We study Label-Smoothing as a means for improving adversarial robustness of supervised deep-learning models. After establishing a thorough and unified framework, we propose several novel Label-Smoothing methods: adversarial, Boltzmann and second-best Label-Smoothing methods. On various datasets (MNIST, CI-FAR10, SVHN) and models (linear models, MLPs, LeNet, ResNet), we show that these methods improve adversarial robustness against a variety of attacks (FGSM, BIM, DeepFool, Carlini-Wargner) by better taking account of the dataset geometry. These proposed Label-Smoothing methods have two main advantages: they can be implemented as a modified cross-entropy loss, thus do not require any modifications of the network architecture nor do they lead to increased training times, and they improve both standard and adversarial accuracy.

Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In general, we show that mean and standard deviation are not always the most appropriate choice for the centering and scaling procedure within the BN transformation, particularly if ReLU follows the normalization step. We present a Generalized Batch Normalization (GBN) transformation, which can utilize a variety of alternative deviation measures for scaling and statistics for centering, choices which naturally arise from the theory of generalized deviation measures and risk theory in general. When used in conjunction with the ReLU non-linearity, the underlying risk theory suggests natural, arguably optimal choices for the deviation measure and statistic. Utilizing the suggested deviation measure and statistic, we show experimentally that training is accelerated more so than with conventional BN, often with improved error rate as well. Overall, we propose a more flexible BN transformation supported by a complimentary theoretical framework that can potentially guide design choices.