulation replaces the bi-linear constraints by linear constraints. OMLT uses this big-M formulation as the default (and only) formulation for GNN layers.\n", - "\n", - "**NOTE:** When the input graph structure is fixed, we can fix $A$ to reduce the big-M formulation.\n", - "\n", - "## Implemented GNN Operations in OMLT\n", - "\n", - "The following operations from `torch_geometric` are implemented in OMLT:\n", - "\n", - "- Convolutional Layers: `Linear`, `GCNConv`, `SAGEConv`\n", - "- Aggregation Operators: `sum`, `mean`\n", - "- Pooling Layers: `global_mean_pool`, `global_add_pool`\n", - "- Activation Functions: all activations supported in OMLT are compatible with these GNN operations.\n", - "\n", - "**NOTE:** When the input graph is not fixed, there is no graph information. `GCNConv` layer and `mean` aggregation are not supported.\n", - "\n", - "OMLT provides two functions `gnn_with_fixed_graph` and `gnn_with_non_fixed_graph` to encode GNNs with fixed/non-fixed input graph structure. Both functions only require (1) a sequential model from `torch_geometric`, and (2) number of nodes $N$ (and the adjacency matrix $A$ for fixed graph cases). The basic pipeline of both functions are:\n", - "\n", - "1.) Transform each operation, e.g., linear layers and pooling layers will be transformed into `DenseLayer` (which is straightforward), GNN layers will be rewritten into `GNNLayer`, activation functions are identified and absorbed into corresponding layers.\n", - "\n", - "2.) Define binary variables $A_{u,v}$ for adjacency matrix. We always assume $A$ is symmetric (i.e., $A_{u,v}=A_{v,u}$) and has non-zero diagonal elements (i.e., $A_{v,v}=1$). When $A$ is given for fixed graph cases, these variables will then be fixed.\n", - "\n", - "3.) Build formulation. Currently, we only support `FullSpaceNNFormulations`. ReLU activation functions are encoded into linear constraints using a big-M formulation. For smooth activation functions (e.g., Sigmoid, LogSoftmax, Tanh), a smooth optimization solvers (such as Ipopt) is needed to handle nonlinear constraints.\n", - "\n", - "## How to Transform Your Own GNN into OMLT\n", - "\n", - "As mentioned before, any GNN that satisfies our GNN definition could be transformed into OMLT and then encoded using big-M formulation. Here we give two examples to show how to transform an outside GNN into OMLT.\n", - "\n", - "The first example corresponds to fixed graph cases. Given a simple GNN consists of a GraphSAGE layer, an add pooling layer, and a dense layer with single output. Let the input and output features of the GraphSAGE layer are 2 and 3, respectively. \n", - "\n", - "The GraphSAGE layer is defined by:\n", - "\\begin{equation*}\n", - " \\mathbf{x}_v^{(l)}=\\sigma\\left(\\mathbf{w_1}^{(l)}\\mathbf{x}_v^{(l-1)}+\\mathbf{w_2}^{(l)}\\sum\\limits_{u\\in\\mathcal N(v)}\\mathbf{x}_u^{(l-1)}+\\mathbf{b}^{(l)}\\right)\n", - "\\end{equation*}\n", - "where a sum aggregation is used.\n", - "\n", - "For the fixed graph structure, assume that it is a line graph with $N=3$ nodes, i.e., the adjacency matrix $A=\\begin{pmatrix}1 & 1 & 0\\\\1 & 1 & 1\\\\ 0 & 1 & 1\\end{pmatrix}$. Then the GraphSAGE layer could be rewritten as a `GNNLayer` with parameters:\n", - "\n", - " \\begin{equation*}\n", - " \\mathbf{W}=\\begin{pmatrix}\n", - " \\mathbf{w_1} & \\mathbf{w_2} & \\mathbf{0} \\\\\n", - " \\mathbf{w_2} & \\mathbf{w_1} & \\mathbf{w_2} \\\\\n", - " \\mathbf{0} & \\mathbf{w_2} & \\mathbf{w_1} \\\\\n", - " \\end{pmatrix},\n", - " \\mathbf{B}=\\begin{pmatrix}\n", - " \\mathbf{b}\\\\\\mathbf{b}\\\\\\mathbf{b}\n", - " \\end{pmatrix}\n", - " \\end{equation*}\n", - " \n", - "See below as a mapping between the given outside GNN and its corresponding GNN inside OMLT in form \"layer type (in_channel, out_channel)\":\n", - "\n", - "\\begin{equation*}\n", - " \\begin{aligned}\n", - " \\text{GraphSAGE(2, 3)} &\\Rightarrow \\text{GNNLayer(6, 9)}\\\\\n", - " \\text{add pooling(9, 3)} &\\Rightarrow \\text{DenseLayer(9, 3)}\\\\\n", - " \\text{dense(3, 1)} &\\Rightarrow \\text{DenseLayer(3, 1)}\n", - " \\end{aligned}\n", - "\\end{equation*}\n", - "\n", - "The second example reuses the GNN architecture but no longer fixes the input graph structure. In such setting, all $\\mathbf{w}_{u\\to v}^{(l)},\\mathbf{b}_v^{(l)}$ should be provided. Therefore, the `GNNLayer` is defined by:\n", - "\n", - "\\begin{equation*}\n", - " \\mathbf{W}=\\begin{pmatrix}\n", - " \\mathbf{w_1} & \\mathbf{w_2} & \\mathbf{w_2} \\\\\n", - " \\mathbf{w_2} & \\mathbf{w_1} & \\mathbf{w_2} \\\\\n", - " \\mathbf{w_2} & \\mathbf{w_2} & \\mathbf{w_1} \\\\\n", - " \\end{pmatrix},\n", - " \\mathbf{B}=\\begin{pmatrix}\n", - " \\mathbf{b}\\\\\\mathbf{b}\\\\\\mathbf{b}\n", - " \\end{pmatrix}\n", - " \\end{equation*}\n", - "\n", "## Example 1: Optimizing a GNN with Fixed Graph\n", "\n", "Define a GCN in `torch_geometric` as follows:" diff --git a/src/omlt/neuralnet/layer.py b/src/omlt/neuralnet/layer.py index b852fc3e..27c465e4 100644 --- a/src/omlt/neuralnet/layer.py +++ b/src/omlt/neuralnet/layer.py @@ -207,7 +207,53 @@ def _eval(self, x): class GNNLayer(DenseLayer): """ - GNN layer implementing `output = activation(dot(input, weights, edge) + biases)`. + Given the number of nodes :math:`N`, implementing a GNN layer defined by: + + .. math:: + + \begin{align*} + y_i = \sigma \left(\sum\limits_{j=0}^{F_{in}-1}A_{u,v}w_{ji}x_j+b_i\right) && \forall 0\le i Date: Wed, 13 Sep 2023 11:50:28 +0100 Subject: [PATCH 13/27] update GNN comments --- src/omlt/neuralnet/layer.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/src/omlt/neuralnet/layer.py b/src/omlt/neuralnet/layer.py index 27c465e4..5daa0ba5 100644 --- a/src/omlt/neuralnet/layer.py +++ b/src/omlt/neuralnet/layer.py @@ -206,13 +206,13 @@ def _eval(self, x): class GNNLayer(DenseLayer): - """ + r""" Given the number of nodes :math:`N`, implementing a GNN layer defined by: .. math:: - + \begin{align*} - y_i = \sigma \left(\sum\limits_{j=0}^{F_{in}-1}A_{u,v}w_{ji}x_j+b_i\right) && \forall 0\le i Date: Wed, 13 Sep 2023 12:02:37 +0100 Subject: [PATCH 14/27] update GNN comments --- src/omlt/neuralnet/layer.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/omlt/neuralnet/layer.py b/src/omlt/neuralnet/layer.py index 5daa0ba5..fe5143a7 100644 --- a/src/omlt/neuralnet/layer.py +++ b/src/omlt/neuralnet/layer.py @@ -222,7 +222,7 @@ class GNNLayer(DenseLayer): .. math:: \begin{align*} - \mathbf{y_v} = \sigma\left(\mathbf{w_1^T}\mathbf{x_v}+\mathbf{w_2}^T\sum\limits_{u\in\mathcal N(v)}\mathbf{x_u}+\mathbf{b}\right) + \mathbf{y_v} = \sigma\left(\mathbf{w_1}^T\mathbf{x_v}+\mathbf{w_2}^T\sum\limits_{u\in\mathcal N(v)}\mathbf{x_u}+\mathbf{b}\right) \end{align*} If the graph structure is fixed, assume that it is a line graph with :math:`N=3` nodes, i.e., the adjacency matrix :math:`A=\begin{pmatrix}1 & 1 & 0\\1 & 1 & 1\\ 0 & 1 & 1\end{pmatrix}`. Then the corresponding GNN layer is defined with parameters: From e0b543e2614c031fcfef6fbacf3a23761102b48b Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 13 Sep 2023 16:40:56 +0100 Subject: [PATCH 15/27] update GNN formulation --- src/omlt/neuralnet/layers/full_space.py | 10 +++------- 1 file changed, 3 insertions(+), 7 deletions(-) diff --git a/src/omlt/neuralnet/layers/full_space.py b/src/omlt/neuralnet/layers/full_space.py index 3f6e1491..56d85ad1 100644 --- a/src/omlt/neuralnet/layers/full_space.py +++ b/src/omlt/neuralnet/layers/full_space.py @@ -57,7 +57,7 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): .. math:: \begin{align*} - z_{j} - (U_{j}-L_{j})(1-A_{I(j),I(i)}) &\le \bar z_{j,I(i)} \le z_{j} + (U_{j}-L_{j})(1-A_{I(j),I(i)})\\ + z_{j} - U_{j}(1-A_{I(j),I(i)}) &\le \bar z_{j,I(i)} \le z_{j} - L_{j}(1-A_{I(j),I(i)})\\ L_{j}A_{I(j),I(i)} &\le \bar z_{j,I(i)} \le U_{j}A_{I(j),I(i)}\\ A_{I(j),I(i)}&\in \{0,1\} \end{align*} @@ -113,9 +113,7 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): local_index, output_node_index ] >= input_layer_block.z[ input_index - ] - ( - ub - lb - ) * ( + ] - ub * ( 1.0 - net_block.A[input_node_index, output_node_index] ) @@ -125,9 +123,7 