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On such problems, rewards provide little useful learning signal. While collecting harder problems is a natural response, it is costly and increasingly difficult. We propose failure-prefix conditioning, a simple method that unlocks the remaining signal in saturated problems by shifting exploration toward failure-prone reasoning states. By conditioning on prefixes of rare incorrect trajectories, the method improves the model's ability to recover from misleading early reasoning. We observe that failure-prefix conditioning consistently improves performance where standard RLVR stalls, and achieves gains comparable to training on newly collected medium-difficu","title":"Training Reasoning Models on Saturated Problems via Failure-Prefix Conditioning","url":"https://arxiv.org/abs/2601.20829","vendor":"arxiv_cs_ai"},"summary":"arXiv:2601.20829v2 Announce Type: replace-cross \nAbstract: As Reinforcement Learning with Verifiable Rewards (RLVR) substantially improves the reasoning abilities of large language models (LLMs), a new bottleneck emerges: more training problems become saturated, that is, the LLM answers the questions correctly for nearly every rollout. On such problems, rewards provide little useful learning signal. While collecting harder problems is a natural response, it is costly and increasingly difficult. We propose failure-prefix conditioning, a simple method that unlocks the remaining signal in saturated problems by shifting exploration toward failure-prone reasoning states. By conditioning on prefixes of rare incorrect trajectories, the method improves the model's ability to recover from misleading early reasoning. We observe that failure-prefix conditioning consistently improves performance where standard RLVR stalls, and achieves gains comparable to training on newly collected medium-difficu","title":"Training Reasoning Models on Saturated Problems via Failure-Prefix Conditioning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-12T04:43:42Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2601.20829"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:06f3f23d78fd19dd13884bca9c22db41048063061a6a89a35009f2277a24c5922c048e0e6e5a6daf5078c83ffc6a088e2687b94b3a66311b20d42709eda6ec0b","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2601.20829"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"82ee521bcf1277ac142ccf9bdb2fa0dcd012ab42cda93a5ad2719af8249842d4","leaf_index":129117,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"e7482e4a9b894fdb83c9f1aaf0dd2ae1d73cfbb8960a4b232b9ee1d46dcbe12a","side":"left"},{"sibling":"801f1918979533d99818f277f77e4789e78a7f0933a1610bd6818f53c3830572","side":"right"},{"sibling":"9e3b4cbae1e74fe9d089f6d2d3cebbbbd2a3cd01b11aa790ae4cc020e1705952","side":"left"},{"sibling":"24e4aa191595bf48aae93a7bb532ba36c65f77164a24ae1115fc2e72224ea1aa","side":"left"},{"sibling":"5a93b44b3d11296cc878aa1303e792689b31d339f6f42747a13ec9e43a2abf58","side":"left"},{"sibling":"c3f585333ceb77a609ecf60a311616a396273be99dcb53b2246827ec141d5801","side":"right"},{"sibling":"de3746873a17cbee8458cf7f279f03cf066292b79b849b56e0cdcff253bd1ee4","side":"left"},{"sibling":"684a7e41697dc4a5ae5bd51e0b1fa452ba8e0ce5866bec279d63e12ce9b1e6cf","side":"right"},{"sibling":"bb93634b6ea81ccfb7b9c5b023ffaff85acd8b3f1ec609973d847fd93873d3ec","side":"right"},{"sibling":"9922155d12ac3db561299f0abaec57fc59dd8e711d91cd590823abd8f3e4647f","side":"right"},{"sibling":"9c71dae5b380aff58527385ccecc23b4cd8ff36395d4fc35ad5236b00fcb6db8","side":"right"},{"sibling":"d32d0a951c1d7e98a8e1951a587d83c97962daeeaa455643bc1d5d53744dc21e","side":"left"},{"sibling":"ffc4d51379293bc3e1910c7d612f409dc610fd9acf8241793fb89f82e1bad4ef","side":"left"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_3281a8781deff44c365166f3300e3d8058aaa72cced1b82b5a2b684b8da0123f"}}