# Looped Transformers as Optimizers

Authors: Yulong Huang, Chen Jiang, Zhanpeng Zhou, Hongtao Zhang, Tianyu Li, Tianyu He, Xiangyu Zhang, Bojun Cheng.

Treats each recurrent hidden-state update as an optimization step and derives loop designs from this view. Introduces OperLoop, combining adaptive step sizes and weight decay.

First public: 2026-09-29.
ArXiv initial submission: 2026-09-29.

[Original paper](https://arxiv.org/abs/2609.37379) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.37379/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.37379/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.37379/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.37379/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.