# Deeper Backpropagation or More Updates? Training Looped Language Models Across Budgets

Authors: Jiarun Shen, Xiao Li.

Compares short and long backpropagation windows in looped language models at matched token and training-time budgets. Extra updates favor shorter windows at small budgets, but that advantage shrinks as training grows.

First public: 2026-10-28.
ArXiv initial submission: 2026-10-28.

[Original paper](https://arxiv.org/abs/2610.38422) · [PDF](https://arxiv.org/pdf/2610.38422) · [HTML](https://arxiv.org/html/2610.38422v1) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.38422/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.38422/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.38422/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.38422/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 0.12.0; literature checked through 2026-11-02.