Joint-Embedding Predictive Architectures (JEPAs) are the leading design for latent world models, yet they are often justified by empirical performance rather than normative principles. This paper shows that the choice of anti-collapse regulariser determines whether a JEPA's training objective—a prediction loss plus a weighted embedding regulariser—is a valid Active Inference (AIF) variational free energy. We organize four non-contrastive regularisers (VICReg, LogDet, PairDist, and SIGReg) into an entropy-estimator hierarchy indexed by a prior-miscalibration gap, demonstrating that the sign of the gap decides whether the AIF surprise bound survives: VICReg and LogDet are unsafe upper bounds, PairDist is a safe lower bound, and SIGReg eliminates the gap.
We then prove a correspondence theorem: under the standard constant-noise encoder model and successful SIGReg enforcement (isotropic-Gaussian embeddings), the gap vanishes, the objective becomes an exact information bottleneck, the surprise bound is preserved, and the latent goal cost becomes an exact proxy for AIF pragmatic value, while VICReg leaves an irreducible second-order anisotropy term. We extend the correspondence to multi-step expected free energy, ensemble epistemic value, and a learned-policy regime, identifying one AIF term not computed by current JEPA world models: the state-epistemic value, a future-state coverage signal. The predictions differ in kind, not degree, and are stated here as theoretical consequences left for empirical test in separate work; full proofs are in Appendix A, with the algebraic core of every result machine-verified in Lean 4 (Appendix D).
Blogger's Review: This paper delves into the theoretical foundation of JEPA models, particularly the crucial role of the SIGReg regulariser in ensuring effective variational free energy. Through systematic analysis, the authors clarify the safety of different regularisers and propose future research directions, which hold significant theoretical and practical implications. The mathematical proofs and machine verification also provide a solid foundation for further studies.