{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/satnet-bridging-deep-learning-and-logical","title":"SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver","arxiv_id":"1905.12149","date":"2019-05-29","proceeding":null,"authors":["Po-Wei Wang","Priya L. Donti","Bryan Wilder","Zico Kolter"],"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 Sudok\" 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.","url_abs":"https://arxiv.org/abs/1905.12149v1","url_pdf":"https://arxiv.org/pdf/1905.12149v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"satnet-bridging-deep-learning-and-logical","repo_url":"https://github.com/Kyubyong/sudoku","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"satnet-bridging-deep-learning-and-logical","repo_url":"https://github.com/locuslab/SATNet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"satnet-bridging-deep-learning-and-logical","repo_url":"https://github.com/SeverTopan/SATNet","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"deep-learning","task_name":"Deep Learning"},{"task_slug":"suduko","task_name":"Game of Sudoku"},{"task_slug":"logical-reasoning","task_name":"Logical Reasoning"}],"methods":[],"datasets_introduced":[{"slug":"satnet-sudoku","name":"satnet-sudoku","full_name":"SATNet's Sudoku training test"}],"methods_introduced":[],"results":[{"leaderboard":"/sota/game-of-sudoku-on-sudoku-9x9","task":"Game of Sudoku","dataset":"Sudoku 9x9","model":"SATNet","rank_in_archive_order":1,"of":1,"metrics":{"Accuracy":"98.3"},"uses_additional_data":false}],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1905.12149","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1905.12149"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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