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arXiv 2610.20009cs.LGstat.ML
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用双曲空间目标条件强化学习超越1000层欧几里得网络

Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL

University of Vienna(维也纳大学);Max Planck Institute of Biochemistry(马克斯·普朗克生物化学研究所)

Timo Klein, Thomas Lang, Andrii Shkabrii, Lukas Miklautz, Yllka Velaj, Sebastian Tschiatschek

AI总结:

该研究提出双曲CRL,用双曲空间测地线距离替代CRL对比目标中的欧几里得距离,64层双曲智能体性能超1024层欧几里得网络,训练更快、参数更少,可替代大量网络深度。

摘要:

将自监督对比强化学习(CRL)扩展到1000层欧几里得神经网络已实现了最先进的目标到达性能,但 wall-clock time(墙钟时间)随深度线性缩放。我们发现,改变几何结构可让更浅的网络实现更强性能,这在复杂导航环境中至关重要,因为墙壁会使路径距离与欧几里得距离大幅偏离。在U型迷宫中,我们证明路径越长,其与欧几里得距离的偏差越大。双曲CRL通过将CRL对比目标中的欧几里得距离替换为双曲空间中的测地线距离,解决了这种不匹配问题。在困难导航任务中,归纳偏置胜过规模:64层的双曲智能体性能超过1024层的欧几里得网络,同时训练速度快12倍以上,参数数量减少约13倍。我们观察到,双曲智能体在困难人形迷宫中的行为质量更优,它们会沿走廊到达目标,而欧几里得智能体会尝试穿墙的直线捷径。我们的结果表明,使表示几何与任务匹配可替代大量网络深度。代码位于此https URL。

英文摘要:

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 .

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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