For Better or For Worse? Learning Minimum Variance Features With Label Augmentation

Data augmentation has been pivotal in successfully training deep learning models on classification tasks over the past decade. An important subclass of data augmentation techniques - which includes both label smoothing and Mixup - involves modifying not only the input data but also the input label during model training. In this work, we analyze the role played by the label augmentation aspect of such methods. We prove that linear models on linearly separable data trained with label augmentation learn only the minimum variance features in the data, while standard training (which includes weight decay) can learn higher variance features. An important consequence of our results is negative: label smoothing and Mixup can be less robust to adversarial perturbations of the training data when compared to standard training. We verify that our theory reflects practice via a range of experiments on synthetic data and image classification benchmarks.