![[2511.00958] The Hidden Power of Normalization Layers in Neural Networks: Exponential Capacity Control](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-fb.png){kind=logo}
[2511.00958] The Hidden Power of Normalization Layers in Neural Networks: Exponential Capacity Control
Summary
This paper explores the theoretical framework behind normalization layers in neural networks, demonstrating their role in controlling capacity and enhancing optimization and generalization.
Why It Matters
Understanding the theoretical underpinnings of normalization layers is crucial for improving neural network design and performance. This research provides insights that can lead to better training dynamics and generalization in AI systems, which is vital for advancing machine learning applications.
Key Takeaways
- Normalization layers stabilize training dynamics in neural networks.
- They reduce the Lipschitz constant exponentially, improving optimization.
- Inserting normalization layers enhances generalization on unseen data.
- The paper provides a theoretical explanation for the empirical success of normalization methods.
- Understanding these mechanisms can guide future neural network architectures.
Computer Science > Machine Learning arXiv:2511.00958 (cs) [Submitted on 2 Nov 2025 (v1), last revised 22 Feb 2026 (this version, v2)] Title:The Hidden Power of Normalization Layers in Neural Networks: Exponential Capacity Control Authors:Khoat Than View a PDF of the paper titled The Hidden Power of Normalization Layers in Neural Networks: Exponential Capacity Control, by Khoat Than View PDF HTML (experimental) Abstract:Normalization layers are critical components of modern AI systems, such as ChatGPT, Gemini, DeepSeek, etc. Empirically, they are known to stabilize training dynamics and improve generalization ability. However, the underlying theoretical mechanism by which normalization layers contribute to both optimization and generalization remains largely unexplained, especially when using many normalization layers in a deep neural network (DNN). In this work, we develop a theoretical framework that elucidates the role of normalization through the lens of capacity control. We prove that an unnormalized DNN can exhibit exponentially large Lipschitz constants with respect to either its parameters or inputs, implying excessive functional capacity and potential overfitting. Such bad DNNs are uncountably many. In contrast, the insertion of normalization layers provably can reduce the Lipschitz constant at an exponential rate in the number of normalization layers. This exponential reduction yields two fundamental consequences: (1) it smooths the loss landscape at an exponentia...
