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News/Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors
arxiv
PublishedJuly 20, 2026 at 4:00 AM
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Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors

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arXiv:2606.25971v2 Announce Type: replace Abstract: Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object. Yet every weight matrix carries two distinct quantities -- a \emph{magnitude} and a \emph{direction} -- and all optimizers

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