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News/How Inefficient Is Natural Gradient Descent? From Exact Optimality to \Theta ( \sqrt{ \log d } ) Divergence
arxiv
PublishedOctober 7, 2026 at 4:00 AM

How Inefficient Is Natural Gradient Descent? From Exact Optimality to \Theta ( \sqrt{ \log d } ) Divergence

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arXiv:2610.07228v1 Announce Type: cross Abstract: Natural gradient descent (NGD) underlies common methods in ML. For dually flat families, idealized NGD on the forward Kullback--Leibler objective follows the mixture geodesic which is often longer than the shortest Fisher--Rao path. We quantify this

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