mlsanityData to 14 Oct 2026

Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RL

arXiv 2610.20009 ↗First posted 14 Oct 2026cs.LG stat.MLcited by 0

On the map: Deep reinforcement learning methods → Deep RL algorithms and representations also fits: RL with diffusion and flow models

Abstract (arXiv)

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 .

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods. Builds on 33 of its 43 references that are in the map. First posted on arXiv 14 Oct 2026.

Builds on

33 of 43 references.

Closest ancestors · 7

Same direction, newest first

  1. 2025Understanding and Improving Hyperbolic Deep Reinforcement Learning16 Dec
  2. 2025Multistep Quasimetric Learning for Scalable Goal-conditioned Reinforcement Learning11 Nov
  3. 20251000 Layer Networks for Self-Supervised RL: Scaling Depth Can Enable New Goal-Reaching Capabilities19 Mar
  4. 2024SimBa: Simplicity Bias for Scaling Up Parameters in Deep Reinforcement Learning13 Oct
  5. 2024Learning Temporal Distances: Contrastive Successor Features Can Provide a Metric Structure for Decision-Making24 Jun
  6. 2024Bigger, Regularized, Optimistic: scaling for compute and sample-efficient continuous control25 May
  7. 2024Mixtures of Experts Unlock Parameter Scaling for Deep RL13 Feb

Other references · 26

  1. 2018Representation Learning with Contrastive Predictive Codingcited by 7,777
  2. 2017Hindsight Experience Replaycited by 1,136
  3. 2021Deep Reinforcement Learning at the Edge of the Statistical Precipicecited by 807
  4. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 684
  5. 2018Hyperbolic Neural Networkscited by 402
  6. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 265
  7. 2022Contrastive Learning as Goal-Conditioned Reinforcement Learningcited by 253
  8. 2024OGBench: Benchmarking Offline Goal-Conditioned RLcited by 238
  9. 2019Hyperbolic Image Embeddingscited by 221
  10. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 206
  11. 2018Riemannian Adaptive Optimization Methodscited by 194
  12. 2023Hyperbolic Image-Text Representationscited by 136
14 more
  1. 2023Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learningcited by 121
  2. 2022Hyperbolic Vision Transformers: Combining Improvements in Metric Learningcited by 111
  3. 2024Compositional Entailment Learning for Hyperbolic Vision-Language Modelscited by 74
  4. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 73
  5. 2022Hyperbolic Contrastive Learning for Visual Representations beyond Objectscited by 61
  6. 2021Learning the Predictability of the Futurecited by 49
  7. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 49
  8. 2024Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Spacecited by 43
  9. 2022Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddingscited by 24
  10. 2025Offline Goal-conditioned Reinforcement Learning with Quasimetric Representationscited by 24
  11. 2023Stabilizing Contrastive RL: Techniques for Robotic Goal Reaching from Offline Datacited by 23
  12. 2025Is Temporal Difference Learning the Gold Standard for Stitching in RL?cited by 4
  13. 2026Fast and Geometrically Grounded Lorentz Neural Networkscited by 3
  14. 2026hyperbolix: Hyperbolic Deep Learning in JAXcited by 1

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  6. 2026Do Better Goal Representations Improve Goal-Conditioned Reinforcement Learning?
  7. 2026Reinforcement Learning for Large-Scale Lifelong Multi-Agent Path Finding with Shared Spatial Fields
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