# FroSSL: Frobenius Norm Minimization for Efficient Multiview Self-Supervised Learning Source: [FroSSL: Frobenius Norm Minimization for Efficient Multiview Self-Supervised Learning]() Collection index: [llms.txt]() Data updated: 2025-10-26T03:08:39.928Z Authors: Oscar Skean, Aayush Dhakal, Nathan Jacobs, Luis Gonzalo Sanchez Giraldo Published: 2023-10-04T15:42:23.000Z ## Abstract Self-supervised learning (SSL) is a popular paradigm for representation learning. Recent multiview methods can be classified as sample-contrastive, dimension-contrastive, or asymmetric network-based, with each family having its own approach to avoiding informational collapse. While these families converge to solutions of similar quality, it can be empirically shown that some methods are epoch-inefficient and require longer training to reach a target performance. Two main approaches to improving efficiency are covariance eigenvalue regularization and using more views. However, these two approaches are difficult to combine due to the computational complexity of computing eigenvalues. We present the objective function FroSSL which reconciles both approaches while avoiding eigendecomposition entirely. FroSSL works by minimizing covariance Frobenius norms to avoid collapse and minimizing mean-squared error to achieve augmentation invariance. We show that FroSSL reaches competitive accuracies more quickly than any other SSL method and provide theoretical and empirical support that this faster convergence is due to how FroSSL affects the eigenvalues of the embedding covariance matrices. We also show that FroSSL learns competitive representations on linear probe evaluation when used to train a ResNet-18 on several datasets, including STL-10, Tiny ImageNet, and ImageNet-100. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()