Combining PSGD-Kron and KL-Shampoo yields an optimizer with no eig/inverse/solve

YouJiacheng · x · 2026-08-26

An interesting optimizer idea (work done by GPT Pro): combine PSGD-Kron's Σ^{-1/2} multiplicative update (Σ=E[ggᵀ]) with KL-Shampoo's KL objective, yielding an optimizer that needs no eigendecomposition, no matrix inversion, and no linear solves.

The method applies multiplicative updates to P with the objective KL(N(0, Σ), N(0, P⁻²)) — a promising route to cheaper second-order optimization.

Related event: GPT Pro Combines PSGD-Kron and KL-Shampoo into Decomposition-Free Optimizer(4 posts)→

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