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.
Summing over i and minimizing over ˆvyields (5); substitutingˆv=λgives the canonical-carry cost
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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.