# Latent Path Exploration via Potential-Guided Subtrajectory Balance

Authors: Xiaoling Zeng, Qi Zhang.

Samples continuous reasoning paths before producing an answer. Trains the paths with explicit-chain supervision, hidden-state distillation, and a balance objective that compares how much intermediate states support the correct answer.

First public: 2026-10-29.
ArXiv initial submission: 2026-10-29.

[Original paper](https://arxiv.org/abs/2610.40283) · [PDF](https://arxiv.org/pdf/2610.40283) · [HTML](https://arxiv.org/html/2610.40283v1) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.40283/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.40283/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.40283/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.40283/record.json)

## 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.

Reading-list version 0.12.0; literature checked through 2026-11-02.