# Bridging the Gap Between Latent and Explicit Reasoning with Looped Transformers

Authors: Ying Fan, Anej Svete, Kangwook Lee.

LOTUS repeatedly refines blocks of continuous reasoning states in parallel, training each position to predict a token from a worked solution. It generates answers from those states and studies accuracy, latency and how much of the reasoning can be read back.

First public: 2026-06-30.
ArXiv initial submission: 2026-06-30.

[Original paper](https://arxiv.org/abs/2606.31779) · [PDF](https://arxiv.org/pdf/2606.31779) · [HTML](https://arxiv.org/html/2606.31779v2) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2606.31779/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2606.31779/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2606.31779/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2606.31779/record.json)
[Code](https://github.com/yingfan-bot/lotus)

## Approaches

- [Internalized reasoning](https://latent-implicit-thinking.github.io/topics/internalized-reasoning/): Learn from worked solutions so that some or all of the reasoning can later happen without writing those steps. Training may use a separate teacher model or progressively remove written steps from the model being trained.
- [Continuous-state reasoning](https://latent-implicit-thinking.github.io/topics/continuous-states/): Use vectors—lists of numbers—to carry intermediate reasoning from one step to the next, instead of selecting a text token at every step. Some methods use the model's hidden states; others combine several candidate token representations.
- [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.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. Some produce written chains of thought.

Reading-list version 0.11.0; literature checked through 2026-10-26.