The SIGReg Objective as Variational Free Energy: A Theoretical Active-Inference Account of JEPA World Models

arXiv:2607.13612 gives a theoretical Active Inference interpretation of JEPA world-model training. It organizes VICReg, LogDet, PairDist, and SIGReg as entropy estimators with different prior-miscalibration gaps, arguing that only SIGReg removes the gap under the standard constant-noise encoder and isotropic-Gaussian embedding assumptions. The paper derives correspondences with information bottlenecks, surprise bounds, pragmatic value, multi-step expected free energy, ensemble epistemic value, and learned policies. It also identifies state-epistemic value as missing from current JEPA objectives. Core algebra is machine-verified in Lean 4, while empirical predictions remain open.