# Curriculum Learning Teaches LLMs Long-Horizon Implicit Reasoning, Up To A Limit

Authors: Jimson Huang, Maxwell Nickell, Ruowang Zhang, Abulhair Saparov.

Trains models to select the next step of a proof without writing intermediate reasoning, gradually increasing required lookahead and the number of attribute labels. Studies how training compute, model size, initialization, and curriculum steps affect learned lookahead and transfer to other reasoning tasks.

First public: 2026-10-19.
ArXiv initial submission: 2026-10-19.

[Original paper](https://arxiv.org/abs/2610.25612) · [PDF](https://arxiv.org/pdf/2610.25612) · [HTML](https://arxiv.org/html/2610.25612v1) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.25612/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.25612/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.25612/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.25612/record.json)

## Approaches

- [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 0.11.0; literature checked through 2026-10-26.