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): local_index, output_node_index ] <= input_layer_block.z[ input_index - ] + ( - ub - lb - ) * ( + ] - lb * ( 1.0 - net_block.A[input_node_index, output_node_index] ) From f2ec3f3211bd76f3f3abf82ca0cd2be694085f59 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 20 Sep 2023 15:01:02 +0100 Subject: [PATCH 16/27] update GNN tests --- setup.cfg | 1 - .../torch_geometric/torch_geometric_reader.py | 5 + tests/io/test_torch_geometric.py | 115 +++++++----------- 3 files changed, 51 insertions(+), 70 deletions(-) diff --git a/setup.cfg b/setup.cfg index aa1ae5e4..e01e4769 100644 --- a/setup.cfg +++ b/setup.cfg @@ -105,7 +105,6 @@ testing_lean = torch torchvision tqdm - torch_geometric [options.entry_points] # Add here console scripts like: diff --git a/src/omlt/io/torch_geometric/torch_geometric_reader.py b/src/omlt/io/torch_geometric/torch_geometric_reader.py index 1acbc2e7..16d5db4d 100644 --- a/src/omlt/io/torch_geometric/torch_geometric_reader.py +++ b/src/omlt/io/torch_geometric/torch_geometric_reader.py @@ -2,6 +2,7 @@ from omlt.neuralnet.layer import DenseLayer, InputLayer, GNNLayer from omlt.neuralnet.network_definition import NetworkDefinition +import warnings def _compute_gcn_norm(A): @@ -172,6 +173,9 @@ def load_torch_geometric_sequential( operations[index] in ["Linear"] + _ACTIVATION_OP_TYPES + _POOLING_OP_TYPES ): + # nonlinear activation results in a MINLP + if operations[index] in ["Sigmoid", "LogSoftmax", "Softplus", "Tanh"]: + warnings.warn("nonlinear activation results in a MINLP") # Linear layers, all activation functions, and all pooling functions are still supported. continue if operations[index] not in _LAYER_OP_TYPES_NON_FIXED_GRAPH: @@ -182,6 +186,7 @@ def load_torch_geometric_sequential( raise ValueError( "this aggregation is not supported when the graph is not fixed" ) + A = np.ones((N, N)) - np.eye(N) for index, l in enumerate(nn): diff --git a/tests/io/test_torch_geometric.py b/tests/io/test_torch_geometric.py index 076dccde..1c52abbf 100644 --- a/tests/io/test_torch_geometric.py +++ b/tests/io/test_torch_geometric.py @@ -14,7 +14,6 @@ from torch.nn import Linear, ReLU, Sigmoid, Softplus, Tanh from torch_geometric.nn import Sequential, GCNConv, SAGEConv from torch_geometric.nn import global_mean_pool, global_add_pool - from torch_geometric.utils import erdos_renyi_graph from omlt.io.torch_geometric import ( load_torch_geometric_sequential, gnn_with_fixed_graph, @@ -27,7 +26,6 @@ reason="Test only valid when torch and torch_geometric are available", ) def GCN_Sequential(activation, pooling): - torch.manual_seed(123) return Sequential( "x, edge_index", [ @@ -49,7 +47,6 @@ def GCN_Sequential(activation, pooling): reason="Test only valid when torch and torch_geometric are available", ) def SAGE_Sequential(activation, pooling, aggr, root_weight): - torch.manual_seed(123) return Sequential( "x, edge_index", [ @@ -70,35 +67,30 @@ def SAGE_Sequential(activation, pooling, aggr, root_weight): not (torch_available and torch_geometric_available), reason="Test only valid when torch and torch_geometric are available", ) -def generate_random_inputs(N, F, seed, p): - torch.manual_seed(seed) - edges = erdos_renyi_graph(N, p, directed=False) - A = np.zeros((N, N), dtype=int) - for k in range(edges.shape[1]): - u = edges[0, k].numpy() - v = edges[1, k].numpy() - A[u, v] = 1 - x = 1.0 * torch.randint(1, (N, F)) - return x, edges, np.squeeze(x.numpy().reshape(1, -1)), A - - -@pytest.mark.skipif( - not (torch_available and torch_geometric_available), - reason="Test only valid when torch and torch_geometric are available", -) -def _test_torch_geometric_reader(nn): +def _test_torch_geometric_reader(nn, activation, pooling): N = 4 - F = 2 - nn.eval() - for seed in range(10): - for p in range(10): - x, edges, x_np, A = generate_random_inputs(N, F, seed, p / 10.0) - net = load_torch_geometric_sequential(nn, N, A) - y = nn(x, edges).detach().numpy() - y_np = x_np - for layer in net.layers: - y_np = layer.eval_single_layer(y_np) - assert abs(y - y_np) < 1e-6 + A = np.ones((N, N), dtype=int) + net = load_torch_geometric_sequential(nn, N, A) + layers = list(net.layers) + assert len(layers) == 7 + assert layers[1].weights.shape == (8, 16) + assert layers[2].weights.shape == (16, 16) + assert layers[3].weights.shape == (16, 16) + assert layers[4].weights.shape == (16, 4) + assert layers[5].weights.shape == (4, 2) + assert layers[6].weights.shape == (2, 1) + for layer_id in [1, 2, 5]: + if activation == ReLU: + assert layers[layer_id].activation == "relu" + elif activation == Sigmoid: + assert layers[layer_id].activation == "sigmoid" + elif activation == Tanh: + assert layers[layer_id].activation == "tanh" + + if pooling == global_mean_pool: + assert sum(sum(layers[4].weights)) == N + elif pooling == global_add_pool: + assert sum(sum(layers[4].weights)) == N**2 @pytest.mark.skipif( @@ -108,22 +100,17 @@ def _test_torch_geometric_reader(nn): def _test_gnn_with_fixed_graph(nn): N = 4 F = 2 - nn.eval() - for p in range(10): - x, edges, x_np, A = generate_random_inputs(N, F, 0, p / 10.0) - y = nn(x, edges).detach().numpy() - input_size = [N * F] - input_bounds = {} - for i in range(input_size[0]): - input_bounds[(i)] = (0.0, 1.0) - m = pyo.ConcreteModel() - m.nn = OmltBlock() - gnn_with_fixed_graph(m.nn, nn, N, A, scaled_input_bounds=input_bounds) - for i in range(N * F): - m.nn.inputs[i].fix(x_np[i]) - m.obj = pyo.Objective(expr=m.nn.outputs[0]) - status = pyo.SolverFactory("cbc").solve(m, tee=False) - assert abs(pyo.value(m.nn.outputs[0]) - y) < 1e-6 + + input_size = [N * F] + input_bounds = {} + for i in range(input_size[0]): + input_bounds[(i)] = (-1.0, 1.0) + m = pyo.ConcreteModel() + m.nn = OmltBlock() + A = np.eye(N, dtype=int) + gnn_with_fixed_graph(m.nn, nn, N, A, scaled_input_bounds=input_bounds) + assert m.nvariables() == 282 + assert m.nconstraints() == 614 @pytest.mark.skipif( @@ -133,26 +120,16 @@ def _test_gnn_with_fixed_graph(nn): def _test_gnn_with_non_fixed_graph(nn): N = 4 F = 2 - nn.eval() - for p in range(10): - x, edges, x_np, A = generate_random_inputs(N, F, 0, p / 10.0) - y = nn(x, edges).detach().numpy() - input_size = [N * F] - input_bounds = {} - for i in range(input_size[0]): - input_bounds[(i)] = (-1.0, 1.0) - m = pyo.ConcreteModel() - m.nn = OmltBlock() - gnn_with_non_fixed_graph(m.nn, nn, N, scaled_input_bounds=input_bounds) - for i in range(N * F): - m.nn.inputs[i].fix(x_np[i]) - for u in range(N): - for v in range(N): - if u != v: - m.nn.A[u, v].fix(A[u, v]) - m.obj = pyo.Objective(expr=m.nn.outputs[0]) - status = pyo.SolverFactory("cbc").solve(m, tee=False) - assert abs(pyo.value(m.nn.outputs[0]) - y) < 1e-6 + + input_size = [N * F] + input_bounds = {} + for i in range(input_size[0]): + input_bounds[(i)] = (-1.0, 1.0) + m = pyo.ConcreteModel() + m.nn = OmltBlock() + gnn_with_non_fixed_graph(m.nn, nn, N, scaled_input_bounds=input_bounds) + assert m.nvariables() == 282 + assert m.nconstraints() == 620 @pytest.mark.skipif( @@ -163,11 +140,11 @@ def test_torch_geometric_reader(): for activation in [ReLU, Sigmoid, Tanh]: for pooling in [global_mean_pool, global_add_pool]: nn = GCN_Sequential(activation, pooling) - _test_torch_geometric_reader(nn) + _test_torch_geometric_reader(nn, activation, pooling) for aggr in ["sum", "mean"]: for root_weight in [False, True]: nn = SAGE_Sequential(activation, pooling, aggr, root_weight) - _test_torch_geometric_reader(nn) + _test_torch_geometric_reader(nn, activation, pooling) @pytest.mark.skipif( From a2e1751020f555ab2b7630d03d15bcce1eccc48c Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 20 Sep 2023 16:15:17 +0100 Subject: [PATCH 17/27] update GNN notebook --- .../graph_neural_network_formulation.ipynb | 426 +++++++++--------- 1 file changed, 219 insertions(+), 207 deletions(-) diff --git a/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb b/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb index d73e8ea1..dd1e74dd 100644 --- a/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb +++ b/docs/notebooks/neuralnet/graph_neural_network_formulation.ipynb @@ -39,13 +39,13 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import torch\n", - "from torch.nn import Linear, ReLU\n", + "from torch.nn import Linear, ReLU, Sigmoid\n", "from torch_geometric.nn import Sequential, GCNConv\n", "from torch_geometric.nn import global_mean_pool\n", "from omlt.io.torch_geometric import gnn_with_fixed_graph\n", @@ -80,7 +80,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -125,7 +125,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -153,7 +153,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -161,10 +161,10 @@ "output_type": "stream", "text": [ "Welcome to the CBC MILP Solver \n", - "Version: 2.10.10 \n", - "Build Date: Aug 1 2023 \n", + "Version: 2.9.9 \n", + "Build Date: Oct 13 2018 \n", "\n", - "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT_test/bin/cbc -printingOptions all -import /var/tmp/pbs.8152010.pbs/tmpo87uiyi0.