Rethinking Bregman Divergences in Kronecker-Factored Optimizers
Shampoo-style optimizers approximate gradient covariance matrices using Kronecker-factored structures. Recent work~\cite{lin2026understanding} showed that such approximations can be viewed as projections under Bregman matrix divergences, leading to different Kronecker-factored preconditioners. However, it remains unclear what role the choice of divergence plays when the covariance is not exactly Kronecker-factored. We study this question through the spectrum of the covariance matrix. We show that Frobenius, von Neumann, and LogDet divergences distribute the unavoidable Kronecker approximation error differently across the covariance spectrum. We further show that their Kronecker factors ar...
| Authors | Bing Liu, Wenjie Zhou, Chengcheng Zhao |
|---|---|
| Primary category | cs.LG |
| Published | 30 May 2026 |
| Last updated at source | 2 June 2026 |
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