Dynamic LeJEPA: Maximum Entropy Representations for Sequential Prediction and Latent Planning with Theoretical Guarantees
Year: 2026
Type: preprint
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 domain×mechanism combina-tion), and a budget replication demonstrating that the encoder-physics violation deepens with training. Phase 3 additionally characterizes an entropy–utility frontier on low-intrinsic-dimension robotics data, discovering that per-dimension variance matching alone produces correlated collapse—a failure mode invisible on high-dimensional data—and that optimization budget, not regularization weight, is the binding entropy constraint. We further show this failure generalizes: a marginal-only VAE-KL encoder collapses identically on the same data, and we introduce a posterior signal-fraction diagnostic revealing that such collapse can hide beneath the encoder’s own sampling-noise floor, invisible to marginal diagnostics. To test whether the placement rule matters beyond repre-sentation quality, we further probe its consequence for downstream control: a latent cross-entropy-method (CEM) planner built on the trained Phase 3 models consistently outperforms real-action replay on model-internal cost across ablation conditions and both encoder mechanisms—an impossible result for genuine planning, since replaying the true actions is itself the ground-truth solution. A model-exploitation diagnostic traces this to the planner discovering action sequences roughly a quarter of the action range away from the true trajectory while still lowering the learned decoder’s cost, uniformly regardless of physics placement and encoder choice. We report this transparently as a boundary condition on the practical claim: offline latent planning against a learned decoder is not, by itself, sufficient evidence that a representation supports downstream control, and we identify closed-loop, simulator-verified execution as the necessary next test. The result is the first formal, cross-domain validated blueprint for physics-informed world models: place physics where the theorem says it is safe, never where intuition suggests—together with a concrete, reproducible cautionary result on how easily offline latent planning can be mistaken for evidence of control competence.
Source: Preprints.org
Author: Mohsen Mostafa
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213448917