A Solver-free Framework for Scalable Learning in Neural ILP Architectures

There is a recent focus on designing architectures that have an Integer Linear Programming (ILP) layer within a neural model (referred to as \emph{Neural ILP} in this paper). Neural ILP architectures are suitable for pure reasoning tasks that require data-driven constraint learning or for tasks requiring both perception (neural) and reasoning (ILP). A recent SOTA approach for end-to-end training of Neural ILP explicitly defines gradients through the ILP black box [Paulus et al. [2021]] - this trains extremely slowly, owing to a call to the underlying ILP solver for every training data point in a minibatch. In response, we present an alternative training strategy that is \emph{solver-free}, i.e., does not call the ILP solver at all at training time. Neural ILP has a set of trainable hyperplanes (for cost and constraints in ILP), together representing a polyhedron.