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.8152010.pbs/tmpo87uiyi0.pyomo.soln (default strategy 1)\n", + "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT_test/bin/cbc -printingOptions all -import /var/tmp/pbs.8259409.pbs/tmpp27h4a9g.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.8259409.pbs/tmpp27h4a9g.pyomo.soln (default strategy 1)\n", "Option for printingOptions changed from normal to all\n", "Presolve 172 (-222) rows, 111 (-75) columns and 608 (-267) elements\n", "Statistics for presolved model\n", @@ -197,79 +197,78 @@ "Continuous objective value is 0.315152 - 0.00 seconds\n", "Cgl0003I 0 fixed, 0 tightened bounds, 2 strengthened rows, 0 substitutions\n", "Cgl0004I processed model has 166 rows, 105 columns (25 integer (25 of which binary)) and 670 elements\n", - "Cbc0038I Initial state - 5 integers unsatisfied sum - 0.124759\n", - "Cbc0038I Pass 1: suminf. 0.00000 (0) obj. 0.317969 iterations 41\n", + "Cbc0038I Initial state - 5 integers unsatisfied sum - 0.191951\n", + "Cbc0038I Pass 1: suminf. 0.00000 (0) obj. 0.317969 iterations 17\n", "Cbc0038I Solution found of 0.317969\n", "Cbc0038I Relaxing continuous gives 0.317969\n", - "Cbc0038I Before mini branch and bound, 20 integers at bound fixed and 63 continuous\n", - "Cbc0038I Full problem 166 rows 105 columns, reduced to 17 rows 13 columns\n", + "Cbc0038I Before mini branch and bound, 19 integers at bound fixed and 48 continuous\n", + "Cbc0038I Full problem 166 rows 105 columns, reduced to 49 rows 27 columns\n", "Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n", "Cbc0038I Round again with cutoff of 0.317791\n", - "Cbc0038I Pass 2: suminf. 0.00876 (1) obj. 0.317791 iterations 11\n", - "Cbc0038I Pass 3: suminf. 0.18897 (1) obj. 0.317791 iterations 20\n", - "Cbc0038I Pass 4: suminf. 0.00876 (1) obj. 0.317791 iterations 58\n", - "Cbc0038I Pass 5: suminf. 0.18897 (1) obj. 0.317791 iterations 13\n", - "Cbc0038I Pass 6: suminf. 0.00876 (1) obj. 0.317791 iterations 21\n", - "Cbc0038I Pass 7: suminf. 0.00876 (1) obj. 0.317791 iterations 32\n", - "Cbc0038I Pass 8: suminf. 0.18897 (1) obj. 0.317791 iterations 16\n", - "Cbc0038I Pass 9: suminf. 0.00876 (1) obj. 0.317791 iterations 19\n", - "Cbc0038I Pass 10: suminf. 0.00876 (1) obj. 0.317791 iterations 57\n", - "Cbc0038I Pass 11: suminf. 0.18897 (1) obj. 0.317791 iterations 7\n", - "Cbc0038I 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"Cbc0038I Pass 5: suminf. 0.18897 (1) obj. 0.317791 iterations 10\n", + "Cbc0038I Pass 6: suminf. 0.00876 (1) obj. 0.317791 iterations 9\n", + "Cbc0038I Pass 7: suminf. 0.00876 (1) obj. 0.317791 iterations 20\n", + "Cbc0038I Pass 8: suminf. 0.18897 (1) obj. 0.317791 iterations 11\n", + "Cbc0038I Pass 9: suminf. 0.00876 (1) obj. 0.317791 iterations 11\n", + "Cbc0038I Pass 10: suminf. 0.00876 (1) obj. 0.317791 iterations 4\n", + "Cbc0038I Pass 11: suminf. 0.18897 (1) obj. 0.317791 iterations 10\n", + "Cbc0038I Pass 12: suminf. 0.00876 (1) obj. 0.317791 iterations 8\n", + "Cbc0038I Pass 13: suminf. 0.00876 (1) obj. 0.317791 iterations 6\n", + "Cbc0038I Pass 14: suminf. 0.18897 (1) obj. 0.317791 iterations 9\n", + "Cbc0038I Pass 15: suminf. 0.00876 (1) obj. 0.317791 iterations 9\n", + "Cbc0038I Pass 16: suminf. 0.00876 (1) obj. 0.317791 iterations 6\n", + "Cbc0038I Pass 17: suminf. 0.18897 (1) obj. 0.317791 iterations 17\n", + "Cbc0038I Pass 18: suminf. 0.00876 (1) obj. 0.317791 iterations 18\n", + "Cbc0038I Pass 19: suminf. 0.00876 (1) obj. 0.317791 iterations 8\n", + "Cbc0038I Pass 20: suminf. 0.18897 (1) obj. 0.317791 iterations 15\n", + "Cbc0038I Pass 21: suminf. 0.00876 (1) obj. 0.317791 iterations 19\n", + "Cbc0038I Pass 22: suminf. 0.00876 (1) obj. 0.317791 iterations 25\n", "Cbc0038I Pass 23: suminf. 0.18897 (1) obj. 0.317791 iterations 6\n", "Cbc0038I Pass 24: suminf. 0.00876 (1) obj. 0.317791 iterations 5\n", - "Cbc0038I Pass 25: suminf. 0.00876 (1) obj. 0.317791 iterations 10\n", + "Cbc0038I Pass 25: suminf. 0.00876 (1) obj. 0.317791 iterations 12\n", "Cbc0038I Pass 26: suminf. 0.18897 (1) obj. 0.317791 iterations 6\n", "Cbc0038I Pass 27: suminf. 0.00876 (1) obj. 0.317791 iterations 5\n", - "Cbc0038I Pass 28: suminf. 0.00876 (1) obj. 0.317791 iterations 30\n", - "Cbc0038I Pass 29: suminf. 0.18897 (1) obj. 0.317791 iterations 5\n", - "Cbc0038I Pass 30: suminf. 0.00876 (1) obj. 0.317791 iterations 6\n", - "Cbc0038I Pass 31: suminf. 0.00876 (1) obj. 0.317791 iterations 3\n", + "Cbc0038I Pass 28: suminf. 0.00876 (1) obj. 0.317791 iterations 13\n", + "Cbc0038I Pass 29: suminf. 0.18897 (1) obj. 0.317791 iterations 6\n", + "Cbc0038I Pass 30: suminf. 0.00876 (1) obj. 0.317791 iterations 15\n", + "Cbc0038I Pass 31: suminf. 0.00876 (1) obj. 0.317791 iterations 6\n", "Cbc0038I No solution found this major pass\n", - "Cbc0038I Before mini branch and bound, 1 integers at bound fixed and 47 continuous\n", + "Cbc0038I Before mini branch and bound, 1 integers at bound fixed and 46 continuous\n", "Cbc0038I Full problem 166 rows 105 columns, reduced to 48 rows 27 columns\n", "Cbc0038I Mini branch and bound did not improve solution (0.02 seconds)\n", - "Cbc0038I After 0.02 seconds - Feasibility pump exiting with objective of 0.317969 - took 0.01 seconds\n", + "Cbc0038I After 0.02 seconds - Feasibility pump exiting with objective of 0.317969 - took 0.02 seconds\n", "Cbc0012I Integer solution of 0.31796885 found by feasibility pump after 0 iterations and 0 nodes (0.02 seconds)\n", - "Cbc0038I Full problem 166 rows 105 columns, reduced to 48 rows 27 columns\n", - "Cbc0031I 3 added rows had average density of 3.3333333\n", - "Cbc0013I At root node, 31 cuts changed objective from 0.31628066 to 0.31796885 in 1 passes\n", - "Cbc0014I Cut generator 0 (Probing) - 19 row cuts average 3.0 elements, 1 column cuts (1 active) in 0.000 seconds - new frequency is 1\n", - "Cbc0014I Cut generator 1 (Gomory) - 3 row cuts average 8.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", + "Cbc0038I Full problem 166 rows 105 columns, reduced to 49 rows 27 columns\n", + "Cbc0031I 6 added rows had average density of 5.5\n", + "Cbc0013I At root node, 25 cuts changed objective from 0.31628066 to 0.31796885 in 1 passes\n", + "Cbc0014I Cut generator 0 (Probing) - 11 row cuts average 3.0 elements, 1 column cuts (1 active) in 0.000 seconds - new frequency is 1\n", + "Cbc0014I Cut generator 1 (Gomory) - 2 row cuts average 13.