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arXiv · 2602.12245

Intrinsic-Energy Joint Embedding Predictive Architectures Induce Quasimetric Spaces

Anthony Kobanda·Waris Radji
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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.

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Anthony Kobanda, Waris Radji. 2026-02-12. Intrinsic-Energy Joint Embedding Predictive Architectures Induce Quasimetric Spaces. https://arxiv.org/abs/2602.12245

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