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This paper introduces a class of mixed-integer formulations for trained ReLUneural networks. The approach balances model size and tightness by partitioningnode inputs into a number of groups and forming the convex hull over thepartitions via disjunctive programming. At one extreme, one partition per inputrecovers the convex hull of a node, i.e., the tightest possible formulation foreach node. For fewer partitions, we develop smaller relaxations thatapproximate the convex hull, and show that they outperform existingformulations. Specifically, we propose strategies for partitioning variablesbased on theoretical motivations and validate these strategies using extensivecomputational experiments. Furthermore, the proposed scheme complements knownalgorithmic approaches, e.g., optimization-based bound tightening capturesdependencies within a partition.

Partition-based formulations for mixed-integer optimization of trained ReLU neural networks