Schatten-p Norms: Optimal Use in Deep Learning Depends on Regime
Key takeaways
- The optimal Schatten-p norm for deep learning optimization is regime-dependent, not universally fixed.
- Smaller Schatten-p geometries can be superior in low-dimensional settings, including Chinchilla scaling.
- The analysis provides insights into why Schatten-infinity optimizers like Muon don't require warm-up and favor large batches.
- A new batch size scaling rule for arbitrary p-values is introduced, guiding optimizer selection.
Who benefits
Summary
Research clarifies the optimal application of Schatten-p norms in deep learning, showing that their benefits are regime-dependent. While Schatten-infinity optimizers like Muon perform well, smaller Schatten-p geometries can be superior in low-dimensional settings, including those relevant to Chinchilla scaling.
Why it matters
Deep learning practitioners and researchers can gain a clearer understanding of how to select appropriate optimization techniques, potentially leading to more efficient training, better model performance, and optimized resource utilization, especially when dealing with different model scales and data dimensions.
How to implement this in your domain
- 1Evaluate the dimensionality of your deep learning models and datasets to determine the most suitable Schatten-p norm for optimization.
- 2Experiment with Schatten-p based optimizers, considering smaller p-values for low-dimensional regimes and larger p-values for high-dimensional scenarios.
- 3Adjust batch sizes according to the newly proposed scaling rules for Schatten-p norms to optimize training efficiency.
- 4Investigate the implications of these findings for specific model architectures and scaling laws, such as Chinchilla scaling.
Original post by Thomas Pethick
"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 con…"
View on XOriginally posted by Thomas Pethick on X · view source
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