{"paper":{"title":"The Unlearnability Phenomenon in RLVR for Language Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A substantial subset of hard examples remains unlearnable in RLVR even when correct rollouts are available.","cross_cats":["cs.CL"],"primary_cat":"cs.LG","authors_text":"Chen Zhao, He He, Yulin Chen","submitted_at":"2026-05-16T03:43:19Z","abstract_excerpt":"Reinforcement Learning with Verifiable Reward (RLVR) has proven effective in improving Large Language Model's (LLM) reasoning ability. However, the learning dynamics of RLVR remain underexplored. In this paper, we reveal a counterintuitive phenomenon: among hard examples that the model initially struggles with, a substantial subset remains unlearnable even when correct rollouts are present. To understand the phenomenon, we first demonstrate that existing optimization and sampling techniques fail to resolve unlearnability. With cross-example gradient analysis, we show that unlearnable examples "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"among hard examples that the model initially struggles with, a substantial subset remains unlearnable even when correct rollouts are present, characterized by low gradient similarity with the rest of the examples and ungeneralizable reasoning patterns.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That cross-example gradient analysis reliably detects fundamental representation issues causing unlearnability, and that failure of data augmentation to improve gradient similarity demonstrates inherent limitations of RL approaches.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"RLVR training for language models exhibits an unlearnability phenomenon where certain hard examples stay unlearnable due to low gradient similarity and ungeneralizable reasoning patterns.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A substantial subset of hard examples remains unlearnable in RLVR even when correct rollouts are available.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0442aa8e0c1996074c647de33d9a9a84f2aa157696221ffb85e432a94d5cab82"},"source":{"id":"2605.16787","kind":"arxiv","version":1},"verdict":{"id":"53416e6d-e9ed-4f2f-b547-ca99d0b58c26","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T21:34:46.572541Z","strongest_claim":"among hard examples that the model initially struggles with, a substantial subset remains unlearnable even when correct rollouts are present, characterized by low gradient similarity with the rest of the examples and ungeneralizable reasoning patterns.","one_line_summary":"RLVR training for language models exhibits an unlearnability phenomenon where certain hard examples stay unlearnable due to low gradient similarity and ungeneralizable reasoning patterns.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That cross-example gradient analysis reliably detects fundamental representation issues causing unlearnability, and that failure of data augmentation to improve gradient similarity demonstrates inherent limitations of RL approaches.","pith_extraction_headline":"A substantial subset of hard examples remains unlearnable in RLVR even when correct rollouts are available."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16787/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:01:19.637991Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:40:53.320904Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.297811Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.433407Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"344db38d5eef81d2f33d7b949bd665284a8db74a5051cbf37cebe9e2c5cd664e"},"references":{"count":22,"sample":[{"doi":"","year":2025,"title":"arXiv preprint arXiv:2512.01775 , year=","work_id":"52575a72-367d-476d-89e4-a3641cc0cecd","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Qwen2.5 Technical Report","work_id":"d8432992-4980-4a81-85c7-9fa2c2b87f85","ref_index":2,"cited_arxiv_id":"2412.15115","is_internal_anchor":true},{"doi":"","year":null,"title":"We have also tried different sampling batch size and gradient update batch size to vary the maximum number of off-policy update","work_id":"f41dc38a-ebeb-4a7d-ad1b-a86cae1a975e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"A reader should be able to solve any single subproblem without seeing the others","work_id":"497a4852-4ee4-4ca8-89d5-c29e360162a1","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Clarity: Each subproblem must be unambiguous and have a unique, well-defined answer","work_id":"925fbace-7d7c-4f4c-ac17-57b13af878b6","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":22,"snapshot_sha256":"aab469435f40f1eb4fdcef417f388936a7b532241aba15ae80bd6bd80f847046","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"b417023e8fbf76db7c06b26d33aabe58271aee8772119b671c6a85aa140b5ef4"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}