{"paper":{"title":"Listwise Policy Optimization: Group-based RLVR as Target-Projection on the LLM Response Simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Group-based RL for LLMs implicitly projects policies toward targets on the response simplex; LPO makes the projection explicit and exact.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Clive Bai, Heming Zou, Kai Yang, Lizhou Cai, Qi Wang, Saiyong Yang, Weijie Liu, Wutong Xu, Xiangyang Ji, Yangkun Chen, Yingyue Li, Yixiu Mao, Yuhang Jiang, Yun Qu","submitted_at":"2026-05-07T12:38:17Z","abstract_excerpt":"Reinforcement learning with verifiable rewards (RLVR) has become a standard approach for large language models (LLMs) post-training to incentivize reasoning capacity. Among existing recipes, group-based policy gradient is prevalent, which samples a group of responses per prompt and updates the policy via group-relative advantage signals. This work reveals that these optimization strategies share a common geometric structure: each implicitly defines a target distribution on the response simplex and projects toward it via first-order approximation. Building on this insight, we propose Listwise P"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"LPO provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the implicit targets defined by existing group-based methods can be exactly recovered or improved upon by restricting the proximal RL objective to the response simplex and performing exact divergence minimization.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"LPO reframes group-based RLVR as explicit target-projection on the LLM response simplex and performs exact divergence minimization to achieve monotonic listwise improvement with bounded gradients.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Group-based RL for LLMs implicitly projects policies toward targets on the response simplex; LPO makes the projection explicit and exact.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2a3211ca39bba360b8e843db855779fe770eacd7c73506edb778bd9392ae86b5"},"source":{"id":"2605.06139","kind":"arxiv","version":2},"verdict":{"id":"6cc46c2c-bc25-4323-9757-eb4547d0eca6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T13:51:51.705037Z","strongest_claim":"LPO provides (i) monotonic improvement on the listwise objective with bounded, zero-sum, and self-correcting projection gradients, and (ii) flexibility in divergence selection with distinct structural properties through the decoupled projection step.","one_line_summary":"LPO reframes group-based RLVR as explicit target-projection on the LLM response simplex and performs exact divergence minimization to achieve monotonic listwise improvement with bounded gradients.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the implicit targets defined by existing group-based methods can be exactly recovered or improved upon by restricting the proximal RL objective to the response simplex and performing exact divergence minimization.","pith_extraction_headline":"Group-based RL for LLMs implicitly projects policies toward targets on the response simplex; LPO makes the projection explicit and exact."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06139/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T13:02:04.296347Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T08:36:39.607964Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:19.376208Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:55:45.727798Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"aa11b66d4e677d0cc7dcc831cb371755b7e60c53f031d482c4143a2cf307e86c"},"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"}