{
  "abstract": "Modern transformers often solve complex tasks by generating and refining intermediate reasoning steps. To develop a theoretical understanding of chain-of-thought (CoT) reasoning, a notable recent study by Huang et al. (2025) viewed transformers as algorithm executors, and showed that when transformers' CoT steps are supervised by a gradient-descent teacher, they can learn to implement gradient descent for in-context weight prediction in linear regression. In this paper, we study the same in-context weight prediction task but ask whether CoT reasoning can go beyond merely imitating the teacher algorithm. We show that, after initial supervision from a gradient-descent teacher, further trajectory-level supervision using the true regression weights leads the model to implement the Heavy-Ball method, thereby achieving acceleration over the original teacher. Notably, this accelerated algorithm emerges without supervision from any Heavy-Ball teacher. Our results provide a concrete theoretical example in which transformer reasoning can discover new algorithms through training, rather than merely imitate the algorithm used for supervision.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31089",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuxuan Cai"
    },
    {
      "name": "Yuan Cao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2zshkjy2058y0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31089",
  "fulltext_url": null,
  "id": "2zshkjy2058y0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31089",
  "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",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7223260751",
  "pdf_url": "https://arxiv.org/pdf/2610.31089",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2zshkjy2058y0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:43Z",
      "native_id": "2610.31089",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31089"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Transformers with CoT Discover Heavy-Ball Acceleration Through Training",
  "title_text": "Transformers with CoT Discover Heavy-Ball Acceleration Through Training",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/2zshkjy2058y0",
  "venue": "arXiv",
  "versions": []
}