# 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.

Studies the internal computation behind grade-school mathematics, including when models learn robust procedures or rely on data shortcuts.

First public: 2024-07-29.
ArXiv initial submission: 2024-07-29.

[Original paper](https://arxiv.org/abs/2407.20311) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2407.20311/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2407.20311/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2407.20311/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2407.20311/record.json)

## Approaches

- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Summary and categories are editorial. Read the original paper to verify claims and limitations. A citation to a paper does not, by itself, establish that a later method builds on it.

Reading-list version 0.9.5; literature checked through 2026-10-18.