arXiv:2606.00542v1 Announce Type: new Abstract: 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 dis
The paper builds on recent work showing Bregman divergences can be used for Kronecker-factored approximations in optimizers, addressing a key unanswered question regarding their role when exact Kronecker-factoring is absent.
Improved understanding and optimization of AI models directly impacts the efficiency, speed, and cost of developing and deploying advanced AI, which is crucial for maintaining competitive advantage.
This research refines the theoretical underpinnings of Kronecker-factored optimizers, potentially leading to more robust and performant AI training algorithms, particularly for large models.
- · AI researchers
- · Deep learning practitioners
- · Cloud AI providers
- · Developers of large language models
- · Inefficient AI training methods
- · Developers slow to adopt new optimization techniques
More efficient training of large-scale AI models becomes possible, reducing computational costs and time.
Faster AI development cycles lead to quicker iteration and deployment of new AI applications across various industries.
The proliferation of more capable and efficiently trained AI systems could accelerate broader technological shifts and economic restructuring.
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Read at arXiv cs.LG