Radial-VCReg: More Informative Representation Learning Through Radial Gaussianization
This work addresses the challenge of explicit information maximization hindered by the curse of dimensionality for researchers in self-supervised learning, representing an incremental improvement over VCReg.
The paper tackled the problem of learning maximally informative representations in self-supervised learning by addressing limitations in existing methods like VCReg, which cannot fully achieve maximum entropy. The result was the proposal of Radial-VCReg, which consistently improved performance on synthetic and real-world datasets by reducing higher-order dependencies and promoting more diverse and informative representations.
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.