An Empirical Study on Regularization of Deep Neural Networks by Local Rademacher Complexity

Yingzhen Yang, Jiahui Yu, Xingjian Li, Jun Huan, Thomas S. Huang

Regularization of Deep Neural Networks (DNNs) for the sake of improving their generalization capability is important and challenging. The development in this line benefits theoretical foundation of DNNs and promotes their usability in different areas of artificial intelligence. In this paper, we investigate the role of Rademacher complexity in improving generalization of DNNs and propose a novel regularizer rooted in Local Rademacher Complexity (LRC). While Rademacher complexity is well known as a distribution-free complexity measure of function class that help boost generalization of statistical learning methods, extensive study shows that LRC, its counterpart focusing on a restricted function class, leads to sharper convergence rates and potential better generalization given finite training sample. Our LRC based regularizer is developed by estimating the complexity of the function class centered at the minimizer of the empirical loss of DNNs. Experiments on various types of network architecture demonstrate the effectiveness of LRC regularization in improving generalization. Moreover, our method features the state-of-the-art result on the CIFAR-$10$ dataset with network architecture found by neural architecture search.

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