Generalization Error Analysis of Neural networks with Gradient Based Regularization

• URL: http://arxiv.org/abs/2107.02797v1
• Date: Tue, 6 Jul 2021 07:54:36 GMT
• Title: Generalization Error Analysis of Neural networks with Gradient Based Regularization
• Authors: Lingfeng Li and Xue-Cheng Tai and Jiang Yang
• Abstract summary: We study gradient-based regularization methods for neural networks. We introduce a general framework to analyze the generalization error of regularized networks. We conduct some experiments on the image classification tasks to show that gradient-based methods can significantly improve the generalization ability.
• Score: 2.7286395031146062
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve some partial differential equations, mostly in high dimensions in practical applications. In this work, we introduce a general framework to analyze the generalization error of regularized networks. The error estimate relies on two assumptions on the approximation error and the quadrature error. Moreover, we conduct some experiments on the image classification tasks to show that gradient-based methods can significantly improve the generalization ability and adversarial robustness of neural networks. A graphical extension of the gradient-based methods are also considered in the experiments.

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