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", "Cbc0014I Cut generator 2 (Knapsack) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", "Cbc0014I Cut generator 3 (Clique) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 3 row cuts average 3.3 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", + "Cbc0014I Cut generator 4 (MixedIntegerRounding2) - 4 row cuts average 3.2 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", "Cbc0014I Cut generator 5 (FlowCover) - 0 row cuts average 0.0 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is -100\n", - "Cbc0014I Cut generator 6 (TwoMirCuts) - 6 row cuts average 6.2 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", - "Cbc0001I Search completed - best objective 0.3179688539269278, took 17 iterations and 0 nodes (0.02 seconds)\n", + "Cbc0014I Cut generator 6 (TwoMirCuts) - 8 row cuts average 6.8 elements, 0 column cuts (0 active) in 0.000 seconds - new frequency is 1\n", + "Cbc0001I Search completed - best objective 0.3179688539269278, took 31 iterations and 0 nodes (0.02 seconds)\n", "Cbc0035I Maximum depth 0, 0 variables fixed on reduced cost\n", "Cuts at root node changed objective from 0.316281 to 0.317969\n", - "Probing was tried 1 times and created 20 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "Gomory was tried 1 times and created 3 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Probing was tried 1 times and created 12 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "Gomory was tried 1 times and created 2 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", "Knapsack was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", "Clique was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "MixedIntegerRounding2 was tried 1 times and created 3 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "MixedIntegerRounding2 was tried 1 times and created 4 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", "FlowCover was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "TwoMirCuts was tried 1 times and created 6 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 1 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", + "TwoMirCuts was tried 1 times and created 8 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", "\n", "Result - Optimal solution found\n", "\n", "Objective value: 0.31796885\n", "Enumerated nodes: 0\n", - "Total iterations: 17\n", - "Time (CPU seconds): 0.02\n", - "Time (Wallclock seconds): 0.02\n", + "Total iterations: 31\n", + "Time (CPU seconds): 0.03\n", + "Time (Wallclock seconds): 0.03\n", "\n", "Total time (CPU seconds): 0.03 (Wallclock seconds): 0.03\n", "\n" @@ -302,7 +301,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -328,6 +327,153 @@ "print(nn1(torch.tensor(X).float(), torch.tensor(edges)).detach().numpy())" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For smooth activation function like Sigmoid, a smooth optimization solvers (such as Ipopt) is needed:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ipopt 3.14.12: \n", + "\n", + "******************************************************************************\n", + "This program contains Ipopt, a library for large-scale nonlinear optimization.\n", + " Ipopt is released as open source code under the Eclipse Public License (EPL).\n", + " For more information visit https://github.com/coin-or/Ipopt\n", + "******************************************************************************\n", + "\n", + "This is Ipopt version 3.14.12, running with linear solver MUMPS 5.2.1.\n", + "\n", + "Number of nonzeros in equality constraint Jacobian...: 395\n", + "Number of nonzeros in inequality constraint Jacobian.: 276\n", + "Number of nonzeros in Lagrangian Hessian.............: 26\n", + "\n", + "Total number of variables............................: 148\n", + " variables with only lower bounds: 0\n", + " variables with lower and upper bounds: 146\n", + " variables with only upper bounds: 0\n", + "Total number of equality constraints.................: 100\n", + "Total number of inequality constraints...............: 216\n", + " inequality constraints with only lower bounds: 0\n", + " inequality constraints with lower and upper bounds: 0\n", + " inequality constraints with only upper bounds: 216\n", + "\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 0 0.0000000e+00 4.73e-01 1.32e-04 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0\n", + " 1 7.5562415e-02 3.99e-01 6.07e+01 -1.0 6.41e-01 - 4.88e-02 1.57e-01f 1\n", + " 2 1.6790548e-01 3.08e-01 4.25e+01 -1.0 4.05e-01 - 1.81e-01 2.28e-01f 1\n", + " 3 2.5794319e-01 2.19e-01 3.18e+01 -1.0 3.13e-01 - 5.10e-01 2.88e-01f 1\n", + " 4 3.9100053e-01 8.85e-02 1.45e+01 -1.0 2.23e-01 - 9.76e-01 5.97e-01h 1\n", + " 5 4.4307883e-01 3.72e-02 2.75e+01 -1.0 1.41e-01 - 1.00e+00 5.79e-01h 1\n", + " 6 4.6540208e-01 1.52e-02 6.33e+01 -1.0 8.16e-02 - 1.00e+00 5.91e-01h 1\n", + " 7 4.7445376e-01 6.31e-03 1.55e+02 -1.0 3.67e-02 - 1.00e+00 5.85e-01h 1\n", + " 8 4.7820844e-01 2.61e-03 3.74e+02 -1.0 1.47e-02 - 1.00e+00 5.86e-01h 1\n", + " 9 4.7976341e-01 1.08e-03 9.04e+02 -1.0 6.36e-03 - 1.00e+00 5.86e-01h 1\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 10 4.8040743e-01 4.48e-04 2.18e+03 -1.0 2.53e-03 - 1.00e+00 5.86e-01h 1\n", + " 11 4.8067424e-01 1.86e-04 5.26e+03 -1.0 1.09e-03 - 1.00e+00 5.86e-01h 1\n", + " 12 4.8078473e-01 7.67e-05 1.27e+04 -1.0 4.34e-04 - 1.00e+00 5.87e-01h 1\n", + " 13 4.8083051e-01 3.16e-05 3.04e+04 -1.0 1.87e-04 - 1.00e+00 5.88e-01h 1\n", + " 14 4.8084947e-01 1.29e-05 7.21e+04 -1.0 7.40e-05 - 1.00e+00 5.91e-01h 1\n", + " 15 4.8085732e-01 5.18e-06 1.67e+05 -1.0 3.15e-05 - 1.00e+00 5.99e-01h 1\n", + " 16 4.8086057e-01 1.98e-06 3.65e+05 -1.0 1.21e-05 - 1.00e+00 6.18e-01h 1\n", + " 17 4.8086191e-01 6.64e-07 6.79e+05 -1.0 4.84e-06 - 1.00e+00 6.65e-01h 1\n", + " 18 4.8086192e-01 6.47e-07 3.49e+06 -1.0 1.54e-06 - 1.00e+00 2.47e-02f 6\n", + " 19 4.8086258e-01 1.04e-10 1.00e-06 -1.0 1.52e-06 - 1.00e+00 1.00e+00h 1\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 20 4.8086253e-01 1.78e-10 4.52e+02 -8.6 7.22e-05 - 1.00e+00 1.00e+00h 1\n", + " 21 4.8001913e-01 2.86e-02 2.80e+02 -8.6 1.17e+00 - 5.24e-01 1.00e+00f 1\n", + " 22 4.8001744e-01 1.08e-02 2.14e+01 -8.6 2.16e-01 - 9.00e-01 6.57e-01h 1\n", + " 23 4.8001271e-01 1.79e-03 2.28e+01 -8.6 3.03e-01 - 8.31e-01 1.00e+00h 1\n", + " 24 4.8000768e-01 1.81e-04 4.39e+01 -8.6 9.74e-02 - 7.32e-01 1.00e+00h 1\n", + " 25 4.8000768e-01 1.80e-04 5.02e+01 -8.6 1.67e-02 - 5.11e-01 4.80e-03h 1\n", + " 26 4.8000768e-01 1.80e-04 7.68e+01 -8.6 1.72e-02 - 2.92e-01 2.94e-04f 2\n", + " 27 4.8000768e-01 1.80e-04 1.18e+02 -8.6 1.73e-02 - 6.38e-01 2.96e-04h 1\n", + " 28 4.8000768e-01 1.80e-04 1.25e+02 -8.6 1.76e-02 - 3.09e-01 6.58e-05h 2\n", + " 29 4.8000768e-01 1.80e-04 1.41e+02 -8.6 1.76e-02 - 1.00e+00 2.94e-04h 1\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 30 4.8000669e-01 5.04e-06 2.97e+00 -8.6 1.77e-02 - 2.99e-01 1.00e+00f 1\n", + " 31 4.8000669e-01 5.04e-06 8.32e+01 -8.6 4.66e-05 - 5.89e-01 2.35e-04h 1\n", + " 32 4.8000669e-01 5.04e-06 1.14e+02 -8.6 5.90e-05 - 5.27e-01 3.92e-05h 1\n", + " 33 4.8000669e-01 5.04e-06 1.25e+02 -8.6 6.02e-05 - 3.88e-01 6.73e-06f 2\n", + " 34 4.8000669e-01 5.04e-06 1.25e+02 -8.6 6.06e-05 - 5.49e-02 2.21e-05h 1\n", + " 35 4.8000669e-01 5.04e-06 1.27e+02 -8.6 4.61e-04 - 8.33e-02 7.28e-08f 2\n", + " 36 4.8000669e-01 5.04e-06 1.34e+02 -8.6 6.09e-05 - 4.80e-01 7.71e-05f 2\n", + " 37 4.8000669e-01 5.04e-06 1.35e+02 -8.6 6.11e-05 - 1.75e-01 1.36e-05h 1\n", + " 38 4.8000669e-01 5.04e-06 1.36e+02 -8.6 1.27e-04 - 9.83e-02 1.38e-07f 2\n", + " 39 4.8000669e-01 5.04e-06 1.37e+02 -8.6 6.12e-05 - 2.54e-01 9.45e-04h 1\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 40 4.8000669e-01 4.94e-06 1.35e+02 -8.6 6.12e-05 - 1.83e-01 1.89e-02f 1\n", + " 41 4.8000669e-01 4.94e-06 1.36e+02 -8.6 2.85e-04 - 9.97e-02 1.10e-07f 2\n", + " 42 4.8000669e-01 4.94e-06 1.37e+02 -8.6 6.00e-05 - 1.72e-01 4.40e-05h 1\n", + " 43 4.8000669e-01 4.94e-06 1.37e+02 -8.6 1.41e-04 - 9.04e-02 1.49e-06f 2\n", + " 44 4.8000669e-01 4.94e-06 1.38e+02 -8.6 6.01e-05 - 1.71e-01 5.97e-06f 2\n", + " 45 4.8000670e-01 2.65e-11 6.17e+01 -8.6 6.01e-05 - 1.56e-01 1.00e+00h 1\n", + " 46 4.8000670e-01 2.64e-11 5.65e+01 -8.6 3.45e-06 - 5.27e-02 4.42e-04h 1\n", + " 47 4.8000670e-01 2.26e-11 7.42e+01 -8.6 1.45e-07 - 6.61e-01 1.47e-01f 2\n", + " 48 4.8000670e-01 2.25e-11 8.82e+01 -8.6 7.27e-06 - 2.11e-01 1.18e-03h 1\n", + " 49 4.8000670e-01 2.25e-11 1.30e+02 -8.6 8.86e-06 - 7.86e-01 1.57e-04f 2\n", + "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", + " 50 4.8000670e-01 2.25e-11 1.33e+02 -8.6 4.24e-05 - 2.54e-01 1.00e-04h 1\n", + " 51 4.8000670e-01 2.25e-11 1.41e+02 -8.6 6.81e-05 - 1.00e+00 2.59e-05f 2\n", + " 52 4.8000670e-01 3.10e-11 2.08e+00 -8.6 1.27e-07 - 2.54e-01 1.00e+00h 1\n", + " 53 4.8000670e-01 3.19e-09 1.41e+02 -8.6 3.37e-05 - 1.00e+00 4.73e-04h 1\n", + " 54 4.8000670e-01 9.74e-11 7.50e-11 -8.6 1.65e-08 - 1.00e+00 1.00e+00f 1\n", + "\n", + "Number of Iterations....: 54\n", + "\n", + " (scaled) (unscaled)\n", + "Objective...............: 4.8000669509937166e-01 4.8000669509937166e-01\n", + "Dual infeasibility......: 7.5043113584813605e-11 7.5043113584813605e-11\n", + "Constraint violation....: 9.7397756526618195e-11 9.7397756526618195e-11\n", + "Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00\n", + "Complementarity.........: 2.5636037643218892e-09 2.5636037643218892e-09\n", + "Overall NLP error.......: 9.7397756526618195e-11 2.5636037643218892e-09\n", + "\n", + "\n", + "Number of objective function evaluations = 72\n", + "Number of objective gradient evaluations = 55\n", + "Number of equality constraint evaluations = 72\n", + "Number of inequality constraint evaluations = 72\n", + "Number of equality constraint Jacobian evaluations = 55\n", + "Number of inequality constraint Jacobian evaluations = 55\n", + "Number of Lagrangian Hessian evaluations = 54\n", + "Total seconds in IPOPT = 0.125\n", + "\n", + "EXIT: Optimal Solution Found.