# Shallow Queries, Mature Values: Depth-Asynchronous Self-Speculation for Looped Transformers

Authors: Guanghao Li, Zihan Su, Hao Yu, Jinyang Jiang, Tao Ren, Zehao Li, Feng Lu, Ming Tang, Chun Yuan.

Uses shallower-loop queries with values from deeper loops to improve draft-token predictions in a looped language model. Studies the different rates at which queries, keys, and values develop, and uses that difference for self-speculative decoding.

First public: 2026-09-28.
ArXiv initial submission: 2026-09-28.

[Original paper](https://arxiv.org/abs/2609.34538) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.34538/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.34538/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.34538/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.34538/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.
- [Alternative generation methods](https://latent-implicit-thinking.github.io/topics/alternative-reasoning-schedules/): Change how intermediate steps are generated, revised, or searched—for example, by refining several steps in parallel. These are related approaches: some still produce written chains of thought.

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.