Intrinsic-Energy Joint Embedding Predictive Architectures Induce Quasimetric Spaces

2026-02-12

AI Summary

This work addresses the limitation of symmetric energy functions in goal-directed control, which fail to capture the unidirectional reachability between states. We propose using intrinsic energy—defined as the minimal action—within a Joint Embedding Predictive Architecture (JEPA) as a compatibility energy function, thereby establishing the first rigorous theoretical connection between JEPA and quasimetric reinforcement learning (QRL). We prove that intrinsic energy satisfying closure and additivity naturally induces a quasimetric, and further show that the optimal cost-to-go function inherently possesses this energy structure. This result clarifies the fundamental inadequacy of symmetric energies in directional tasks. Our approach unifies representation learning with goal-conditioned reinforcement learning, offering a theoretically grounded and structurally coherent framework for achieving directional goals.

Technology Category

• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Intelligent Robots: Learning & Optimization for ROB
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Joint-Embedding Predictive Architectures (JEPAs) aim to learn representations by predicting target embeddings from context embeddings, inducing a scalar compatibility energy in a latent space. In contrast, Quasimetric Reinforcement Learning (QRL) studies goal-conditioned control through directed distance values (cost-to-go) that support reaching goals under asymmetric dynamics. In this short article, we connect these viewpoints by restricting attention to a principled class of JEPA energy functions : intrinsic (least-action) energies, defined as infima of accumulated local effort over admissible trajectories between two states. Under mild closure and additivity assumptions, any intrinsic energy is a quasimetric. In goal-reaching control, optimal cost-to-go functions admit exactly this intrinsic form ; inversely, JEPAs trained to model intrinsic energies lie in the quasimetric value class targeted by QRL. Moreover, we observe why symmetric finite energies are structurally mismatched with one-way reachability, motivating asymmetric (quasimetric) energies when directionality matters.

Problem

• Joint-Embedding Predictive Architectures
• Quasimetric
• Intrinsic Energy
• Goal-conditioned Control
• Asymmetric Reachability

Innovation

• Intrinsic Energy
• Quasimetric
• Joint-Embedding Predictive Architecture
• Cost-to-Go
• Asymmetric Reachability