Pith Number

pith:23J2LGEK

pith:2026:23J2LGEKOOQ2WZOMQUWVIVVKOI

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ICRL: Learning to Internalize Self-Critique with Reinforcement Learning

Chengwei Qin, Heqing Zou, Hui Xiong, Jianbo Lin, Weishi Wang, Xiaomin Yu, Yifu Guo, Yi Xin, Zhongqi Yue, Zhuosong Jiang

ICRL jointly trains a solver and critic from one backbone so critique gains become part of unassisted performance.

arxiv:2605.15224 v1 · 2026-05-13 · cs.AI · cs.MA

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Claims

C1strongest claim

ICRL jointly trains a solver and a critic from a shared backbone to convert critique-induced success into unassisted solver ability, with results showing average gains of 6.4 points over GRPO on agentic tasks and 7.0 points on mathematical reasoning using Qwen3-4B and Qwen3-8B backbones.

C2weakest assumption

The distribution-calibration re-weighting ratio successfully selects critique-guided improvements that remain compatible with the solver's own prompt distribution, without introducing bias or reducing performance on critique-free queries.

C3one line summary

ICRL uses joint RL training of solver and critic with distribution-calibration re-weighting and role-wise advantage estimation to internalize critique into unassisted LLM performance, yielding 6.4-point gains on agentic tasks and 7.0 on math reasoning with Qwen3 models.

References

45 extracted · 45 resolved · 12 Pith anchors

[1] Advances in neural information processing systems , volume=

[2] Advances in neural information processing systems , volume=

[3] CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing · arXiv:2305.11738

[4] Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection , author=. ArXiv , year=

[5] arXiv preprint arXiv:2303.16755 , year=

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:47.193945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6d3a5988a73a1ab65cc852d5456aa722a1bbb89089139b366d27d177770154e

Aliases

arxiv: 2605.15224 · arxiv_version: 2605.15224v1 · doi: 10.48550/arxiv.2605.15224 · pith_short_12: 23J2LGEKOOQ2 · pith_short_16: 23J2LGEKOOQ2WZOM · pith_short_8: 23J2LGEK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/23J2LGEKOOQ2WZOMQUWVIVVKOI \
  | 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: d6d3a5988a73a1ab65cc852d5456aa722a1bbb89089139b366d27d177770154e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fdc1d3d1bd380c0214ee6bf2cb1932af79419a7933be850497b565dc9bfeb89",
    "cross_cats_sorted": [
      "cs.MA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-05-13T08:50:05Z",
    "title_canon_sha256": "3a24ce8aed65cb35d8fad1a68935797323fb6d2b6763ded61970ac03e6bdc42e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15224",
    "kind": "arxiv",
    "version": 1
  }
}