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.

翻译：联合嵌入预测架构旨在通过从上下文嵌入预测目标嵌入来学习表示，从而在潜在空间中诱导标量兼容性能量。相比之下，拟度量强化学习通过有向距离值（目标达成成本）研究目标条件控制，该距离值支持在非对称动力学下达成目标。在这篇短文中，我们通过将注意力限制在一类原则性的JEPA能量函数上——即内在（最小作用量）能量，来连接这两种观点。内在能量被定义为两个状态间允许轨迹上累积局部努力的下确界。在温和的闭包性和可加性假设下，任何内在能量都是一个拟度量。在目标达成控制中，最优目标达成成本函数恰好具有这种内在形式；反之，经过训练以建模内在能量的JEPA则属于QRL所针对的拟度量值类。此外，我们阐释了为何对称的有限能量在结构上与单向可达性不匹配，从而在方向性重要时，需要非对称（拟度量）能量。