Computer Science > Machine Learning
arXiv:2206.07085 (cs)
[Submitted on 14 Jun 2022 (v1), last revised 17 Jan 2023 (this version, v3)]
Title:Understanding the Generalization Benefit of Normalization Layers: Sharpness Reduction
View a PDF of the paper titled Understanding the Generalization Benefit of Normalization Layers: Sharpness Reduction, by Kaifeng Lyu and 2 other authors
View PDFAbstract:Normalization layers (e.g., Batch Normalization, Layer Normalization) were introduced to help with optimization difficulties in very deep nets, but they clearly also help generalization, even in not-so-deep nets. Motivated by the long-held belief that flatter minima lead to better generalization, this paper gives mathematical analysis and supporting experiments suggesting that normalization (together with accompanying weight-decay) encourages GD to reduce the sharpness of loss surface. Here "sharpness" is carefully defined given that the loss is scale-invariant, a known consequence of normalization. Specifically, for a fairly broad class of neural nets with normalization, our theory explains how GD with a finite learning rate enters the so-called Edge of Stability (EoS) regime, and characterizes the trajectory of GD in this regime via a continuous sharpness-reduction flow.
| Comments: | 76 pages, many figures; NeurIPS 2022 camera-ready version; fixes minor typos |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2206.07085 [cs.LG] |
| (orarXiv:2206.07085v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2206.07085 arXiv-issued DOI via DataCite |
Submission history
From: Kaifeng Lyu [view email][v1] Tue, 14 Jun 2022 18:19:05 UTC (6,756 KB)
[v2] Tue, 25 Oct 2022 06:13:12 UTC (5,271 KB)
[v3] Tue, 17 Jan 2023 03:58:13 UTC (5,243 KB)
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View a PDF of the paper titled Understanding the Generalization Benefit of Normalization Layers: Sharpness Reduction, by Kaifeng Lyu and 2 other authors
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