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AI Research
arXiv CS.AI·Jun 12·5 min read
Different Layers, Different Manifolds: Module-Wise Weight-Space Geometry in Transformer Optimization
TL;DR
Neural network optimization often applies uniform constraints across weight matrices, which may not be ideal. This study introduces Manifold Muon, analyzing the impact of different geometric constraints on transformer modules, specifically Stiefel and DGram geometries.
✦ Why It Matters
Engineers should consider module-specific geometric constraints to enhance transformer optimization and performance.
Key Takeaways
- Experiment with Stiefel geometry for attention layers.
- Use DGram geometry for MLP layers to enhance performance.
- Monitor singular value growth in attention weights.
- Adopt module-specific optimization strategies for transformers.
How It Works
The study introduces Manifold Muon, a method for analyzing weight-space geometry in transformers. It evaluates the performance of different geometric constraints—Stiefel and DGram—on attention and MLP layers.
Stiefel geometry helps maintain orthogonality in attention weights, while DGram geometry is suited for MLP layers, leading to better optimization outcomes.