\n", + "\b" + ] + } + ], + "source": [ + "# define a GCN sequential model\n", + "nn2 = GCN_Sequential(Sigmoid, global_mean_pool)\n", + "\n", + "# create pyomo model\n", + "m2 = pyo.ConcreteModel()\n", + "\n", + "# create an OMLT block for the neural network and build its formulation\n", + "m2.nn = OmltBlock()\n", + "\n", + "# build formulation in block m.nn\n", + "gnn_with_fixed_graph(m2.nn, nn2, N, A, scaled_input_bounds=input_bounds)\n", + "\n", + "# set the objective as the single output of the model\n", + "m2.obj = pyo.Objective(expr=m2.nn.outputs[0])\n", + "\n", + "# solve the optimization problem\n", + "status = pyo.SolverFactory(\"ipopt\").solve(m2, tee=True)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -345,7 +491,7 @@ "source": [ "import numpy as np\n", "import torch\n", - "from torch.nn import Linear, ReLU, Sigmoid\n", + "from torch.nn import Linear, ReLU\n", "from torch_geometric.nn import Sequential, SAGEConv\n", "from torch_geometric.nn import global_add_pool\n", "from omlt.io.torch_geometric import gnn_with_non_fixed_graph\n", @@ -389,12 +535,12 @@ "output_type": "stream", "text": [ "Welcome to the CBC MILP Solver \n", - "Version: 2.10.10 \n", - "Build Date: Aug 1 2023 \n", + "Version: 2.9.9 \n", + "Build Date: Oct 13 2018 \n", "\n", - "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT_test/bin/cbc -printingOptions all -import /var/tmp/pbs.8152010.pbs/tmpnzmuzmeh.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.8152010.pbs/tmpnzmuzmeh.pyomo.soln (default strategy 1)\n", + "command line - /rds/general/user/sz421/home/anaconda3/envs/OMLT_test/bin/cbc -printingOptions all -import /var/tmp/pbs.8259409.pbs/tmp1n22ks_r.pyomo.lp -stat=1 -solve -solu /var/tmp/pbs.8259409.pbs/tmp1n22ks_r.pyomo.soln (default strategy 1)\n", "Option for printingOptions changed from normal to all\n", - "Presolve 260 (-137) rows, 141 (-51) columns and 876 (-197) elements\n", + "Presolve 260 (-137) rows, 141 (-51) columns and 852 (-173) elements\n", "Statistics for presolved model\n", "Original problem has 32 integers (32 of which binary)\n", "Presolved problem has 29 integers (29 of which binary)\n", @@ -413,7 +559,7 @@ "===== end objective counts\n", "\n", "\n", - "Problem has 260 rows, 141 columns (2 with objective) and 876 elements\n", + "Problem has 260 rows, 141 columns (2 with objective) and 852 elements\n", "Column breakdown:\n", "0 of type 0.0->inf, 62 of type 0.0->up, 0 of type lo->inf, \n", "50 of type lo->up, 0 of type free, 0 of type fixed, \n", @@ -421,17 +567,17 @@ "Row breakdown:\n", "0 of type E 0.0, 0 of type E 1.0, 0 of type E -1.0, \n", "26 of type E other, 0 of type G 0.0, 0 of type G 1.0, \n", - "0 of type G other, 130 of type L 0.0, 24 of type L 1.0, \n", - "80 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", + "0 of type G other, 154 of type L 0.0, 24 of type L 1.0, \n", + "56 of type L other, 0 of type Range 0.0->1.0, 0 of type Range other, \n", "0 of type Free \n", "Continuous objective value is 0.107106 - 0.00 seconds\n", - "Cgl0003I 0 fixed, 0 tightened bounds, 4 strengthened rows, 0 substitutions\n", - "Cgl0004I processed model has 237 rows, 118 columns (29 integer (29 of which binary)) and 989 elements\n", - "Cbc0038I Initial state - 17 integers unsatisfied sum - 3.14435\n", - "Cbc0038I Pass 1: suminf. 1.01765 (9) obj. 0.107106 iterations 71\n", + "Cgl0003I 0 fixed, 0 tightened bounds, 1 strengthened rows, 0 substitutions\n", + "Cgl0004I processed model has 237 rows, 118 columns (29 integer (29 of which binary)) and 969 elements\n", + "Cbc0038I Initial state - 17 integers unsatisfied sum - 1.66726\n", + "Cbc0038I Pass 1: suminf. 1.01765 (9) obj. 0.107106 iterations 47\n", "Cbc0038I Solution found of 0.107106\n", "Cbc0038I Relaxing continuous gives 0.107106\n", - "Cbc0038I Before mini branch and bound, 12 integers at bound fixed and 38 continuous\n", + "Cbc0038I Before mini branch and bound, 12 integers at bound fixed and 40 continuous\n", "Cbc0038I Mini branch and bound did not improve solution (0.01 seconds)\n", "Cbc0038I After 0.01 seconds - Feasibility pump exiting with objective of 0.107106 - took 0.00 seconds\n", "Cbc0012I Integer solution of 0.10710584 found by feasibility pump after 0 iterations and 0 nodes (0.01 seconds)\n", @@ -445,7 +591,6 @@ "MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", "FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", "TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", - "ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)\n", "\n", "Result - Optimal solution found\n", "\n", @@ -453,7 +598,7 @@ "Enumerated nodes: 0\n", "Total iterations: 0\n", "Time (CPU seconds): 0.01\n", - "Time (Wallclock seconds): 0.01\n", + "Time (Wallclock seconds): 0.02\n", "\n", "Total time (CPU seconds): 0.01 (Wallclock seconds): 0.02\n", "\n" @@ -462,140 +607,7 @@ ], "source": [ "# define a GAGE sequential model\n", - "nn2 = SAGE_Sequential(ReLU, global_add_pool)\n", - "# number of nodes\n", - "N = 3\n", - "\n", - "# size of inputs = number of nodes x number of input features\n", - "input_size = [6]\n", - "# define lower and upper bounds for each input\n", - "input_bounds = {}\n", - "for i in range(input_size[0]):\n", - " input_bounds[(i)] = (-1.0, 1.0)\n", - "\n", - "# create pyomo model\n", - "m2 = pyo.ConcreteModel()\n", - "\n", - "# create an OMLT block for the neural network and build its formulation\n", - "m2.nn = OmltBlock()\n", - "\n", - "# build formulation in block m.nn\n", - "gnn_with_non_fixed_graph(m2.nn, nn2, N, scaled_input_bounds=input_bounds)\n", - "\n", - "# set the objective as the single output of the model\n", - "m2.obj = pyo.Objective(expr=m2.nn.outputs[0])\n", - "\n", - "# solve the optimization problem\n", - "status = pyo.SolverFactory(\"cbc\").solve(m2, tee=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For smooth activation function like Sigmoid, a smooth optimization solvers (such as Ipopt) is needed:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Ipopt 3.14.12: \n", - "==> Warning: Treating 6 binary and 0 integer variables as continuous.\n", - "\n", - "\n", - "******************************************************************************\n", - "This program contains Ipopt, a library for large-scale nonlinear optimization.\n", - " Ipopt is released as open source code under the Eclipse Public License (EPL).\n", - " For more information visit https://github.com/coin-or/Ipopt\n", - "******************************************************************************\n", - "\n", - "This is Ipopt version 3.14.12, running with linear solver MUMPS 5.2.1.