{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:JSGQNCS373K3IA2JVXJNDZTAHC","short_pith_number":"pith:JSGQNCS3","schema_version":"1.0","canonical_sha256":"4c8d068a5bfed5b40349add2d1e66038acec8c2f36076f1ce2af35dc3673dd9a","source":{"kind":"arxiv","id":"2608.02149","version":1},"attestation_state":"computed","paper":{"title":"Beyond the Mean: Multi-Moment Policy Optimization for LLM Reasoning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Fan Xu, Haoxiang Zhang, Jiaxin Ding, Luoyi Fu, Xin Ding, Yijun Zhang, Yule Xie","submitted_at":"2026-08-03T12:34:04Z","abstract_excerpt":"Reinforcement learning has become a central paradigm for improving the reasoning capabilities of large language models. Existing methods generally aim to reduce the failure probabilities induced across problems. In this paper, we introduce a moment-based perspective on policy optimization for LLM reasoning by treating the failure probability of a randomly sampled problem as a random variable and characterizing optimization objectives through its moments. Under this perspective, many existing methods optimize only a single moment of the failure-probability distribution, leaving its broader dist"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2608.02149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2026-08-03T12:34:04Z","cross_cats_sorted":[],"title_canon_sha256":"ce50c9438758c2421233e6b5665b28a1a4cc02fbbae73ce1eadfc4157a7322e0","abstract_canon_sha256":"408818e9b99934ebf49c99e7f856dbe2972145fd892ebfb6e175e6cc9b35cdef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:11:06.877112Z","signature_b64":"/VTMIQ4NedIRTCjB0Xjm2Rtp04fIbH92N+d7LoI34yBZI1M3G1BoDhu76YiqZRhckCGvIxo857SEV1GKwZ+7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c8d068a5bfed5b40349add2d1e66038acec8c2f36076f1ce2af35dc3673dd9a","last_reissued_at":"2026-08-04T02:11:06.875511Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:11:06.875511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beyond the Mean: Multi-Moment Policy Optimization for LLM Reasoning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Fan Xu, Haoxiang Zhang, Jiaxin Ding, Luoyi Fu, Xin Ding, Yijun Zhang, Yule Xie","submitted_at":"2026-08-03T12:34:04Z","abstract_excerpt":"Reinforcement learning has become a central paradigm for improving the reasoning capabilities of large language models. Existing methods generally aim to reduce the failure probabilities induced across problems. In this paper, we introduce a moment-based perspective on policy optimization for LLM reasoning by treating the failure probability of a randomly sampled problem as a random variable and characterizing optimization objectives through its moments. Under this perspective, many existing methods optimize only a single moment of the failure-probability distribution, leaving its broader dist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02149","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/2608.02149/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2608.02149","created_at":"2026-08-04T02:11:06.877101+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.02149v1","created_at":"2026-08-04T02:11:06.877101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.02149","created_at":"2026-08-04T02:11:06.877101+00:00"},{"alias_kind":"pith_short_12","alias_value":"JSGQNCS373K3","created_at":"2026-08-04T02:11:06.877101+00:00"},{"alias_kind":"pith_short_16","alias_value":"JSGQNCS373K3IA2J","created_at":"2026-08-04T02:11:06.877101+00:00"},{"alias_kind":"pith_short_8","alias_value":"JSGQNCS3","created_at":"2026-08-04T02:11:06.877101+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC","json":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC.json","graph_json":"https://pith.science/api/pith-number/JSGQNCS373K3IA2JVXJNDZTAHC/graph.json","events_json":"https://pith.science/api/pith-number/JSGQNCS373K3IA2JVXJNDZTAHC/events.json","paper":"https://pith.science/paper/JSGQNCS3"},"agent_actions":{"view_html":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC","download_json":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC.json","view_paper":"https://pith.science/paper/JSGQNCS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.02149&json=true","fetch_graph":"https://pith.science/api/pith-number/JSGQNCS373K3IA2JVXJNDZTAHC/graph.json","fetch_events":"https://pith.science/api/pith-number/JSGQNCS373K3IA2JVXJNDZTAHC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC/action/storage_attestation","attest_author":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC/action/author_attestation","sign_citation":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC/action/citation_signature","submit_replication":"https://pith.science/pith/JSGQNCS373K3IA2JVXJNDZTAHC/action/replication_record"}},"created_at":"2026-08-04T02:11:06.877101+00:00","updated_at":"2026-08-04T02:11:06.877101+00:00"}