SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver

Po-Wei Wang, Priya Donti, Bryan Wilder, Zico Kolter
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:6545-6554, 2019.

Abstract

Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. Our (approximate) solver is based upon a fast coordinate descent approach to solving the semidefinite program (SDP) associated with the MAXSAT problem. We show how to analytically differentiate through the solution to this SDP and efficiently solve the associated backward pass. We demonstrate that by integrating this solver into end-to-end learning systems, we can learn the logical structure of challenging problems in a minimally supervised fashion. In particular, we show that we can learn the parity function using single-bit supervision (a traditionally hard task for deep networks) and learn how to play 9x9 Sudoku solely from examples. We also solve a “visual Sudoku” problem that maps images of Sudoku puzzles to their associated logical solutions by combining our MAXSAT solver with a traditional convolutional architecture. Our approach thus shows promise in integrating logical structures within deep learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-wang19e, title = {{SATN}et: Bridging deep learning and logical reasoning using a differentiable satisfiability solver}, author = {Wang, Po-Wei and Donti, Priya and Wilder, Bryan and Kolter, Zico}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {6545--6554}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/wang19e/wang19e.pdf}, url = {https://proceedings.mlr.press/v97/wang19e.html}, abstract = {Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. Our (approximate) solver is based upon a fast coordinate descent approach to solving the semidefinite program (SDP) associated with the MAXSAT problem. We show how to analytically differentiate through the solution to this SDP and efficiently solve the associated backward pass. We demonstrate that by integrating this solver into end-to-end learning systems, we can learn the logical structure of challenging problems in a minimally supervised fashion. In particular, we show that we can learn the parity function using single-bit supervision (a traditionally hard task for deep networks) and learn how to play 9x9 Sudoku solely from examples. We also solve a “visual Sudoku” problem that maps images of Sudoku puzzles to their associated logical solutions by combining our MAXSAT solver with a traditional convolutional architecture. Our approach thus shows promise in integrating logical structures within deep learning.} }
Endnote
%0 Conference Paper %T SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver %A Po-Wei Wang %A Priya Donti %A Bryan Wilder %A Zico Kolter %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-wang19e %I PMLR %P 6545--6554 %U https://proceedings.mlr.press/v97/wang19e.html %V 97 %X Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. Our (approximate) solver is based upon a fast coordinate descent approach to solving the semidefinite program (SDP) associated with the MAXSAT problem. We show how to analytically differentiate through the solution to this SDP and efficiently solve the associated backward pass. We demonstrate that by integrating this solver into end-to-end learning systems, we can learn the logical structure of challenging problems in a minimally supervised fashion. In particular, we show that we can learn the parity function using single-bit supervision (a traditionally hard task for deep networks) and learn how to play 9x9 Sudoku solely from examples. We also solve a “visual Sudoku” problem that maps images of Sudoku puzzles to their associated logical solutions by combining our MAXSAT solver with a traditional convolutional architecture. Our approach thus shows promise in integrating logical structures within deep learning.
APA
Wang, P., Donti, P., Wilder, B. & Kolter, Z.. (2019). SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:6545-6554 Available from https://proceedings.mlr.press/v97/wang19e.html.

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