# Right Direction, Wrong Step: Geometric Analysis of Finite-Step Failure in Looped Transformers

Authors: Zhihao Guo, Zonghan Wu, Haizhou Du, Huan Huo, Yilei Shao, Athanasios V. Vasilakos, Qingsong Wen.

Studies updates that initially increase support for a reference answer but overshoot when applied in full. Uses curvature along each update to explain failures and identify smaller useful steps.

First public: 2026-09-15.
ArXiv initial submission: 2026-09-15.

[Original paper](https://arxiv.org/abs/2609.16665) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.16665/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.16665/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.16665/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.16665/record.json)

## Approaches

- [Recurrent reasoning](https://latent-implicit-thinking.github.io/topics/recurrent-reasoning/): Repeat parts of the model or keep intermediate information in memory while working through a problem. Some methods also learn how many passes to run.
- [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.