# Accordion: Elastic-Depth Inference via Fixed-Prefix Layer Looping

Authors: Yudong Zhang, Wei Ding, Kaili Zheng, Yuchen Ding, Zhenyu Zhang.

Trains one mixture-of-experts model with five inference budgets by repeating selected layers. Samples a budget during pretraining and preserves all five paths through instruction tuning and reinforcement learning, allowing callers to trade extra computation for stronger predictions without switching models.

First public: 2026-10-23.
ArXiv initial submission: 2026-10-23.

[Original paper](https://arxiv.org/abs/2610.32492) · [PDF](https://arxiv.org/pdf/2610.32492) · [HTML](https://arxiv.org/html/2610.32492v1) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.32492/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.32492/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.32492/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.32492/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.