Pith Number

pith:CHS6VQH4

pith:2026:CHS6VQH4UVNWF746MQKITXQQC2

not attested not anchored not stored refs pending

Breaking $\textit{Winner-Takes-All}$: Cooperative Policy Optimization Improves Diverse LLM Reasoning

Haoxuan Chen, Jian-Fang Hu, Tianming Liang, Wei-Shi Zheng

GCPO replaces individual rollout competition with team-level credit assignment based on contributions to collective solution coverage.

arxiv:2605.11461 v2 · 2026-05-12 · cs.AI · cs.LG

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\usepackage{pith}
\pithnumber{CHS6VQH4UVNWF746MQKITXQQC2}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Experiments across multiple reasoning benchmarks demonstrate that GCPO significantly improves both reasoning accuracy and solution diversity over existing approaches.

C2weakest assumption

That the determinant volume over reward-weighted semantic embeddings provides a reliable, unbiased measure of non-redundant solution coverage whose marginal contributions can be computed and redistributed without introducing new optimization pathologies or sensitivity to embedding choice.

C3one line summary

GCPO shifts RLVR from rollout competition to team cooperation by assigning advantages via marginal contributions to a determinant-based coverage volume over semantic embeddings, yielding higher accuracy and solution diversity on reasoning benchmarks.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:35.997203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11e5eac0fca55b62ff9e641489de10169af9b1dc277c8d906bbd50b85a04bcae

Aliases

arxiv: 2605.11461 · arxiv_version: 2605.11461v2 · doi: 10.48550/arxiv.2605.11461 · pith_short_12: CHS6VQH4UVNW · pith_short_16: CHS6VQH4UVNWF746 · pith_short_8: CHS6VQH4

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CHS6VQH4UVNWF746MQKITXQQC2 \
  | 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: 11e5eac0fca55b62ff9e641489de10169af9b1dc277c8d906bbd50b85a04bcae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0d9d3e90b3fd7695e1ed94d53f540403a43942bc2635c99228a2160b908a606",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-05-12T03:20:24Z",
    "title_canon_sha256": "a553f839b835ffb46dcb0fb8d8eb8c3995e64ab782e4b0ea08b0881da51eb5f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11461",
    "kind": "arxiv",
    "version": 2
  }
}