Different Layers, Different Manifolds: Module-Wise Weight-Space Geometry in Transformer Optimization
arXiv:2606.13276v1 Announce Type: cross Abstract: Weight-space geometry plays a central role in neural network optimization, yet manifold constraints are often applied uniformly across all weight matrices. In this work, we ask whether different transformer modules prefer different manifold geometries. We study Manifold Muon for GPT-2 pretraining and compare layer-wise assignments of Stiefel and DGram constraints across attention and MLP blocks. Our results show a clear asymmetry: constraining attention layers with Stiefel geometry while assigning DGram geometry to MLP layers gives the best per
The continuous drive for more efficient and performant transformer models necessitates deeper understanding of their underlying optimization landscapes, pushing research into architectural nuances like layer-wise geometry.
This research provides a more granular understanding of transformer optimization, which could lead to significant improvements in training efficiency, model performance, and reduced computational costs for large AI systems.
The understanding that different transformer layers might benefit from distinct optimization geometries challenges the uniform application of constraints, opening new avenues for architectural design specific to deep learning models.
- · AI model developers
- · Cloud providers
- · AI research institutions
- · Inefficient AI training methods
Improved transformer training algorithms that are specifically tailored to the unique properties of different model layers.
Faster development cycles for large language models and other transformer-based AI, leading to more frequent and capable model updates.
Reduced hardware requirements for achieving state-of-the-art performance due to optimization efficiencies, possibly democratizing access to powerful AI models.
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Read at arXiv cs.AI