Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL
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 × faster and using about 13 × 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 .
Related
- DAGR: State-Conditioned Goal Representations via Difference-Aware Goal Cross-Attention
- Learning Multiple Timescales for Goal-Conditioned Reinforcement Learning
- A Frankel type theorem in Euclidean and hyperbolic spaces
- Sharp mean-width and Jacobian bounds for Euclidean and hyperbolic harmonic maps
- Goal-Oriented Ordered Autoencoding for Successive Refinement in Progressive Communication
BibTeX
@misc{klein2026outperforming,
title = {{Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL}},
author = {Timo Klein and Thomas Lang and Andrii Shkabrii and Lukas Miklautz and Yllka Velaj and Sebastian Tschiatschek},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20009},
eprint = {2610.20009},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20009},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL
AU - Timo Klein
AU - Thomas Lang
AU - Andrii Shkabrii
AU - Lukas Miklautz
AU - Yllka Velaj
AU - Sebastian Tschiatschek
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20009
UR - https://arxiv.org/abs/2610.20009
AB - 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 × faster and using about 13 × 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 .
ER -