Iterative Orthogonalization Scaling Laws

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Main Author:	Selvaraj, Devan
Format:	Preprint
Published:	2025
Subjects:	Machine Learning 68T07
Online Access:	Acceder al recurso
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author	Selvaraj, Devan
author_facet	Selvaraj, Devan
contents	The muon optimizer has picked up much attention as of late as a possible replacement to the seemingly omnipresent Adam optimizer. Recently, care has been taken to document the scaling laws of hyper-parameters under muon such as weight decay and learning rate. However, at much larger scales the iterative orthogonalization procedure present in muon may suffer a possible issue as the singular values of random matrices shrink with scale. This paper shows this scaling behavior theoretically and empirically on random matrices but does not suggest what to do about it.
format	Preprint
id	arxiv_https___arxiv_org_abs_2505_04005
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Iterative Orthogonalization Scaling Laws Selvaraj, Devan Machine Learning 68T07 The muon optimizer has picked up much attention as of late as a possible replacement to the seemingly omnipresent Adam optimizer. Recently, care has been taken to document the scaling laws of hyper-parameters under muon such as weight decay and learning rate. However, at much larger scales the iterative orthogonalization procedure present in muon may suffer a possible issue as the singular values of random matrices shrink with scale. This paper shows this scaling behavior theoretically and empirically on random matrices but does not suggest what to do about it.
title	Iterative Orthogonalization Scaling Laws
topic	Machine Learning 68T07
url	https://arxiv.org/abs/2505.04005

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