Reparametrizing Shampoo and SOAP for Subspace Basis Updates and BFloat16 Storage
Shampoo-based methods, such as KL-Shampoo and SOAP, have demonstrated strong performance in training neural networks and rely on QR decomposition. Because existing QR implementations require single-precision (FP32) arithmetic and remain computationally expensive, these methods become time- and memory-intensive when their preconditioning matrices are large. Moreover, using BFloat16 (BFP16) storage to reduce memory usage can degrade the performance of Shampoo-based methods. We propose a reparametrization of the preconditioner that supports BFP16 storage and forms a complete basis by combining updated basis vectors with unchanged ones. By updating only part of the basis through QR decomposit...
| Authors | Alan Milligan, Zikun Xu, Simon Lacoste-Julien et al. |
|---|---|
| Primary category | cs.LG |
| Published | 25 May 2026 |
| Last updated at source | 25 May 2026 |
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