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

Sara Neri, Eugenio Gaeta, Andrea Ceschini, Andrea Facchinetti, Giuseppe Fico · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26666 · cited by 0 works (OpenAlex) · open-access PDF

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Los modelos de razonamiento recursivo refinan los estados internos persistentes mediante la aplicación repetida de los operadores aprendidos. Investigamos si la adición de un estado intermedio persistente que integra las actualizaciones repetidas de un estado más rápido a través del mismo operador mejora el rendimiento predictivo en relación con la línea de base de cada familia de modelos en cuentas de parámetros coincidentes. Definimos esta organización de forma operativa y la implementamos dentro de tres arquitecturas: el Modelo de razonamiento jerárquico (HRM), el Modelo recursivo pequeño (TRM) y el Modelo de razonamiento universal (URM). Usando las bases de códigos oficiales en ARC-AGI-1, comparamos cada línea de base con su variante enlazada de parámetros. Valoramos las consultas realizadas de

Machine translation (Meta M2M100); the English original follows.

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.

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Topics: Nesting (process), Computer science, Recursion (computer science), Baseline (sea), Operator (biology), Zero (linguistics)

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