\n", - "\n", - "Number of nonzeros in equality constraint Jacobian...: 449\n", - "Number of nonzeros in inequality constraint Jacobian.: 468\n", - "Number of nonzeros in Lagrangian Hessian.............: 26\n", - "\n", - "Total number of variables............................: 166\n", - " variables with only lower bounds: 0\n", - " variables with lower and upper bounds: 164\n", - " variables with only upper bounds: 0\n", - "Total number of equality constraints.................: 103\n", - "Total number of inequality constraints...............: 216\n", - " inequality constraints with only lower bounds: 0\n", - " inequality constraints with lower and upper bounds: 0\n", - " inequality constraints with only upper bounds: 216\n", - "\n", - "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", - " 0 0.0000000e+00 6.52e-01 7.52e-04 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0\n", - " 1 1.4746296e-02 6.32e-01 1.39e+00 -1.0 8.66e-01 - 1.28e-02 3.08e-02f 1\n", - " 2 3.1873491e-01 2.12e-01 1.91e+01 -1.0 1.08e+00 - 3.20e-02 6.65e-01f 1\n", - " 3 3.3291931e-01 1.93e-01 1.56e+01 -1.0 3.34e-01 - 7.50e-01 9.04e-02f 1\n", - " 4 4.1605860e-01 8.12e-02 6.77e+00 -1.0 3.72e-01 - 5.03e-01 5.79e-01f 1\n", - " 5 4.4666096e-01 4.00e-02 1.79e+01 -1.0 3.96e-01 - 7.08e-01 5.07e-01h 1\n", - " 6 4.6317765e-01 1.82e-02 8.24e+01 -1.0 2.77e-01 - 1.00e+00 5.44e-01h 1\n", - " 7 4.7137936e-01 7.43e-03 1.79e+02 -1.0 1.71e-01 - 1.00e+00 5.93e-01h 1\n", - " 8 4.7469933e-01 3.08e-03 4.39e+02 -1.0 6.74e-02 - 1.00e+00 5.85e-01h 1\n", - " 9 4.7608122e-01 1.28e-03 1.06e+03 -1.0 2.81e-02 - 1.00e+00 5.86e-01h 1\n", - "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", - " 10 4.7665353e-01 5.29e-04 2.55e+03 -1.0 1.16e-02 - 1.00e+00 5.86e-01h 1\n", - " 11 4.7689072e-01 2.19e-04 6.15e+03 -1.0 4.81e-03 - 1.00e+00 5.86e-01h 1\n", - " 12 4.7698895e-01 9.04e-05 1.48e+04 -1.0 1.99e-03 - 1.00e+00 5.87e-01h 1\n", - " 13 4.7702965e-01 3.72e-05 3.54e+04 -1.0 8.22e-04 - 1.00e+00 5.88e-01h 1\n", - " 14 4.7703175e-01 3.44e-05 1.90e+05 -1.0 3.38e-04 - 1.00e+00 7.40e-02f 4\n", - " 15 4.7705226e-01 7.65e-06 8.24e+04 -1.0 3.13e-04 - 1.00e+00 7.78e-01h 1\n", - " 16 4.7705268e-01 7.10e-06 7.71e+05 -1.0 6.96e-05 - 1.00e+00 7.20e-02f 4\n", - " 17 4.7705708e-01 1.35e-06 2.87e+05 -1.0 6.46e-05 - 1.00e+00 8.10e-01h 1\n", - " 18 4.7705717e-01 1.24e-06 2.66e+06 -1.0 1.23e-05 - 1.00e+00 8.39e-02f 4\n", - " 19 4.7705812e-01 1.73e-12 1.00e-06 -1.0 1.13e-05 - 1.00e+00 1.00e+00h 1\n", - "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", - " 20 4.7704910e-01 6.57e-09 9.15e+03 -5.7 5.47e-04 - 9.99e-01 1.00e+00f 1\n", - " 21 4.7241100e-01 2.07e-03 4.56e+03 -5.7 2.94e-01 - 5.74e-01 9.31e-01f 1\n", - " 22 4.7107356e-01 1.09e-03 1.39e+03 -5.7 1.83e-01 - 6.98e-01 8.54e-01h 1\n", - " 23 4.7049903e-01 3.12e-03 2.62e+02 -5.7 3.65e-01 - 8.13e-01 8.89e-01f 1\n", - " 24 4.7022019e-01 3.61e-03 3.33e+01 -5.7 5.62e-01 - 8.71e-01 5.90e-01f 1\n", - " 25 4.7016027e-01 4.04e-04 7.29e-01 -5.7 2.34e-01 - 9.79e-01 1.00e+00f 1\n", - " 26 4.7014863e-01 2.24e-05 7.68e-08 -5.7 3.49e-02 - 1.00e+00 1.00e+00h 1\n", - " 27 4.7014848e-01 2.14e-08 1.85e-11 -5.7 8.68e-04 - 1.00e+00 1.00e+00h 1\n", - " 28 4.7004983e-01 2.73e-04 3.48e+00 -8.6 1.95e-01 - 8.70e-01 8.51e-01h 1\n", - " 29 4.7002727e-01 1.61e-04 1.42e-01 -8.6 7.82e-02 - 9.74e-01 9.83e-01h 1\n", - "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", - " 30 4.7002699e-01 1.53e-06 2.93e-09 -8.6 7.19e-03 - 1.00e+00 1.00e+00f 1\n", - " 31 4.7002699e-01 1.63e-10 2.98e-13 -8.6 7.38e-05 - 1.00e+00 1.00e+00h 1\n", - "\n", - "Number of Iterations....: 31\n", - "\n", - " (scaled) (unscaled)\n", - "Objective...............: 4.7002698793134651e-01 4.7002698793134651e-01\n", - "Dual infeasibility......: 2.9843906102589463e-13 2.9843906102589463e-13\n", - "Constraint violation....: 1.6278367542810201e-10 1.6278367542810201e-10\n", - "Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00\n", - "Complementarity.........: 2.5060961140067687e-09 2.5060961140067687e-09\n", - "Overall NLP error.......: 2.5060961140067687e-09 2.5060961140067687e-09\n", - "\n", - "\n", - "Number of objective function evaluations = 41\n", - "Number of objective gradient evaluations = 32\n", - "Number of equality constraint evaluations = 41\n", - "Number of inequality constraint evaluations = 41\n", - "Number of equality constraint Jacobian evaluations = 32\n", - "Number of inequality constraint Jacobian evaluations = 32\n", - "Number of Lagrangian Hessian evaluations = 31\n", - "Total seconds in IPOPT = 0.065\n", - "\n", - "EXIT: Optimal Solution Found.\n", - "\b" - ] - } - ], - "source": [ - "# define a GAGE sequential model\n", - "nn3 = SAGE_Sequential(Sigmoid, global_add_pool)\n", + "nn3 = SAGE_Sequential(ReLU, global_add_pool)\n", "# number of nodes\n", "N = 3\n", "\n", @@ -619,7 +631,7 @@ "m3.obj = pyo.Objective(expr=m3.nn.outputs[0])\n", "\n", "# solve the optimization problem\n", - "status = pyo.SolverFactory(\"ipopt\").solve(m3, tee=True)\n" + "status = pyo.SolverFactory(\"cbc\").solve(m3, tee=True)" ] }, { From 24f3b96e6f61542032c204177ea5dccb0098586b Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 4 Oct 2023 11:29:25 +0100 Subject: [PATCH 18/27] add documentations --- src/omlt/io/torch_geometric/torch_geometric_reader.py | 8 ++++++-- src/omlt/neuralnet/layer.py | 10 ++++++++-- 2 files changed, 14 insertions(+), 4 deletions(-) diff --git a/src/omlt/io/torch_geometric/torch_geometric_reader.py b/src/omlt/io/torch_geometric/torch_geometric_reader.py index 16d5db4d..8644301a 100644 --- a/src/omlt/io/torch_geometric/torch_geometric_reader.py +++ b/src/omlt/io/torch_geometric/torch_geometric_reader.py @@ -33,10 +33,12 @@ def _compute_sage_norm(A, aggr): A : matrix-like the adjacency matrix. aggr : str - the aggregation function. + the aggregation function, "sum" (default) or "mean" """ N = A.shape[0] + # sum aggregation sage_norm = A + np.eye(N) + # mean aggregation if aggr == "mean": degrees = np.sum(A, axis=0) for u in range(N): @@ -175,7 +177,9 @@ def load_torch_geometric_sequential( ): # nonlinear activation results in a MINLP if operations[index] in ["Sigmoid", "LogSoftmax", "Softplus", "Tanh"]: - warnings.warn("nonlinear activation results in a MINLP") + warnings.warn( + "nonlinear activation results in a MINLP", stacklevel=2 + ) # Linear layers, all activation functions, and all pooling functions are still supported. continue if operations[index] not in _LAYER_OP_TYPES_NON_FIXED_GRAPH: diff --git a/src/omlt/neuralnet/layer.py b/src/omlt/neuralnet/layer.py index fe5143a7..7f1dad8b 100644 --- a/src/omlt/neuralnet/layer.py +++ b/src/omlt/neuralnet/layer.py @@ -292,8 +292,14 @@ def __init__( activation=activation, input_index_mapper=input_index_mapper, ) - assert input_size[-1] % N == 0 - assert output_size[-1] % N == 0 + if input_size[-1] % N != 0: + raise ValueError( + "Input size must equal to the number of nodes multiply the number of input node features" + ) + if output_size[-1] % N != 0: + raise ValueError( + "Output size must equal to the number of nodes multiply the number of output node features" + ) self.__N = N self.__gnn_input_size = input_size[-1] // N self.__gnn_output_size = output_size[-1] // N From 5879b3e21196af2c7c9eb0fb1b7d0a12ecfd6391 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 4 Oct 2023 16:08:42 +0100 Subject: [PATCH 19/27] add tests for exceptions --- .../torch_geometric/torch_geometric_reader.py | 4 +- src/omlt/neuralnet/layers/full_space.py | 5 +- tests/io/test_torch_geometric.py | 54 ++++++++++++++++++- tests/neuralnet/test_layer.py | 14 +++++ 4 files changed, 74 insertions(+), 3 deletions(-) diff --git a/src/omlt/io/torch_geometric/torch_geometric_reader.py b/src/omlt/io/torch_geometric/torch_geometric_reader.py index 8644301a..beee1516 100644 --- a/src/omlt/io/torch_geometric/torch_geometric_reader.py +++ b/src/omlt/io/torch_geometric/torch_geometric_reader.py @@ -271,9 +271,11 @@ def load_torch_geometric_sequential( for input_index in range(n_layer_inputs): for output_index in range(n_layer_outputs): if input_index % n_layer_outputs == output_index: + # mean pooling if operations[index] == "global_mean_pool": weights[input_index, output_index] = 1.0 / N - elif operations[index] == "global_add_pool": + # add pooling + else: weights[input_index, output_index] = 1.0 curr_layer = DenseLayer( [n_layer_inputs], diff --git a/src/omlt/neuralnet/layers/full_space.py b/src/omlt/neuralnet/layers/full_space.py index 56d85ad1..c8967924 100644 --- a/src/omlt/neuralnet/layers/full_space.py +++ b/src/omlt/neuralnet/layers/full_space.py @@ -97,13 +97,16 @@ def full_space_gnn_layer(net_block, net, layer_block, layer): input_node_index = local_index[-1] // layer.gnn_input_size for output_node_index in range(layer.N): + # this edge is not fixed if not net_block.A[input_node_index, output_node_index].fixed: input_layer_block.zbar[input_index, output_node_index].setlb(min(0, lb)) input_layer_block.zbar[input_index, output_node_index].setub(max(0, ub)) + # this edge is fixed to be 1 elif pyo.value(net_block.A[input_node_index, output_node_index]) == 1: input_layer_block.zbar[input_index, output_node_index].setlb(lb) input_layer_block.zbar[input_index, output_node_index].setub(ub) - elif pyo.value(net_block.A[input_node_index, output_node_index]) == 0: + # this edge is fixed to be 0 + else: input_layer_block.zbar[input_index, output_node_index].setlb(0) input_layer_block.zbar[input_index, output_node_index].setub(0) diff --git a/tests/io/test_torch_geometric.py b/tests/io/test_torch_geometric.py index 1c52abbf..d80d176b 100644 --- a/tests/io/test_torch_geometric.py +++ b/tests/io/test_torch_geometric.py @@ -13,7 +13,7 @@ if torch_available and torch_geometric_available: from torch.nn import Linear, ReLU, Sigmoid, Softplus, Tanh from torch_geometric.nn import Sequential, GCNConv, SAGEConv - from torch_geometric.nn import global_mean_pool, global_add_pool + from torch_geometric.nn import global_mean_pool, global_add_pool, global_max_pool from omlt.io.torch_geometric import ( load_torch_geometric_sequential, gnn_with_fixed_graph, @@ -171,3 +171,55 @@ def test_gnn_with_non_fixed_graph(): for root_weight in [False, True]: nn = SAGE_Sequential(ReLU, pooling, aggr, root_weight) _test_gnn_with_non_fixed_graph(nn) + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def _test_gnn_value_error(nn, error_info, error_type="ValueError"): + N = 4 + F = 2 + + input_size = [N * F] + input_bounds = {} + for i in range(input_size[0]): + input_bounds[(i)] = (-1.0, 1.0) + if error_type == "ValueError": + with pytest.raises(ValueError) as excinfo: + load_torch_geometric_sequential( + nn=nn, + N=N, + A=None, + scaled_input_bounds=input_bounds, + ) + assert str(excinfo.value) == error_info + elif error_type == "warns": + with pytest.warns() as record: + load_torch_geometric_sequential( + nn=nn, + N=N, + A=None, + scaled_input_bounds=input_bounds, + ) + assert str(record[0].message) == error_info + + +@pytest.mark.skipif( + not (torch_available and torch_geometric_available), + reason="Test only valid when torch and torch_geometric are available", +) +def test_gnn_value_error(): + nn = SAGE_Sequential(ReLU, global_max_pool, "mean", True) + _test_gnn_value_error(nn, "this operation is not supported") + + nn = SAGE_Sequential(Sigmoid, global_mean_pool, "sum", True) + _test_gnn_value_error(nn, "nonlinear activation results in a MINLP", "warns") + + nn = SAGE_Sequential(ReLU, global_mean_pool, "mean", True) + _test_gnn_value_error( + nn, "this aggregation is not supported when the graph is not fixed" + ) + + nn = GCN_Sequential(ReLU, global_mean_pool) + _test_gnn_value_error(nn, "this layer is not supported when the graph is not fixed") diff --git a/tests/neuralnet/test_layer.py b/tests/neuralnet/test_layer.py index fa0bc085..e7ddaf1a 100644 --- a/tests/neuralnet/test_layer.py +++ b/tests/neuralnet/test_layer.py @@ -132,3 +132,17 @@ def test_gnn_layer_with_input_index_mapper(): A3 = np.array([[1, 1, 0], [1, 1, 1], [0, 1, 1]]) y3 = np.array([[[-6, 4, 0, -12, 11, 1, -5, 5, 2], [-1, 0, 1, -1, 0, 1, -1, 0, 1]]]) assert np.array_equal(layer._eval_with_adjacency(inputs, A3), y3) + + with pytest.raises(ValueError) as excinfo: + layer = GNNLayer([5], [9], weights, biases, N=3) + assert ( + str(excinfo.value) + == "Input size must equal to the number of nodes multiply the number of input node features" + ) + + with pytest.raises(ValueError) as excinfo: + layer = GNNLayer([6], [8], weights, biases, N=3) + assert ( + str(excinfo.value) + == "Output size must equal to the number of nodes multiply the number of output node features" + ) From 85aead155405de3496a7fa6e477cfdc216298eb4 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Tue, 10 Oct 2023 11:17:47 +0100 Subject: [PATCH 20/27] add full path in __init__.py --- src/omlt/neuralnet/activations/__init__.py | 12 +++++++++--- src/omlt/neuralnet/layers/__init__.py | 4 ++-- tests/neuralnet/test_layer.py | 4 ++-- 3 files changed, 13 insertions(+), 7 deletions(-) diff --git a/src/omlt/neuralnet/activations/__init__.py b/src/omlt/neuralnet/activations/__init__.py index b2aecb1b..d18af03e 100644 --- a/src/omlt/neuralnet/activations/__init__.py +++ b/src/omlt/neuralnet/activations/__init__.py @@ -1,6 +1,12 @@ -from .linear import linear_activation_constraint, linear_activation_function -from .relu import ComplementarityReLUActivation, bigm_relu_activation_constraint -from .smooth import ( +from omlt.neuralnet.activations.linear import ( + linear_activation_constraint, + linear_activation_function, +) +from omlt.neuralnet.activations.relu import ( + ComplementarityReLUActivation, + bigm_relu_activation_constraint, +) +from omlt.neuralnet.activations.smooth import ( sigmoid_activation_constraint, sigmoid_activation_function, softplus_activation_constraint, diff --git a/src/omlt/neuralnet/layers/__init__.py b/src/omlt/neuralnet/layers/__init__.py index 776ab8ec..b536e83b 100644 --- a/src/omlt/neuralnet/layers/__init__.py +++ b/src/omlt/neuralnet/layers/__init__.py @@ -1,6 +1,6 @@ -from .full_space import ( +from omlt.neuralnet.layers.full_space import ( full_space_conv2d_layer, full_space_dense_layer, full_space_gnn_layer, ) -from .reduced_space import reduced_space_dense_layer +from omlt.neuralnet.layers.reduced_space import reduced_space_dense_layer diff --git a/tests/neuralnet/test_layer.py b/tests/neuralnet/test_layer.py index e7ddaf1a..7b865faf 100644 --- a/tests/neuralnet/test_layer.py +++ b/tests/neuralnet/test_layer.py @@ -137,12 +137,12 @@ def test_gnn_layer_with_input_index_mapper(): layer = GNNLayer([5], [9], weights, biases, N=3) assert ( str(excinfo.value) - == "Input size must equal to the number of nodes multiply the number of input node features" + == "Input size must equal to the number of nodes multiplied by the number of input node features" ) with pytest.raises(ValueError) as excinfo: layer = GNNLayer([6], [8], weights, biases, N=3) assert ( str(excinfo.value) - == "Output size must equal to the number of nodes multiply the number of output node features" + == "Output size must equal to the number of nodes multiplied by the number of output node features" ) From 18ffcc5a1f52d72410a76e8157239de700befec5 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Tue, 10 Oct 2023 11:19:43 +0100 Subject: [PATCH 21/27] update comments --- src/omlt/neuralnet/layer.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/omlt/neuralnet/layer.py b/src/omlt/neuralnet/layer.py index 7f1dad8b..dbf3f2ac 100644 --- a/src/omlt/neuralnet/layer.py +++ b/src/omlt/neuralnet/layer.py @@ -294,11 +294,11 @@ def __init__( ) if input_size[-1] % N != 0: raise ValueError( - "Input size must equal to the number of nodes multiply the number of input node features" + "Input size must equal to the number of nodes multiplied by the number of input node features" ) if output_size[-1] % N != 0: raise ValueError( - "Output size must equal to the number of nodes multiply the number of output node features" + "Output size must equal to the number of nodes multiplied by the number of output node features" ) self.__N = N self.