# Loop-μP: Residual Scaling and Hyperparameter Transfer in Looped Transformers

Authors: Shaowen Wang, Bingrui Li, Tansheng Zhu, Ge Zhang, Wenhao Huang, Shen Yan, Jian Li.

Scales each residual update inversely with the number of shared-weight loops, while keeping the learning rate independent of that loop count. Derives the scaling rule and tests whether hyperparameters transfer across loop counts and model depths during language-model pretraining.

First public: 2026-06-16.
ArXiv initial submission: 2026-06-16.

[Original paper](https://arxiv.org/abs/2606.18524) · [PDF](https://arxiv.org/pdf/2606.18524) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2606.18524/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2606.18524/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2606.18524/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2606.18524/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.
- [Analysis and evaluation](https://latent-implicit-thinking.github.io/topics/implicit-reasoning-evaluation/): Measure how well these methods work, investigate what their internal computation does, and identify where they fail. This includes experiments, studies of model internals, and mathematical results.

Reading-list version 0.15.2; literature checked through 2026-11-03.