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 are often vulnerable to attack%2C 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%2C it encodes a wide variety of subproblems%2C for example it admits (i) both adding and removing edges%2C (ii) both global and local budgets%2C and (iii) both topological perturbations and feature modifications. Our key technology%2C topology-based bounds tightening%2C 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%2C 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.?quality=80&w=800)
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