LinSATNet: The Positive Linear Satisfiability Neural Networks

Runzhong Wang, Yunhao Zhang, Ziao Guo, Tianyi Chen, Xiaokang Yang, Junchi Yan
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:36605-36625, 2023.

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, and the underlying formulation is also derived. 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-wang23at, title = {{L}in{SATN}et: The Positive Linear Satisfiability Neural Networks}, author = {Wang, Runzhong and Zhang, Yunhao and Guo, Ziao and Chen, Tianyi and Yang, Xiaokang and Yan, Junchi}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {36605--36625}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/wang23at/wang23at.pdf}, url = {https://proceedings.mlr.press/v202/wang23at.html}, 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, and the underlying formulation is also derived. 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.} }
Endnote
%0 Conference Paper %T LinSATNet: The Positive Linear Satisfiability Neural Networks %A Runzhong Wang %A Yunhao Zhang %A Ziao Guo %A Tianyi Chen %A Xiaokang Yang %A Junchi Yan %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-wang23at %I PMLR %P 36605--36625 %U https://proceedings.mlr.press/v202/wang23at.html %V 202 %X 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, and the underlying formulation is also derived. 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.
APA
Wang, R., Zhang, Y., Guo, Z., Chen, T., Yang, X. & Yan, J.. (2023). LinSATNet: The Positive Linear Satisfiability Neural Networks. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:36605-36625 Available from https://proceedings.mlr.press/v202/wang23at.html.

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