How Bregman Divergences Shape Shampoo
Understanding the principles behind Shampoo has recently guided the development of more effective neural network optimizers. These methods learn a preconditioner by optimizing the Frobenius or Kullback-Leibler (KL) divergence against the gradient second moment. In this work, we investigate how the choice of divergence shapes preconditioning, which remains unclear and blocks further improvements. To do so, we develop a unified Bregman divergence framework that connects all popular divergences, allowing us to study them jointly. Through empirical spectral analysis of gradient second moments, we examine how divergence choice shapes Kronecker approximation and interacts with finite-sample err...
| Authors | Bing Liu, Wenjie Zhou, Chengcheng Zhao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 6 October 2026 |
| Last updated at source | 6 October 2026 |
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