{
  "id": "2407.20311",
  "title": "Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process",
  "authors": "Tian Ye, Zicheng Xu, Yuanzhi Li, Zeyuan Allen-Zhu",
  "first_public": "2024-07-29",
  "venue": "arXiv",
  "arxiv": "2407.20311",
  "paper_url": "https://arxiv.org/abs/2407.20311",
  "lens": [
    "analysis"
  ],
  "representation": [
    "hidden-state"
  ],
  "computation": [
    "depth-wise"
  ],
  "training": [
    "analysis-only"
  ],
  "questions": [
    "capability",
    "interpretability",
    "generalization"
  ],
  "evidence": [
    "empirical",
    "boundary"
  ],
  "modality": [
    "language",
    "symbolic"
  ],
  "summary": "Studies the internal computation behind grade-school mathematics, including when models learn robust procedures or rely on data shortcuts.",
  "provenance": "Primary-source literature search, 2026-09-04",
  "author_names": [
    "Tian Ye",
    "Zicheng Xu",
    "Yuanzhi Li",
    "Zeyuan Allen-Zhu"
  ],
  "record_url": "https://latent-implicit-thinking.github.io/papers/2407.20311/",
  "legacy_record_url": "https://latent-implicit-thinking.github.io/papers/#paper-2407-20311",
  "citation_date": "2024-07-29",
  "json_url": "https://latent-implicit-thinking.github.io/papers/2407.20311/record.json",
  "markdown_url": "https://latent-implicit-thinking.github.io/papers/2407.20311/index.md",
  "bibtex_url": "https://latent-implicit-thinking.github.io/papers/2407.20311/citation.bib",
  "csl_url": "https://latent-implicit-thinking.github.io/papers/2407.20311/citation.csl.json"
}