Understanding Robustness in Teacher-Student Setting: A New Perspective

Adversarial examples have appeared as a ubiquitous property of machine learning models where bounded adversarial perturbation could mislead the models to make arbitrarily incorrect predictions. Such examples provide a way to assess the robustness of machine learning models as well as a proxy for understanding the model training process. There have been extensive studies trying to explain the existence of adversarial examples and provide ways to improve model robustness, e.g., adversarial training. Different from prior works that mostly focus on models trained on datasets with predefined labels, we leverage the teacher-student framework and assume a teacher model, or oracle, to provide the labels for given instances. In this setting, we extend Tian (2019) in the case of low-rank input data, and show that student specialization (the trained student neuron is highly correlated with certain teacher neuron at the same layer) still happens within the input subspace, but the teacher and student nodes could differ wildly out of the data subspace, which we conjecture leads to adversarial examples. Extensive experiments show that student specialization correlates strongly with model robustness in different scenarios, including students trained via standard training, adversarial training, confidence-calibrated adversarial training, and training with the robust feature dataset. Our studies could shed light on the future exploration of adversarial examples, and potential approaches to enhance model robustness via principled data augmentation. Proceedings of the 24 International Conference on Artificial Intelligence and Statistics (AISTATS) 2021, San Diego, California, USA. PMLR: Volume 130. Copyright 2021 by the author(s).