# WaveFront Decoding: Parallelized Self-Speculative Decoding for Looped Language Models

Authors: Hyeongju Ha, Jae-Joon Kim.

Uses intermediate loop depths to propose tokens that later loops verify. Arranges speculation across recurrent depths so that more of the draft and verification work can run together.

First public: 2026-09-19.
ArXiv initial submission: 2026-09-19.

[Original paper](https://arxiv.org/abs/2609.23033) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.23033/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.23033/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.23033/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.23033/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.