Improve the Robustness and Accuracy of Deep Neural Network with $L_{2,\infty}$ Normalization

• URL: http://arxiv.org/abs/2010.04912v1
• Date: Sat, 10 Oct 2020 05:45:45 GMT
• Title: Improve the Robustness and Accuracy of Deep Neural Network with $L_{2,\infty}$ Normalization
• Authors: Lijia Yu and Xiao-Shan Gao
• Abstract summary: The robustness and accuracy of the deep neural network (DNN) was enhanced by introducing the $L_2,infty$ normalization. It is proved that the $L_2,infty$ normalization leads to large dihedral angles between two adjacent faces of the polyhedron graph of the DNN function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, the robustness and accuracy of the deep neural network (DNN) was enhanced by introducing the $L_{2,\infty}$ normalization of the weight matrices of the DNN with Relu as the activation function. It is proved that the $L_{2,\infty}$ normalization leads to large dihedral angles between two adjacent faces of the polyhedron graph of the DNN function and hence smoother DNN functions, which reduces over-fitting. A measure is proposed for the robustness of a classification DNN, which is the average radius of the maximal robust spheres with the sample data as centers. A lower bound for the robustness measure is given in terms of the $L_{2,\infty}$ norm. Finally, an upper bound for the Rademacher complexity of DNN with $L_{2,\infty}$ normalization is given. An algorithm is given to train a DNN with the $L_{2,\infty}$ normalization and experimental results are used to show that the $L_{2,\infty}$ normalization is effective to improve the robustness and accuracy.

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