# PonderLM: Pretraining Language Models to Ponder in Continuous Space

Authors: Boyi Zeng, Shixiang Song, Siyuan Huang, Yixuan Wang, He Li, Ziwei He, Xinbing Wang, Zhiyu Li, Zhouhan Lin.

Pretrains language models with repeated continuous-space pondering steps before token prediction.

First public: 2025-05-27.
ArXiv initial submission: 2025-05-27.

[Original paper](https://arxiv.org/abs/2505.20674) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2505.20674/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2505.20674/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2505.20674/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2505.20674/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.
- [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.