The Devil is in the Condition Numbers: Why is GLU Better than non-GLU Structure?
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Computer Science > Machine Learning
Title:The Devil is in the Condition Numbers: Why is GLU Better than non-GLU Structure?
Abstract:Gated Linear Units (GLU) and their variants are widely adopted in modern open-source large language model architectures and consistently outperform their non-gated counterparts, yet the underlying reasons for this advantage remain unclear. In this work, we study GLU by analyzing two-layer networks in the neural tangent kernel (NTK) regime. Our analysis reveals that the GLU structure reshapes the NTK spectrum, leading to a smaller condition number and a more compact eigenvalue distribution. Building on this finding, we further analyze the resulting training dynamics and show how the reshaped spectrum leads to faster convergence of GLU models, including a characteristic loss-crossing phenomenon observed between GLU and non-GLU models. Finally, we empirically observe that GLU has limited impact in reducing the generalization gap on various models, including ViT and GPT-2, suggesting that its primary benefit lies in accelerating optimization rather than reducing the generalization gap.
| Comments: | Accepted by ICML 2026 |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.20749 [cs.LG] |
| (or arXiv:2605.20749v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.20749
arXiv-issued DOI via DataCite (pending registration)
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