The top-r gradient subspace GaLore refreshes is largely non-identifiable noise beyond ~39 of 128 directions; the apparent rotation is estimator noise, and optimizer state should be transported rather than carried blindly.
On some properties of orthogonal Weingarten functions.Journal of Mathematical Physics, 50(11):113516,
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No Subspace to Track: Non-Identifiability and Optimizer State in Low-Rank Training
The top-r gradient subspace GaLore refreshes is largely non-identifiable noise beyond ~39 of 128 directions; the apparent rotation is estimator noise, and optimizer state should be transported rather than carried blindly.