# Parallel Continuous Chain-of-Thought with Jacobi Iteration

Authors: Haoyi Wu, Zhihao Teng, Kewei Tu.

Applies Jacobi-style iteration to update continuous reasoning states in parallel rather than strictly one step at a time.

First public: 2025-06-23.
ArXiv initial submission: 2025-06-23.

[Original paper](https://arxiv.org/abs/2506.18582) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2506.18582/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2506.18582/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2506.18582/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2506.18582/record.json)

## Approaches

- [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.
- [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. These are related approaches: some still produce written chains of thought.

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.