外观
论文arXiv 2610.2000914 天前
用双曲目标条件RL超越1000层欧氏网络
原文链接：Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL（arXiv 2610.20009 · 发布日期：2026-10-14）
Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL
针对复杂导航中欧氏距离与路线距离不匹配，方法用双曲测地距离改造CRL，并在困难导航任务上验证。
核心要点
- 复杂导航中墙体会使路线距离显著偏离欧氏距离，深层欧氏CRL耗时随深度线性增长。
- Hyperbolic CRL将对比目标中的欧氏距离替换为双曲空间测地距离，引入几何归纳偏置。
- 在困难导航任务中，64层双曲智能体优于1024层欧氏网络，训练更快且参数更少。
- 代码已在GitHub发布；在困难humanoid迷宫中，双曲智能体更倾向沿走廊到达目标。
验证范围与局限：验证范围包括U形迷宫、困难导航任务和困难humanoid迷宫，摘要未说明真机实验。
英文摘要 (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 https://github.com/Probabilistic-and-Interactive-ML/HypGCRL .
作者：Timo Klein, Thomas Lang, Andrii Shkabrii, Lukas Miklautz, Yllka Velaj, Sebastian Tschiatschek
来源
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