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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

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: · Added to this list: October 22, 2026

Cite this paper

ArXiv preprint

arXiv:2610.26666 · Initial submission: 2026-10-19

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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 — 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.