Learning Branching Heuristics for Propositional Model Counting

TL;DR

Neuro# introduces a machine learning approach to improve the efficiency of exact #SAT solvers by learning effective branching heuristics, leading to significant speedups on various problem families.

Contribution

The paper presents Neuro#, a novel method for learning branching heuristics that enhance the performance of #SAT solvers on diverse problem instances.

Findings

Reduces step count on held-out instances

Generalizes to larger instances within the same problem family

Achieves orders of magnitude speedups on larger instances

Abstract

Propositional model counting, or #SAT, is the problem of computing the number of satisfying assignments of a Boolean formula. Many problems from different application areas, including many discrete probabilistic inference problems, can be translated into model counting problems to be solved by #SAT solvers. Exact #SAT solvers, however, are often not scalable to industrial size instances. In this paper, we present Neuro#, an approach for learning branching heuristics to improve the performance of exact #SAT solvers on instances from a given family of problems. We experimentally show that our method reduces the step count on similarly distributed held-out instances and generalizes to much larger instances from the same problem family. It is able to achieve these results on a number of different problem families having very different structures. In addition to step count improvements, Neuro# can also achieve orders of magnitude wall-clock speedups over the vanilla solver on larger instances in some problem families, despite the runtime overhead of querying the model.