arXiv：cs.AI· Sumin Park, T. Konstantin Rusch·· 19 小时前
QRR：具有相位旋转对称性的循环推理架构，收敛更快
Looped Reasoning Finishes Earlier Than You Think
AI 导读
研究提出 QRR（Quotient Recurrent Reasoner），一种具备精确逐 token 相位旋转对称性的规范等变循环架构，可让对称方向的运动不改变商表示、与推理相关动态解耦。QRR 在商空间中更快更稳定地收敛到解根，且不形成主导的慢振荡瓶颈，在 Sudoku、Maze 和 Mini-ARC 上匹配或超越近期循环推理模型。
正文
Abstract:Looped reasoning with dynamic depth can be viewed as relaxation toward solution attractors in a learned dynamical landscape. In practice, however, latent trajectories often oscillate, cycle, or drift rather than cleanly converge to stable fixed points. How these non-stationary dynamics contribute to reasoning and constrain convergence remains unclear. We show that slowly decaying oscillatory modes can impose their convergence rate on coupled latent dynamics, creating a bottleneck. Yet damping these modes indiscriminately can disrupt the reasoning computation they support. This tension motivates an architectural approach: introducing rotational degrees of freedom along which symmetry-generated rotational motion leaves the reasoning-relevant quotient dynamics unchanged by construction. We propose QRR (Quotient Recurrent Reasoner), a gauge-equivariant recurrent architecture with an exact per-token phase-rotation symmetry. Motion along these symmetry directions leaves the quotient representation unchanged and is dynamically decoupled from reasoning-relevant dynamics. Empirically, QRR achieves stable and faster convergence to solution roots in quotient space, without forming a dominant slow oscillatory bottleneck, while matching or surpassing recent recurrent reasoning models on Sudoku, Maze, and Mini-ARC.
| Comments: | 25 pages |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.18174 [cs.LG] |
| (or arXiv:2610.18174v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.18174 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Sumin Park [view email]
[v1]
Tue, 13 Oct 2026 11:20:24 UTC (388 KB)
来源：arXiv：cs.AI · arxiv.org