Pro-KLShampoo projects KL-Shampoo preconditioners to a spike-and-flat parametric form on an r-dimensional subspace and recovers the full algebraic preconditioner via orthogonalization, outperforming KL-Shampoo on GPT-2 and LLaMA pre-training scales.
SOAP [Vyas et al., 2024] improved its practical efficiency by running Adam in Shampoo’s eigenbasis
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Pro-KLShampoo: Projected KL-Shampoo with Whitening Recovered by Orthogonalization
Pro-KLShampoo projects KL-Shampoo preconditioners to a spike-and-flat parametric form on an r-dimensional subspace and recovers the full algebraic preconditioner via orthogonalization, outperforming KL-Shampoo on GPT-2 and LLaMA pre-training scales.