Uniform Sampling from High-dimensional Spectral Norm Balls

arXiv:2606.24134v1 Announce Type: cross Abstract: Motivated by an application in machine learning optimization, this paper focuses on the challenges of sampling a matrix uniformly from the unit spectral norm ball. It is proven that all singular values of sampled matrices converge to 1 almost surely as the matrix dimensions increase. This result provides the theoretical justification for a proposed simple sampling method applicable for large dimension sizes matching matrices found in modern large language models. Experimental results demonstrate both the convergence of the singular values, as w

Source: arXiv cs.LG — read the full report at the original publisher.

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