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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

Indonesian

Model pertimbangan recursive memperbaiki keadaan internal persisten dengan mengaplikasikan operator yang dipelajari berulang kali. Kami menyelidiki apakah menambahkan kondisi persisten menengah yang mengintegrasikan pembaruan berulang dari keadaan yang lebih cepat melalui operator yang sama meningkatkan kinerja prediktif dibandingkan dengan basis basis dari setiap keluarga model pada hitungan parameter yang cocok. Kami mendefinisikan organisasi ini secara operasional dan menerapkannya dalam tiga arsitektur: Hierarchical Reasoning Model (HRM), Tiny Recursive Model (TRM) dan Universal Reasoning Model (URM). Menggunakan basis kode resmi pada ARC-AGI-1, kami membandingkan setiap garis dasar dengan varian berpasangan parameternya. Kami mengevaluasi kueri-out dari tugas-tugas yang demonstrasi yang tersedia selama pelatihan. Eksperimen menggunakan anggaran tunggal-GPU jauh di bawah protokol pel

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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