arXiv:2606.15268v1 Announce Type: new Abstract: Schatten-$\infty$ based optimizers such as Muon have shown promising empirical performance, but there remains seemingly conflicting observations regarding whether they are beneficial. We resolve this conflict by showing that the conclusion is regime dependent. Even when the objective is smooth in the Schatten-$\infty$ geometry, smaller Schatten-$p$ geometries can be optimal, specifically in the low-dimensional regime, which we show includes Chinchilla scaling. This conclusion follows from a new noise-robust acceleration result for the SODA framew
This paper offers a new theoretical framework for understanding the optimal choice of Schatten-p norms in deep learning optimization, driven by recent empirical observations of techniques like Muon.
Understanding the fundamental mathematical properties of optimization algorithms directly impacts the efficiency, performance, and scaling laws of future AI models.
This research refines the theoretical understanding of deep learning optimizers, suggesting that optimal techniques are regime-dependent, which could lead to more targeted and efficient model development.
- · AI researchers
- · Deep learning practitioners
- · AI model developers
- · Inefficient AI optimization techniques
- · Companies relying on sub-optimal deep learning frameworks
Improved theoretical understanding of deep learning's mathematical foundations.
Development of more efficient and context-aware AI optimization algorithms.
Acceleration of AI model training and potentially reduced computational costs for specific tasks, impacting the compute supply chain.
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