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

Askar Tsyganov, Sergey Samsonov, Maxim Rakhuba

Keywords: matrix two-to-infinity norm, randomized matrix norm estimation

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++ modification. We provide sample 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.

Submission Number: 4