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This paper establishes a theoretical foundation for Joint-Embedding Predictive Architectures (JEPAs) by demonstrating that the choice of anti-collapse regularizer influences whether the training objective aligns with Active Inference (AIF) variational free energy. It organizes four non-contrastive regularizers into an entropy-estimator hierarchy and shows that only SIGReg eliminates the prior-miscalibration gap, allowing the AIF surprise bound to be preserved. The authors prove that under specific conditions, SIGReg transforms the training objective into an exact information bottleneck, revealing the latent goal cost as a precise proxy for AIF pragmatic value, while highlighting the limitations of other regularizers like VICReg.
SIGReg not only resolves the prior-miscalibration gap but also transforms JEPA objectives into exact proxies for Active Inference value, revealing a crucial oversight in current models.
Joint-Embedding Predictive Architectures (JEPAs) are the dominant design for latent world models, yet they are usually justified by empirical performance rather than a normative principle. We show 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 organise four non-contrastive regularisers (VICReg, LogDet, PairDist, and SIGReg) into an entropy-estimator hierarchy indexed by a prior-miscalibration gap, and show that the gap's sign, whether the estimator bounds the latent entropy from above or below, decides whether the AIF surprise bound survives: VICReg and LogDet are unsafe upper bounds, PairDist 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, whereas 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, and we identify the one AIF term no current JEPA world model computes: 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, and the algebraic core of every result is machine-verified in Lean 4 (Appendix D).