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In this paper, the robustness and accuracy of the deep neural network (DNN)was enhanced by introducing the $L_{2,\infty}$ normalization of the weightmatrices of the DNN with Relu as the activation function. It is proved that the$L_{2,\infty}$ normalization leads to large dihedral angles between twoadjacent faces of the polyhedron graph of the DNN function and hence smootherDNN functions, which reduces over-fitting. A measure is proposed for therobustness of a classification DNN, which is the average radius of the maximalrobust spheres with the sample data as centers. A lower bound for therobustness measure is given in terms of the $L_{2,\infty}$ norm. Finally, anupper 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 andaccuracy.

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