Radial-VCReg: More Informative Representation Learning Through Radial Gaussianization

Abstract

Self-supervised learning aims to learn maximally informative representations, but explicit information maximization is hindered by the curse of dimensionality. Existing methods like VCReg address this by regularizing first and second-order feature statistics, which cannot fully achieve maximum entropy. We propose Radial-VCReg, which augments VCReg with a radial Gaussianization loss that aligns feature norms with the Chi distribution-a defining property of high-dimensional Gaussians. We prove that Radial-VCReg transforms a broader class of distributions towards normality compared to VCReg and show on synthetic and real-world datasets that it consistently improves performance by reducing higher-order dependencies and promoting more diverse and informative representations.

Published in the Unifying Representations in Neural Models (UniReps) and Symmetry and Geometry in Neural Representations (NeurReps) Workshops at NeurIPS 2025