  This paper introduces a class of mixed-integer formulations for trained ReLU
neural networks. The approach balances model size and tightness by partitioning
node inputs into a number of groups and forming the convex hull over the
partitions via disjunctive programming. At one extreme, one partition per input
recovers the convex hull of a node, i.e., the tightest possible formulation for
each node. For fewer partitions, we develop smaller relaxations that
approximate the convex hull, and show that they outperform existing
formulations. Specifically, we propose strategies for partitioning variables
based on theoretical motivations and validate these strategies using extensive
computational experiments. Furthermore, the proposed scheme complements known
algorithmic approaches, e.g., optimization-based bound tightening captures
dependencies within a partition.
