{"paper":{"title":"Learning How to Cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LO"],"primary_cat":"cs.LG","authors_text":"Byron Cook, Ferhat Erata, Robert B. Jones, Ruzica Piskac, Sam Kouteili, Thanos Typaldos, Timos Antonopoulos","submitted_at":"2026-05-15T21:03:42Z","abstract_excerpt":"Despite the effectiveness of Cube-and-Conquer (C&C) for solving challenging Boolean Satisfiability (SAT) problems, no prior work has shown that transformer-based models can learn effective cubing heuristics. We introduce a neuro-symbolic post-training framework for this task. We design an MCTS-based data curation pipeline that uses symbolic heuristics to explore splitting decisions over SAT competition formulas, producing preference data grounded in solver statistics and augmented with reasoning traces from a teacher model. Our two-stage post-training, supervised fine-tuning (SFT) followed by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16632","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/2605.16632/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T19:21:56.741858Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.580940Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"98b68bd54af6ab33c3437858f6ee6662edae07a8e8775b5af3edb2f771db3d52"},"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"}