# PAR: Progress-Aligned Recurrence for Length Generalization in State Tracking

Authors: Pan Wang, Yihao Hu, Guangyuan Dong, Yitong Lin, Hang Wang, Zimi Liu, Zhihao Wen, Jianshe Li, Jiang-Ming Yang, Wei Wu, Yongqi Tong.

Trains each loop of a language model to represent the state after one more operation, while keeping hidden-state norms stable. Combines this supervision with learned stopping and prefix self-distillation to test generalization to longer state-tracking problems without generating intermediate tokens.

First public: 2026-10-20.
ArXiv initial submission: 2026-10-20.

[Original paper](https://arxiv.org/abs/2610.27628) · [PDF](https://arxiv.org/pdf/2610.27628) · [HTML](https://arxiv.org/html/2610.27628v1) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.27628/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.27628/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.27628/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.27628/record.json)

## Approaches

- [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.

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