KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learning

Breakthroughs in self-supervised Joint-Embedding Predictive Architectures (JEPAs) have established that regularizing Euclidean representations toward isotropic Gaussian priors yields provable gains in training stability and downstream generalization. We introduce a new, flexible family of Euclidean joint embedding self-supervised learning algorithms with kernel-based regularizers. One instance of this family corresponds to the SIGReg Epps-Pulley regularizer which approximates a sliced Maximum Mean Discrepancy (MMD) with a Gaussian prior and Gaussian kernel. By expanding the class of viable kernels and priors and computing the closed-form high-dimensional limit of sliced discrepancies, we develop alternative methods with improved training stability and design flexibility and leverage those techniques to train strong vision learners at scale.