Intrinsic-Energy Joint Embedding Predictive Architectures Induce Quasimetric Spaces
This work provides a theoretical link between representation learning and control for researchers in machine learning and reinforcement learning, but it is incremental as it builds on existing frameworks without introducing new methods or data.
The paper connects Joint-Embedding Predictive Architectures (JEPAs) and Quasimetric Reinforcement Learning (QRL) by showing that intrinsic energy functions in JEPAs are quasimetrics, which align with optimal cost-to-go functions in goal-reaching control, addressing the mismatch between symmetric energies and directional reachability.
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.