__gnn_input_size = input_size[-1] // N From 51263ecfdff814ef546bcaace755a0ea9a84c2b2 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Tue, 5 Dec 2023 09:44:53 +0000 Subject: [PATCH 22/27] add contributors --- README.rst | 19 +++++++++++++++++-- 1 file changed, 17 insertions(+), 2 deletions(-) diff --git a/README.rst b/README.rst index cb90ed8e..e31c8164 100644 --- a/README.rst +++ b/README.rst @@ -149,11 +149,11 @@ Contributors * - |jalving|_ - Jordan Jalving - - This work was funded by Sandia National Laboratories, Laboratory Directed Research and Development program + - This work was funded by Sandia National Laboratories, Laboratory Directed Research and Development program. * - |fracek|_ - Francesco Ceccon - - This work was funded by an Engineering & Physical Sciences Research Council Research Fellowship [GrantNumber EP/P016871/1] + - This work was funded by an Engineering & Physical Sciences Research Council Research Fellowship [GrantNumber EP/P016871/1]. * - |carldlaird|_ - Carl D. Laird @@ -171,6 +171,13 @@ Contributors - Bashar L. Ammari - This work was funded by Sandia National Laboratories, Laboratory Directed Research and Development program. + * - |juan-campos|_ + - Juan S. Campos + - This work was funded by an Engineering & Physical Sciences Research Council Research Fellowship [GrantNumber EP/W003317/1]. + + * - |zshiqiang|_ + - Shiqiang Zhang + - This work was funded by an Imperial College Hans Rausing PhD Scholarship. .. _jalving: https://github.com/jalving .. |jalving| image:: https://avatars1.githubusercontent.com/u/16785413?s=120&v=4 @@ -195,3 +202,11 @@ Contributors .. _bammari: https://github.com/bammari .. |bammari| image:: https://avatars.githubusercontent.com/u/96192809?v=4 :width: 80px + +.. _juan-campos: https://github.com/juan-campos +.. |juan-campos| image:: https://avatars.githubusercontent.com/u/65016230?v=4 + :width: 80px + +.. _zshiqiang: https://github.com/zshiqiang +.. |zshiqiang| image:: https://avatars.githubusercontent.com/u/91337036?v=4 + :width: 80px From 72b9f65d0de9ce078dcbc5542ae648ebb4a60635 Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 6 Dec 2023 14:29:34 +0000 Subject: [PATCH 23/27] update documentations --- src/omlt/neuralnet/activations/__init__.py | 12 ------------ src/omlt/neuralnet/layers/__init__.py | 9 --------- 2 files changed, 21 deletions(-) diff --git a/src/omlt/neuralnet/activations/__init__.py b/src/omlt/neuralnet/activations/__init__.py index f0272385..fcae4cc8 100644 --- a/src/omlt/neuralnet/activations/__init__.py +++ b/src/omlt/neuralnet/activations/__init__.py @@ -1,14 +1,3 @@ -<<<<<<< HEAD -from omlt.neuralnet.activations.linear import ( - linear_activation_constraint, - linear_activation_function, -) -from omlt.neuralnet.activations.relu import ( - ComplementarityReLUActivation, - bigm_relu_activation_constraint, -) -from omlt.neuralnet.activations.smooth import ( -======= r""" Since all activation functions are element-wised, we only consider how to formulate activation functions for a single neuron, where :math:`x` denotes pre-activation variable, and :math:`y` denotes post-activation variable. @@ -16,7 +5,6 @@ from .linear import linear_activation_constraint, linear_activation_function from .relu import ComplementarityReLUActivation, bigm_relu_activation_constraint from .smooth import ( ->>>>>>> a3d128d569b9b7cbf13315ea6be813f076d56b22 sigmoid_activation_constraint, sigmoid_activation_function, softplus_activation_constraint, diff --git a/src/omlt/neuralnet/layers/__init__.py b/src/omlt/neuralnet/layers/__init__.py index e068fb26..aa4944fd 100644 --- a/src/omlt/neuralnet/layers/__init__.py +++ b/src/omlt/neuralnet/layers/__init__.py @@ -1,11 +1,3 @@ -<<<<<<< HEAD -from omlt.neuralnet.layers.full_space import ( - full_space_conv2d_layer, - full_space_dense_layer, - full_space_gnn_layer, -) -from omlt.neuralnet.layers.reduced_space import reduced_space_dense_layer -======= r""" Since OMLT builds layer and activation functions in layer level, we ignore the layer index and use the following notations to describe the :math:`l`-th layer: @@ -23,4 +15,3 @@ """ from .full_space import full_space_conv2d_layer, full_space_dense_layer from .reduced_space import reduced_space_dense_layer ->>>>>>> a3d128d569b9b7cbf13315ea6be813f076d56b22 From 6add77b1baa8cbd918c728b0a4b00cf7f0f5e75f Mon Sep 17 00:00:00 2001 From: zshiqiang Date: Wed, 6 Dec 2023 17:05:23 +0000 Subject: [PATCH 24/27] update documentations --- .../citeseer/processed/data.pt | Bin 0 -> 49160739 bytes .../citeseer/processed/pre_filter.pt | Bin 0 -> 431 bytes .../citeseer/processed/pre_transform.pt | Bin 0 -> 431 bytes .../citeseer/raw/__MACOSX/._citeseer.attr | Bin 0 -> 220 bytes .../raw/__MACOSX/citeseer.attr/._.DS_Store | Bin 0 -> 120 bytes .../raw/__MACOSX/citeseer.attr/._edgelist.txt | Bin 0 -> 212 bytes .../raw/__MACOSX/citeseer.attr/._labels.txt | Bin 0 -> 212 bytes .../citeseer/raw/attrs.npz | Bin 0 -> 180368 bytes .../citeseer/raw/edgelist.txt | 4715 +++++++++++++++++ .../citeseer/raw/labels.txt | 3312 ++++++++++++ src/omlt/neuralnet/layer.py | 54 +- src/omlt/neuralnet/layers/full_space.py | 39 +- 12 files changed, 8089 insertions(+), 31 deletions(-) create mode 100644 data/AttributedGraphDataset/citeseer/processed/data.pt create mode 100644 data/AttributedGraphDataset/citeseer/processed/pre_filter.pt create mode 100644 data/AttributedGraphDataset/citeseer/processed/pre_transform.pt create mode 100644 data/AttributedGraphDataset/citeseer/raw/__MACOSX/._citeseer.attr create mode 100644 data/AttributedGraphDataset/citeseer/raw/__MACOSX/citeseer.attr/._.DS_Store create mode 100644 data/AttributedGraphDataset/citeseer/raw/__MACOSX/citeseer.attr/._edgelist.txt create mode 100644 data/AttributedGraphDataset/citeseer/raw/__MACOSX/citeseer.attr/._labels.txt create mode 100644 data/AttributedGraphDataset/citeseer/raw/attrs.npz create mode 100644 data/AttributedGraphDataset/citeseer/raw/edgelist.txt create mode 100644 data/AttributedGraphDataset/citeseer/raw/labels.txt diff --git a/data/AttributedGraphDataset/citeseer/processed/data.pt b/data/AttributedGraphDataset/citeseer/processed/data.pt new file mode 100644 index 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Campos and Christian Feldmann and Frederik Sandfort and Miriam Mathea and Ruth Misener}, + journal={arXiv preprint arXiv:2312.03613}, + year = {2023}, + } + Documentation ============== The latest OMLT documentation can be found at the `readthedocs page `_. Additionally, much of the current functionality is demonstrated using Jupyter notebooks available in the `notebooks folder `_.

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.../raw/__MACOSX/citeseer.attr/._labels.txt | Bin 212 -> 0 bytes .../citeseer/raw/attrs.npz | Bin 180368 -> 0 bytes .../citeseer/raw/edgelist.txt | 4715 ----------------- .../citeseer/raw/labels.txt | 3312 ------------ 11 files changed, 8085 deletions(-) delete mode 100644 .github/workflows/main.yml delete mode 100644 data/AttributedGraphDataset/citeseer/processed/data.pt delete mode 100644 data/AttributedGraphDataset/citeseer/processed/pre_filter.pt delete mode 100644 data/AttributedGraphDataset/citeseer/processed/pre_transform.pt delete mode 100644 data/AttributedGraphDataset/citeseer/raw/__MACOSX/._citeseer.attr delete mode 100644 data/AttributedGraphDataset/citeseer/raw/__MACOSX/citeseer.attr/._.DS_Store delete mode 100644 data/AttributedGraphDataset/citeseer/raw/__MACOSX/citeseer.attr/._edgelist.txt delete mode 100644 data/AttributedGraphDataset/citeseer/raw/__MACOSX/citeseer.attr/._labels.txt delete mode 100644 data/AttributedGraphDataset/citeseer/raw/attrs.npz delete mode 100644 data/AttributedGraphDataset/citeseer/raw/edgelist.txt delete mode 100644 data/AttributedGraphDataset/citeseer/raw/labels.txt diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml deleted file mode 100644 index 55870dbc..00000000 --- a/.github/workflows/main.yml +++ /dev/null @@ -1,58 +0,0 @@ ---- -name: CI - -on: - push: - branches: ["main","github-actions"] - pull_request: - branches: ["main"] - workflow_dispatch: - -jobs: - tests: - name: "Python ${{ matrix.python-version }}" - runs-on: "ubuntu-latest" - - strategy: - matrix: - # python-version: ["3.7", "3.8", "3.9"] - python-version: ["3.8", "3.9", "3.10"] - - steps: - - uses: "actions/checkout@v2" - - uses: "actions/setup-python@v2" - - uses: "s-weigand/setup-conda@v1" - with: - python-version: "${{ matrix.python-version }}" - - - name: Install solvers - run: sudo apt-get install -y glpk-utils coinor-cbc - - - name: "Install dependencies" - run: | - set -xe - python -VV - python -m site - python -m pip install 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