SIGReg Objective Aligns JEPA World Models with Active Inference

Joint-Embedding Predictive Architectures (JEPAs) are a dominant paradigm for building latent world models, often justified by their empirical success rather than a foundational normative principle. This research provides a theoretical underpinning for JEPAs by demonstrating a profound connection to Active Inference (AIF). The key insight is that the choice of anti-collapse regularizer within a JEPA's training objective—which combines a prediction loss with a weighted embedding regularizer—determines whether this objective can be interpreted as a valid variational free energy in the AIF framework. The paper categorizes four non-contrastive regularizers (VICReg, LogDet, PairDist, and SIGReg) based on an entropy-estimator hierarchy and a "prior-miscalibration gap." It reveals that the sign of this gap dictates whether the AIF surprise bound is preserved. Specifically, VICReg and LogDet are identified as unsafe upper bounds, PairDist as a safe lower bound, while SIGReg uniquely eliminates this gap. A crucial correspondence theorem is then proven: under standard assumptions (constant-noise encoder and successful SIGReg enforcement leading to isotropic-Gaussian embeddings), the gap vanishes, the JEPA objective transforms into an exact information bottleneck, the surprise bound remains intact, and the latent goal cost precisely proxies AIF pragmatic value. The correspondence is further extended to multi-step expected free energy, ensemble epistemic value, and a learned-policy regime. The research also highlights one AIF term that current JEPA world models do not compute: the state-epistemic value, which signals future-state coverage. These findings offer distinct theoretical predictions, differing in kind rather than degree, setting the stage for future empirical validation.