Verifying message-passing neural networks via topology-based bounds tightening

TL;DR

This paper introduces a topology-based bounds tightening method for verifying message-passing neural networks (MPNNs), enhancing robustness certification against various topological and feature perturbations using mixed-integer optimization.

Contribution

It presents a novel topology-based bounds tightening technique for MPNNs, enabling effective robustness certification under diverse graph perturbations and integrating it into an open-source solver.

Findings

Effective bounds tightening improves verification accuracy

Handles both edge addition and removal attacks

Integrates with SCIP solver for practical testing

Abstract

Since graph neural networks (GNNs) are often vulnerable to attack, we need to know when we can trust them. We develop a computationally effective approach towards providing robust certificates for message-passing neural networks (MPNNs) using a Rectified Linear Unit (ReLU) activation function. Because our work builds on mixed-integer optimization, it encodes a wide variety of subproblems, for example it admits (i) both adding and removing edges, (ii) both global and local budgets, and (iii) both topological perturbations and feature modifications. Our key technology, topology-based bounds tightening, uses graph structure to tighten bounds. We also experiment with aggressive bounds tightening to dynamically change the optimization constraints by tightening variable bounds. To demonstrate the effectiveness of these strategies, we implement an extension to the open-source branch-and-cut solver SCIP. We test on both node and graph classification problems and consider topological attacks that both add and remove edges.