Intrinsic-Energy Joint Embedding Predictive Architectures Induce Quasimetric Spaces
2026-02-12 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors connect two ideas: one about learning to represent information by predicting between different points (JEPAs), and another about controlling actions to reach goals efficiently (QRL). They show that a special type of energy used in JEPAs, called intrinsic energy, behaves like a directed distance measure used in goal-reaching tasks. This means that the way JEPAs learn and how QRL plans actions can be understood through the same mathematical concept. They also explain why energies that work both ways (symmetric) do not fit well when you need to consider direction, supporting the use of asymmetric energies instead.
Joint-Embedding Predictive ArchitecturesQuasimetric Reinforcement Learningintrinsic energyleast-action principlegoal-conditioned controlcost-to-go functionquasimetricasymmetric energylatent space embeddingreachability
Authors
Anthony Kobanda, Waris Radji
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.