arXiv:2606.14560v1 Announce Type: cross Abstract: Non-Euclidean optimisation methods with matrix-valued updates, such as Muon and Scion, have recently shown strong empirical performance for training Transformer models, yet their theoretical advantages over Euclidean methods remain poorly understood. We address this gap in the heavy-tailed non-convex regime, where stochastic gradients have bounded $p$-th central moments, $p \in (1,2]$. We show that certain non-Euclidean methods achieve optimal sample complexity under stronger stationarity measures, while Euclidean methods incur additional dimen
The rapid development and widespread adoption of large transformer models have created an urgent need for more efficient and robust optimization methods.
This research provides theoretical grounding for observed empirical successes in AI optimization, which can accelerate future model development and deployment.
The understanding of why certain non-Euclidean optimization methods outperform traditional methods in specific conditions is now theoretically justified, guiding further research and application.
- · AI researchers
- · Deep learning developers
- · Cloud computing providers
- · AI start-ups
- · Developers solely relying on Euclidean optimization
Improved training efficiency and performance for transformer-based AI models.
Faster innovation cycles in AI research and more powerful AI applications becoming feasible.
Increased competition and potential consolidation in the AI development landscape due to enhanced capabilities.
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Read at arXiv cs.LG