{"paper":{"title":"Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Supervised fine-tuning for math reasoning succeeds when models learn to apply theorems explicitly instead of memorizing individual problem-answer pairs.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Jing Lei, Mengyu Yang, Ruiying Peng, Xiaohui Li, Xinlei Chen, Xueyu Wu","submitted_at":"2026-05-10T02:39:05Z","abstract_excerpt":"Supervised Fine-Tuning (SFT) is widely used for task-specific adaptation, yet recent work shows it systematically undermines reasoning generalization. We argue the root cause is not memorization itself, but its target: vanilla SFT drives models to exploit and memorize spurious surface correlations in problem-solution pairs, leaving them brittle to superficial input variations. To address this, we propose Theorem-SFT, which reorients supervision toward explicit theorem application by teaching models how rules are invoked rather than what answers look like. Theorem-SFT yields consistent gains ac"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Generalization failures stem not from memorization as a mechanism, but from memorizing the wrong inductive targets.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the reported performance gains are caused by the shift to theorem-level supervision rather than by other unspecified differences in data construction, prompting, or training hyperparameters between vanilla SFT and Theorem-SFT.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Theorem-SFT improves mathematical reasoning generalization by teaching theorem application rather than instance memorization, delivering gains of +8.8% on MATH and +20.27% on GeoQA across model families.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Supervised fine-tuning for math reasoning succeeds when models learn to apply theorems explicitly instead of memorizing individual problem-answer pairs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2ac3c3605335d47feb2fce4ee18293ae8490f872b3ee468d2f940c37bf81d2ad"},"source":{"id":"2605.09270","kind":"arxiv","version":2},"verdict":{"id":"d59a00fe-0325-4e05-a41f-c3b14d40b8ff","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T04:47:26.502142Z","strongest_claim":"Generalization failures stem not from memorization as a mechanism, but from memorizing the wrong inductive targets.","one_line_summary":"Theorem-SFT improves mathematical reasoning generalization by teaching theorem application rather than instance memorization, delivering gains of +8.8% on MATH and +20.27% on GeoQA across model families.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the reported performance gains are caused by the shift to theorem-level supervision rather than by other unspecified differences in data construction, prompting, or training hyperparameters between vanilla SFT and Theorem-SFT.","pith_extraction_headline":"Supervised fine-tuning for math reasoning succeeds when models learn to apply theorems explicitly instead of memorizing individual problem-answer pairs."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09270/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T08:02:08.944337Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T20:34:31.582370Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T13:31:17.837425Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:22:17.241840Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"83df298cf3e2c2c390afdf01fcaf3a6efeeb248bd79cbd9c70a7c5a47a0dae34"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e90073efb785a850c8bbcb483d17bd3ecc03cc98414f435b4534a6c1a00a2f58"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}