SE-RRM: 2M-Parameter Equivariant Model Beats HRM/TRM on Sudoku and ARC-AGI
gklambauer · x · 2026-09-05
Responding to a thread on Flow Reasoning Models, the authors highlight their ICML 2026 paper Symbol-Equivariant Recurrent Reasoning Models (SE-RRMs), extending the HRM/TRM family of tiny recursive reasoners.
- Key idea: Prior RRMs handle symbol symmetries only implicitly via costly data augmentation; SE-RRMs enforce permutation equivariance architecturally with symbol-equivariant layers, guaranteeing identical solutions under symbol/color permutations.
- Results: Outperforms prior RRMs on 9x9 Sudoku and generalizes from 9x9-only training to 4x4, 16x16, and 25x25 instances that existing RRMs cannot extrapolate to.
- ARC-AGI: Competitive performance on ARC-AGI-1/2 with far less augmentation and only 2 million parameters, showing explicit symmetry encoding boosts robustness and scalability.
Code is open-sourced. The quoted Flow Reasoning Models work applies continuous flows to discrete data, recurrently refining mistakes via self-conditioning on structured problems like Sudoku.
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