# How Model Growth, Recursion, and Boundary Operators Influence Scaling Exponents

Authors: Zixi Chen, Akshay Vegesna, Samip Dahal, Andrew Gordon Wilson.

Studies how growing a model during training, reusing layers, and modifying the connections between repeated blocks affect language-model scaling. Compares shared and unshared weights and operators that normalize or reintroduce earlier representations.

First public: 2026-09-16.
ArXiv initial submission: 2026-09-16.

[Original paper](https://arxiv.org/abs/2609.19107) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2609.19107/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2609.19107/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2609.19107/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2609.19107/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.

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.