Unsat Core Prediction through Polarity-Aware Representation Learning over Clause-Literal Hypergraphs

TL;DR

This paper introduces a polarity-aware hypergraph neural network framework for SAT unsat core prediction, capturing higher-order interactions and literal polarities more effectively than prior models.

Contribution

It proposes a novel clause-literal hypergraph model with polarity-aware mechanisms and regularization, improving structural and polarity representation in SAT tasks.

Findings

Outperforms existing models on multiple SAT datasets.

Effectively captures higher-order clause-literal interactions.

Enhances polarity modeling with regularization.

Abstract

Graph neural networks have been widely used in Boolean satisfiability (SAT) tasks to learn structural information from SAT formulas. The goal of these studies is to solve SAT instances or to enhance SAT solvers, including tasks such as unsat-core prediction. However, most existing approaches model a SAT formula as a bipartite graph or a directed acyclic graph, which are less expressive in capturing higher-order interactions among literals and clauses. Moreover, these approaches are limited in modeling intrinsic polarity-related properties of SAT, such as the complementary relationship between the positive and negative literals of a variable. To address these limitations, we propose a polarity-aware representation learning framework over clause-literal hypergraphs. We model SAT formulas as clause-literal hypergraphs augmented with a clause incidence graph to capture higher-order structural interactions. We then introduce a polarity-aware decomposed mechanism that separates variable representations into polarity invariant and equivariant components, explicitly modeling the relationship between positive and negative literals, with the resulting literal representations propagated along the hypergraph structure. We further incorporate a polarity-inversion consistency regularization to reinforce polarity-consistent representations during training. Experimental results on multiple SAT datasets demonstrate the effectiveness of the proposed approach.