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

arXiv: https://arxiv.org/abs/2509.07289 · HTML: https://mlsanity.com/paper/2509.07289/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [An Empirical Study of Graph Contrastive Learning](https://mlsanity.com/paper/2109.01116/) (2021)
- [Self-Supervised Learning with Kernel Dependence Maximization](https://mlsanity.com/paper/2106.08320/) (2021)
- [Eigenvalue and Generalized Eigenvalue Problems: Tutorial](https://mlsanity.com/paper/1903.11240/) (2019)
- [On the Stepwise Nature of Self-Supervised Learning](https://mlsanity.com/paper/2303.15438/) (2023)
- [A Comprehensive Survey on Spectral Clustering with Graph Structure Learning](https://mlsanity.com/paper/2501.13597/) (2025)
- [Pseudo-keypoint RKHS Learning for Self-supervised 6DoF Pose Estimation](https://mlsanity.com/paper/2311.09500/) (2023)
- [Self-Supervised Learning Using Nonlinear Dependence](https://mlsanity.com/paper/2501.18875/) (2025)
- [SinSim: Sinkhorn-Regularized SimCLR](https://mlsanity.com/paper/2502.10478/) (2025)

## Built on by (most cited first, 3 of 3)

- [Self-Supervised Learning by Curvature Alignment](https://mlsanity.com/paper/2511.17426/) (2025)
- [Joint-Embedding Predictive Architecture for Sensor-based Activity Recognition](https://mlsanity.com/paper/2607.16350/) (2026)
- [On the Geometry of Multimodal Saturation: Riemannian VICReg](https://mlsanity.com/paper/2610.06096/) (2026)

## Abstract (arXiv)

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 pulls 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 mitigates the risk of representational collapse under challenging conditions and improves performance on datasets exhibiting nonlinear structure or limited sample regimes. 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 are provided only as a qualitative illustration of embedding geometry and are not used as a calibration or statistical validation. Our results suggest that kernelizing SSL objectives is a promising direction for bridging classical kernel methods with modern representation learning.