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This paper connects Joint-Embedding Predictive Architectures (JEPAs) with Quasimetric Reinforcement Learning (QRL) by focusing on a specific class of JEPA energy functions: intrinsic (least-action) energies defined as infima of accumulated local effort. It demonstrates that under closure and additivity assumptions, intrinsic energies are quasimetrics, aligning JEPAs trained on these energies with the quasimetric value functions used in QRL for goal-reaching control. The work highlights the structural mismatch between symmetric energies and one-way reachability, advocating for asymmetric (quasimetric) energies in scenarios where directionality is important.
JEPA's latent space energy functions can be understood as quasimetrics, bridging representation learning and goal-conditioned control.
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.