Kernel VICReg for Self-Supervised Learning in Reproducing Kernel Hilbert Space

• URL: http://arxiv.org/abs/2509.07289v1
• Date: Mon, 08 Sep 2025 23:49:21 GMT
• Title: Kernel VICReg for Self-Supervised Learning in Reproducing Kernel Hilbert Space
• Authors: M. Hadi Sepanj, Benyamin Ghojogh, Paul Fieguth,
• Abstract summary: Kernel VICReg is a self-supervised learning framework that lifts the VICReg objective into a Reproducing Kernel Hilbert Space.<n>We demonstrate that Kernel VICReg not only avoids representational collapse but also improves performance on tasks with complex or small-scale data.
• Score: 0.15293427903448018
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Self-supervised learning (SSL) has emerged as a powerful paradigm for representation learning by optimizing geometric objectives--such as invariance to augmentations, variance preservation, and feature decorrelation--without requiring labels. However, most existing methods operate in Euclidean space, limiting their ability to capture nonlinear dependencies and geometric structures. In this work, we propose Kernel VICReg, a novel self-supervised learning framework that lifts the VICReg objective into a Reproducing Kernel Hilbert Space (RKHS). By kernelizing each term of the loss-variance, invariance, and covariance--we obtain a general formulation that operates on double-centered kernel matrices and Hilbert-Schmidt norms, enabling nonlinear feature learning without explicit mappings. We demonstrate that Kernel VICReg not only avoids representational collapse but also improves performance on tasks with complex or small-scale data. Empirical evaluations across MNIST, CIFAR-10, STL-10, TinyImageNet, and ImageNet100 show consistent gains over Euclidean VICReg, with particularly strong improvements on datasets where nonlinear structures are prominent. UMAP visualizations further confirm that kernel-based embeddings exhibit better isometry and class separation. Our results suggest that kernelizing SSL objectives is a promising direction for bridging classical kernel methods with modern representation learning.

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