arXiv：cs.LG· Timo Klein, Thomas Lang, Andrii Shkabrii, Lukas Miklautz, Yllka Velaj, Sebastian Tschiatschek·· 10 小时前
双曲目标条件 RL 用 64 层击败 1024 层欧几里得网络
Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL
AI 导读
双曲 CRL 把对比目标中的欧几里得距离换成双曲空间测地距离，在困难导航任务上，64 层双曲智能体性能超过 1024 层欧几里得网络，训练速度提升超 12 倍、参数量约少 13 倍。在 U 型迷宫和类人迷宫实验中，路线越长偏离欧几里得距离越多，双曲智能体沿走廊抵达目标，而欧几里得智能体倾向于直线穿墙。代码已公开。
正文
Abstract:Scaling self-supervised contrastive reinforcement learning (CRL) to 1000-layer Euclidean neural networks has enabled state-of-the-art goal-reaching performance, yet wall-clock time scales linearly with depth. We find that changing the geometry achieves stronger performance with far shallower networks. This matters in complex navigation environments, where walls can make route distance deviate substantially from Euclidean distance. In a U-shaped maze, we show that the longer the route, the more it deviates from Euclidean distance. Hyperbolic CRL addresses this mismatch by replacing Euclidean distances in CRL's contrastive objective with geodesic distances in hyperbolic space. On hard navigation tasks, inductive bias beats scale: depth 64 hyperbolic agents outperform 1024-layer-deep Euclidean networks while training more than $12 \times$ faster and using about $13 \times$ fewer parameters. We observe that hyperbolic agents behave qualitatively better in hard humanoid mazes, where they follow corridors to reach goals, whereas Euclidean agents try straight-line shortcuts over walls. Our results show that matching the representation geometry to the task can substitute for substantial network depth. Code is at this https URL .
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.20009 [cs.LG] |
| (or arXiv:2610.20009v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.20009 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Timo Klein [view email]
[v1]
Wed, 14 Oct 2026 11:23:28 UTC (2,905 KB)
来源：arXiv：cs.LG · arxiv.org