Differentiable MaxSAT Message Passing

Francesco Alesiani, Cristóbal Corvalán Morbiducci, Markus Zopf

Keywords: SAT, MAXSAT, Graph, Message Passing

TL;DR: We explore the use of a differentiable maxSAT solver and the message passing architecture to model logic rules in graph structured data

Abstract:

The message-passing principle is used in the most popular neural networks for graph-structured data. However, current message-passing approaches use black-box neural models that transform features over continuous domain, thus limiting the description capability of GNNs.

In this work, we explore a novel type of message passing based on a differentiable satisfiability solver. Our model learns logical rules that
encode which and how messages are passed from one node to another node. The rules are learned in a relaxed continuous space, which renders the training process end-to-end differentiable and thus enables standard gradient-based training. In our experiments we show that MAXSAT-MP learns arithmetic operations and that is on par with state-of-the-art GNNs on graph structured data.

Submission Number: 38