IAAIQRR
Looped Reasoning Finishes Earlier Than You Think
The Quotient Recurrent Reasoner adds an exact per-token phase-rotation symmetry so that slow oscillatory motion lives along directions that do not change the reasoning-relevant quotient state, avoiding an oscillation bottleneck in dynamic-depth looped reasoning.
Inside the method
[ Gauge-equivariant recurrent block ] × r → quotient-space readout
Simplified conceptual schematic. Consult the paper for the complete architecture.
- Recurrence family
- Adaptive depth
- Depth control
- Dynamic depth until convergence in quotient space
- KV / state strategy
- See paper
Reading note
Reports stable, faster convergence and matches or exceeds recent recurrent reasoning models on Sudoku, Maze and Mini-ARC.
Sources checked 2026-10-28. This catalog does not imply independent reproduction.
Related works
Cite this work
@misc{qrr2026,
title = {Looped Reasoning Finishes Earlier Than You Think},
author = {Sumin Park and T. Konstantin Rusch},
year = {2026},
eprint = {2610.18174},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18174}
}