{
  "abstract": "Chain-of-Thought (CoT) reasoning substantially improves Large Language Models (LLMs), yet its out-of-distribution (OOD) generalization mechanism remains theoretically underexplored. We study CoT as compositional OOD generalization: the target task lacks complete reasoning trajectories or direct input-output pairs, while training provides only in-distribution (ID) atomic step data. We show that CoT generalizes by repeatedly applying a shared single-step predictor to compose reusable ID transitions. Theoretically, let $T$ denote the number of reasoning steps in the target task, $n$ the number of training samples per sub-task, and $k$ the number of output tokens per step; then the OOD task risk is controlled by the sum of the ID sub-task risks, scaled by a coefficient of order $\\mathcal{O}(k)$ that is independent of $T$, although the summed risk itself may still grow with $T$. A Rademacher-complexity analysis further shows that the estimation term is of order $\\mathcal{O}(\\sqrt{T/n})$, rather than linear in $T$, due to predictor sharing under a uniform capacity control on the shared class. For autoregressive Next-Token Prediction, the final-task risk is bounded by the best-in-class step-level risk scaled by the same coefficient of order $\\mathcal{O}(k)$, plus an estimation term of order $\\widetilde{\\mathcal{O}}\\big(k\\sqrt{T/n}\\big)$. A parity-coupled construction further shows that, for the sub-task empirical risk minimizer, the expected final-task risk is at least the best in-class risk plus $Ω(\\sqrt{T/n})$ when $T\\le n$. Experiments on Atom-Task and GSM8K support the theory: CoT enables short-to-long and compositional generalization, while explicit state tracking is crucial. Our code is available at https://github.com/maxliang114514/CoT-OOD.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06438",
  "author_total": 3,
  "authors": [
    {
      "name": "Nuo-Jing Liang"
    },
    {
      "name": "Xiao-Tong Yuan"
    },
    {
      "name": "Pan Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6xmyhp3kqys9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06438",
  "fulltext_url": null,
  "id": "f6xmyhp3kqys9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06438",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6xmyhp3kqys9.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:06Z",
      "native_id": "2611.06438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06438"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Understanding the Out-of-Distribution Generalization of Chain-of-Thought Reasoning in LLMs",
  "title_text": "Understanding the Out-of-Distribution Generalization of Chain-of-Thought Reasoning in LLMs",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:32Z",
  "url": "https://research.draconitic.com/paper/f6xmyhp3kqys9",
  "venue": "arXiv",
  "versions": []
}