Pith Number

pith:BCAIFHOP

pith:2026:BCAIFHOP6NLL7UEUZTO5NQ5J2X

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Listwise Policy Optimization: Group-based RLVR as Target-Projection on the LLM Response Simplex

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

Group-based RL for LLMs implicitly projects policies toward targets on the response simplex; LPO makes the projection explicit and exact.

arxiv:2605.06139 v2 · 2026-05-07 · cs.LG · cs.AI

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\pithnumber{BCAIFHOP6NLL7UEUZTO5NQ5J2X}

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Receipt and verification

First computed	2026-05-21T01:05:20.390028Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0880829dcff356bfd094ccddd6c3a9d5e6d42ed0aff31d36e228015d8e78af88

Aliases

arxiv: 2605.06139 · arxiv_version: 2605.06139v2 · doi: 10.48550/arxiv.2605.06139 · pith_short_12: BCAIFHOP6NLL · pith_short_16: BCAIFHOP6NLL7UEU · pith_short_8: BCAIFHOP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BCAIFHOP6NLL7UEUZTO5NQ5J2X \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0880829dcff356bfd094ccddd6c3a9d5e6d42ed0aff31d36e228015d8e78af88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cd68bc954a2a0014707915b20910a779644b64c252b024558bfbda80aa3dd1f",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-07T12:38:17Z",
    "title_canon_sha256": "2a779b4493234406e077ac567af69c5e1cdcfa6ec05c6092ab9b0e7fd7c50c8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.06139",
    "kind": "arxiv",
    "version": 2
  }
}