Uniform Sampling from High-dimensional Spectral Norm Balls
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Mathematics > Probability
Title:Uniform Sampling from High-dimensional Spectral Norm Balls
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 well as the exact and proposed approximate sampling methods.
| Subjects: | Probability (math.PR); Machine Learning (cs.LG) |
| Cite as: | arXiv:2606.24134 [math.PR] |
| (or arXiv:2606.24134v1 [math.PR] for this version) | |
| https://doi.org/10.48550/arXiv.2606.24134
arXiv-issued DOI via DataCite (pending registration)
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