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Deep neural networks are easily attacked by imperceptible perturbation.Presently, adversarial training (AT) is the most effective method to enhancethe robustness of the model against adversarial examples. However, becauseadversarial training solved a min-max value problem, in comparison with naturaltraining, the robustness and generalization are contradictory, i.e., therobustness improvement of the model will decrease the generalization of themodel. To address this issue, in this paper, a new concept, namely confidencethreshold (CT), is introduced and the reducing of the confidence threshold,known as confidence threshold reduction (CTR), is proven to improve both thegeneralization and robustness of the model. Specifically, to reduce the CT fornatural training (i.e., for natural training with CTR), we propose amask-guided divergence loss function (MDL) consisting of a cross-entropy lossterm and an orthogonal term. The empirical and theoretical analysisdemonstrates that the MDL loss improves the robustness and generalization ofthe model simultaneously for natural training. However, the model robustnessimprovement of natural training with CTR is not comparable to that ofadversarial training. Therefore, for adversarial training, we propose astandard deviation loss function (STD), which minimizes the difference in theprobabilities of the wrong categories, to reduce the CT by being integratedinto the loss function of adversarial training. The empirical and theoreticalanalysis demonstrates that the STD based loss function can further improve therobustness of the adversarially trained model on basis of guaranteeing thechangeless or slight improvement of the natural accuracy.

Improving the Robustness and Generalization of Deep Neural Network with Confidence Threshold Reduction