mlsanityData to 14 Oct 2026

Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddings

arXiv 2211.15120 ↗First posted 28 Nov 2022cs.LGcited by 24

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Abstract (arXiv)

Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives and are gaining more attention in machine learning applications. Imposing such quasimetric structures in model representations has been shown to improve many tasks, including reinforcement learning (RL) and causal relation learning. In this work, we present four desirable properties in such quasimetric models, and show how prior works fail at them. We propose Interval Quasimetric Embedding (IQE), which is designed to satisfy all four criteria. On three quasimetric learning experiments, IQEs show strong approximation and generalization abilities, leading to better performance and improved efficiency over prior methods. Project Page: https://www.tongzhouwang.info/interval_quasimetric_embedding Quasimetric Learning Code Package: https://www.github.com/quasimetric-learning/torch-quasimetric

Key facts. Cited by 24 papers in the map (data through 14 Oct 2026). Builds on 22 of its 36 references that are in the map. First posted on arXiv 28 Nov 2022.

Builds on

22 of 36 references.

References · 22

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10 more
  1. 2015Order-Embeddings of Images and Languagecited by 113
  2. 2022Denoised MDPs: Learning World Models Better Than the World Itselfcited by 68
  3. 2020Model-Based Visual Planning with Self-Supervised Functional Distancescited by 42
  4. 2020An Inductive Bias for Distances: Neural Nets that Respect the Triangle Inequalitycited by 24
  5. 2019Hyperbolic Disk Embeddings for Directed Acyclic Graphscited by 21
  6. 2019Self-supervised Learning of Distance Functions for Goal-Conditioned Reinforcement Learningcited by 18
  7. 2022On the Learning and Learnability of Quasimetricscited by 15
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Citing papers per year: 2023: 1; 2024: 3; 2025: 11; 2026: 9.

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  1. 2024OGBench: Benchmarking Offline Goal-Conditioned RLcited by 238
  2. 2023Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learningcited by 121
  3. 2025Offline Goal-conditioned Reinforcement Learning with Quasimetric Representationscited by 24
  4. 2025Option-aware Temporally Abstracted Value for Offline Goal-Conditioned Reinforcement Learningcited by 23
  5. 2025Value-guided action planning with JEPA world modelscited by 21
  6. 2025Horizon Generalization in Reinforcement Learningcited by 17
  7. 2025Self-Predictive Representations for Combinatorial Generalization in Behavioral Cloningcited by 12
  8. 2025Flattening Hierarchies with Policy Bootstrappingcited by 11
  9. 2025Physics-informed Temporal Difference Metric Learning for Robot Motion Planningcited by 6
  10. 2025Goal Reaching with Eikonal-Constrained Hierarchical Quasimetric Reinforcement Learningcited by 6
  11. 2025Offline Goal-Conditioned Reinforcement Learning with Projective Quasimetric Planningcited by 5
  12. 2024State Chrono Representation for Enhancing Generalization in Reinforcement Learningcited by 3
12 more
  1. 2025VLD: Visual Language Goal Distance for Reinforcement Learning Navigationcited by 2
  2. 2025Learning The Minimum Action Distancecited by 1
  3. 2026Compositional Transduction with Latent Analogies for Offline Goal-Conditioned Reinforcement Learningcited by 1
  4. 2026Latent Representation Alignment for Offline Goal-Conditioned Reinforcement Learningcited by 1
  5. 2024QuasiNav: Asymmetric Cost-Aware Navigation Planning with Constrained Quasimetric Reinforcement Learningcited by 0
  6. 2026Intrinsic-Energy Joint Embedding Predictive Architectures Induce Quasimetric Spacescited by 0
  7. 2026ChronoForest: Closed-Loop Multi-Tree Diffusion Planning for Efficient Bridge Search and Route Compositioncited by 0
  8. 2026GTRL: Grounding Divide-and-Conquer Value Learning with Temporal Differencescited by 0
  9. 2026Learning Transferable Skills using Goal-Conditioned Bisimulationcited by 0
  10. 2026Learning Goal-Reaching Quasimetric Geometry From Finite-Time Reachabilitycited by 0
  11. 2026World Modeling through Spectral Alignmentcited by 0
  12. 2026Outperforming 1000 Euclidean Layers With Hyperbolic Goal-Conditioned RLcited by 0