LinSATNet: The Positive Linear Satisfiability Neural Networks

TL;DR

LinSATNet introduces a differentiable neural network layer based on an extended Sinkhorn algorithm to solve positive linear satisfiability problems in a one-shot manner, applicable to routing, graph matching, and portfolio optimization.

Contribution

The paper presents the first differentiable satisfiability layer for neural networks, extending Sinkhorn for multiple marginals and enabling one-shot solutions to complex satisfiability problems.

Findings

Successfully applied to neural routing without supervision

Effective in partial graph matching with outliers

Achieved continuous constraint satisfaction in portfolio prediction

Abstract

Encoding constraints into neural networks is attractive. This paper studies how to introduce the popular positive linear satisfiability to neural networks. We propose the first differentiable satisfiability layer based on an extension of the classic Sinkhorn algorithm for jointly encoding multiple sets of marginal distributions. We further theoretically characterize the convergence property of the Sinkhorn algorithm for multiple marginals. In contrast to the sequential decision e.g.\ reinforcement learning-based solvers, we showcase our technique in solving constrained (specifically satisfiability) problems by one-shot neural networks, including i) a neural routing solver learned without supervision of optimal solutions; ii) a partial graph matching network handling graphs with unmatchable outliers on both sides; iii) a predictive network for financial portfolios with continuous constraints. To our knowledge, there exists no one-shot neural solver for these scenarios when they are formulated as satisfiability problems. Source code is available at https://github.com/Thinklab-SJTU/LinSATNet