Improving Generalization of Deep Neural Networks by Leveraging Margin Distribution
This work addresses generalization issues for deep learning practitioners, offering a novel theoretical and practical approach, though it is incremental in building on existing margin theory.
The paper tackles the problem of improving generalization in deep neural networks by focusing on the entire margin distribution rather than just the minimum margin, proving a new generalization bound and demonstrating through experiments that optimizing the margin ratio reduces the generalization gap.
Recent research has used margin theory to analyze the generalization performance for deep neural networks (DNNs). The existed results are almost based on the spectrally-normalized minimum margin. However, optimizing the minimum margin ignores a mass of information about the entire margin distribution, which is crucial to generalization performance. In this paper, we prove a generalization upper bound dominated by the statistics of the entire margin distribution. Compared with the minimum margin bounds, our bound highlights an important measure for controlling the complexity, which is the ratio of the margin standard deviation to the expected margin. We utilize a convex margin distribution loss function on the deep neural networks to validate our theoretical results by optimizing the margin ratio. Experiments and visualizations confirm the effectiveness of our approach and the correlation between generalization gap and margin ratio.