Matrix-Free Two-to-Infinity and One-to-Two Norms Estimation

Authors: Askar Tsyganov, Evgeny Frolov, Sergey Samsonov, Maxim Rakhuba
Published: 2025-08-06

Source: https://arxiv.org/abs/2508.04444

PDF: https://arxiv.org/pdf/2508.04444

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性能評価手法 深層学習 ロバスト最適化

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Abstract

In this paper, we propose new randomized algorithms for estimating the two-to-infinity and one-to-two norms in a matrix-free setting, using only matrix-vector multiplications. Our methods are based on appropriate modifications of Hutchinson’s diagonal estimator and its Hutch++ version. We provide oracle complexity bounds for both modifications. We further illustrate the practical utility of our algorithms for Jacobian-based regularization in deep neural network training on image classification tasks. We also demonstrate that our methodology can be applied to mitigate the effect of adversarial attacks in the domain of recommender systems.