# Nested Shared-Operator Recursion on ARC-AGI-1: An Empirical Study of HRM, TRM and URM

Authors: Sara Neri, Eugenio Gaeta, Andrea Ceschini, Andrea Facchinetti, Giuseppe Fico.

Adds a persistent intermediate state to nested updates in HRM, TRM and URM, then compares the variants on ARC-AGI-1. Finds no consistent advantage under the tested training budgets and separates token accuracy from exact puzzle solving.

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

[Original paper](https://arxiv.org/abs/2610.26666) · [PDF](https://arxiv.org/pdf/2610.26666) · [HTML](https://arxiv.org/html/2610.26666v1) · [Reading-list entry](https://latent-implicit-thinking.github.io/papers/2610.26666/)
[Preprint BibTeX](https://latent-implicit-thinking.github.io/papers/2610.26666/citation.bib) · [Preprint CSL-JSON](https://latent-implicit-thinking.github.io/papers/2610.26666/citation.csl.json) · [JSON record](https://latent-implicit-thinking.github.io/papers/2610.26666/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 0.11.0; literature checked through 2026-10-26.