Dynamic LeJEPA: Maximum Entropy Representations for Sequential Prediction and Latent Planning with Theoretical Guarantees
Abstract
Joint-Embedding Predictive Architectures (JEPAs) are emerging as the backbone for latent world models in robotics and autonomous driving, yet inject-ing domain knowledge (physics, kinematics, geometry) into these models consistently degrades performance—with no theoretical explanation. We resolve this para-dox by proving, through six theorems, that the isotropic maximum-entropy embedding is symmetry-stable under sequential prediction losses—no first-order incentive exists to rotate away from it under any Lipschitz, Euclidean-invariant prediction objective—and by validating across a phased empirical protocol that no non-Gaussian alter-native outperforms it in practice. This yields a world-model design principle with a provable guarantee: encoder maximum-entropy, predictor dynamics, decoder physics—and explains why prior physics-informed JEPAs failed: they constrained the encoder, where constraints provably destroy the entropy guarantee, instead of the decoder, where they are provably benign. We validate this prin-ciple across two domains and two encoder mechanisms through a phased protocol covering measurement artifacts (Proposition 1: the N/K ≥ 5 reliability threshold), pow- ered statistical testing (110 seeded ablation runs across autonomous driving and bimanual robotic manipulation, under both a SIGReg-regularized encoder and a marginal-only VAE-KL encoder—the encoder family of classical world models—with paired Wilcoxon significance and joint Holm correction in every…
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