# Invariant-Measure Reasoners: Stable Representations for Latent Reasoning

Authors: Yuto Inui, Takuya Konishi, Yoshinobu Kawahara.

Predicts by averaging over the long-run distribution of recurrent hidden states instead of reading a single final state. This lets the model use changing hidden states without requiring them to settle at one fixed point.

First public: 2026-10-07.
ArXiv initial submission: 2026-10-07.

[Original paper](https://arxiv.org/abs/2610.10996) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.10996/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.10996/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.10996/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.10996/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.

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.