Intrinsic-Energy Joint Embedding Predictive Architectures Induce Quasimetric Spaces

2026-02-12 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

Joint-Embedding Predictive Architectures (JEPAs) learn representations by predicting target embeddings from context embeddings, generating a scalar compatibility energy in a latent space. This article connects JEPAs with Quasimetric Reinforcement Learning (QRL), which uses directed distance values (cost-to-go) for goal-conditioned control under asymmetric dynamics. The key insight is that a principled class of JEPA energy functions, specifically intrinsic (least-action) energies, are quasimetrics. Intrinsic energies are defined as the infima of accumulated local effort along trajectories between states. Under mild assumptions, any intrinsic energy functions as a quasimetric. Optimal cost-to-go functions in goal-reaching control exhibit this intrinsic form, meaning JEPAs modeling intrinsic energies align with the quasimetric value class used in QRL. The analysis also explains why symmetric finite energies are unsuitable for one-way reachability, underscoring the need for asymmetric quasimetric energies when directionality is critical.

Key takeaway

For AI Researchers developing goal-conditioned control systems, understanding that intrinsic JEPA energies are quasimetrics is crucial. This connection implies that JEPAs can directly learn the asymmetric cost-to-go functions required by Quasimetric Reinforcement Learning, offering a principled approach to modeling directed reachability in complex environments. Your research should explore training JEPAs with intrinsic energy objectives to improve performance in tasks with asymmetric dynamics.

Key insights

Intrinsic (least-action) energy functions in JEPAs are quasimetrics, aligning with optimal cost-to-go functions in QRL.

Principles

• Intrinsic energy functions are quasimetrics.
• Symmetric energies mismatch one-way reachability.

Topics

• Joint-Embedding Predictive Architectures
• Quasimetric Reinforcement Learning
• Intrinsic Energy
• Quasimetric Spaces
• Goal-Conditioned Control

Best for: AI Researcher, AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.