# Structural Process Supervision for Latent Chain-of-Thought Reasoning

Authors: Yiqi Li, Xu Chen, Chen Ju, Jiangchao Yao, Zhaoyang Li, Jinsong Lan, Xiaoyong Zhu, Yu Wang.

Aligns continuous thoughts with written reasoning through shared, learnable prototypes, allowing several text steps to supervise several latent states. A positional alignment constraint is gradually relaxed during training.

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

[Original paper](https://arxiv.org/abs/2609.09928) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.09928/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.09928/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.09928/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.09928/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.

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.