# Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers

Authors: Sajad Movahedi, Vera Milovanović, Shlomo Libo Feigin, Alexander Theus, Thomas Hofmann, Valentina Boeva, T. Konstantin Rusch, Antonio Orvieto.

Stabilizes repeated transformer layers and stops looping when the hidden state converges, allowing the model to spend different amounts of computation on different problems.

First public: 2026-06-16.
ArXiv initial submission: 2026-06-16.

[Original paper](https://arxiv.org/abs/2606.18206) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2606.18206/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2606.18206/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2606.18206/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2606.18206/record.json)
[Code](https://github.com/nilskiKonjIzDunava/fprm)

## 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.

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.