Researchers spot online PCA cost equals KL-shampoo objective in optimizer discussion

_arohan_ · x · 2026-09-01

@YouJiacheng observes that the online PCA cost in appendix H.3 of a paper is exactly the KL objective in KL-shampoo, though the original didn't frame it as a KL divergence, and asks whether this cost is known in online PCA literature. @HessianFree says these formulations were sketched on a whiteboard with Xilin years ago, with more variants never written down, and they may help when gradients are noisy or low-rank.

Related event: PSGD's Objective Shown Equivalent to KL-Shampoo, Sparking Optimizer Discussion(6 posts)→

Original post →

More from Research

Research channel →