LinSATNet: The Positive Linear Satisfiability Neural Networks
This work addresses the challenge of integrating constraints into neural networks for researchers and practitioners in AI, offering a novel one-shot solver for satisfiability problems, though it is incremental in extending existing Sinkhorn methods.
The paper tackles the problem of encoding positive linear satisfiability constraints into neural networks by proposing LinSATNet, a differentiable satisfiability layer based on an extended Sinkhorn algorithm for multiple marginals, and demonstrates its application in unsupervised neural routing, partial graph matching with outliers, and financial portfolio prediction with constraints, achieving one-shot solutions without prior optimal solution supervision.
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