{"paper":{"title":"Learning Modulo Theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"cs.LG","authors_text":"Kaiji Lu, Matt Fredrikson, Saranya Vijayakumar, Somesh Jha, Vijay Ganesh, Zifan Wang","submitted_at":"2023-01-26T21:46:23Z","abstract_excerpt":"Recent techniques that integrate \\emph{solver layers} into Deep Neural Networks (DNNs) have shown promise in bridging a long-standing gap between inductive learning and symbolic reasoning techniques. In this paper we present a set of techniques for integrating \\emph{Satisfiability Modulo Theories} (SMT) solvers into the forward and backward passes of a deep network layer, called SMTLayer. Using this approach, one can encode rich domain knowledge into the network in the form of mathematical formulas. In the forward pass, the solver uses symbols produced by prior layers, along with these formula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.11435","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.11435/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}