SSRN paper: https://ssrn.com/abstract=5250639 (v4, updated May 2025)
(arxiv link is deprecated)
Authors: Zeyuan Allen-Zhu and Yuanzhi Li

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@article{AL2023-cfg,
  author = {{Allen-Zhu}, Zeyuan and Li, Yuanzhi},
  title = {{Physics of Language Models: Part 1, Learning Hierarchical Language Structures}},
  journal = {SSRN Electronic Journal},
  year = 2023,
  month = may,
  note = {Full version available at \url{https://ssrn.com/abstract=5250639}}

}