Nested recursion operators show no clear gains in reasoning models
Nested Shared-Operator Recursion on ARC-AGI-1: An Empirical Study of HRM, TRM and URM
Machine Learning
Summary
Some artificial intelligence models try to think better by applying the same reasoning steps repeatedly. This study tested whether adding an extra step of combining these repeated updates helps these models improve their predictions. The researchers compared standard models with these ‘nested’ versions on a specific benchmark but found no consistent advantage in accuracy or solving ability. The results do not prove the approach is better or worse, leaving the question open for future studies.
What this means in practice
- •For machine learning engineers: Use this study to guide the design of reasoning models by reconsidering nested recursion techniques under cost constraints.
- •For benchmark developers: Incorporate insights from this paper to create clearer evaluation protocols for testing recursive reasoning models.
Tested on one dataset.
Authors
Sara Neri, Eugenio Gaeta, Andrea Ceschini, Andrea Facchinetti, Giuseppe Fico
Abstract
Recursive reasoning models refine persistent internal states by repeatedly applying learned operators. We investigate whether adding a persistent intermediate state that integrates repeated updates of a faster state through the same operator improves predictive performance relative to each model family's baseline at matched parameter counts. We define this organisation operationally and implement it within three architectures: the Hierarchical Reasoning Model (HRM), Tiny Recursive Model (TRM) and Universal Reasoning Model (URM). Using the official codebases on ARC-AGI-1, we compare each baseline with its parameter-matched nested variant. We evaluate held-out queries from tasks whose demonstrations were available during training. The experiments use a single-GPU budget far below the published training protocols. Under the tested conditions, nested variants show no consistent advantage in token accuracy, predictive loss or exact solving, which remains near zero for all configurations. The results therefore leave the hypothesis open. We specify a confirmatory comparison, with an informative baseline, multiple seeds, controls that isolate nesting and predefined criteria, to determine whether this organisation merits further development.