On the (Non-)Robustness of Two-Layer Neural Networks in Different Learning Regimes
This work addresses the problem of adversarial vulnerability in neural networks for researchers and practitioners, providing theoretical insights into robustness tradeoffs, though it is incremental in focusing on specific scenarios.
The paper investigates adversarial robustness in two-layer neural networks across different learning regimes, revealing a tradeoff where improving test error can worsen robustness and vice versa, with linearized lazy training regimes further reducing robustness due to initialization scaling.
Neural networks are known to be highly sensitive to adversarial examples. These may arise due to different factors, such as random initialization, or spurious correlations in the learning problem. To better understand these factors, we provide a precise study of the adversarial robustness in different scenarios, from initialization to the end of training in different regimes, as well as intermediate scenarios, where initialization still plays a role due to "lazy" training. We consider over-parameterized networks in high dimensions with quadratic targets and infinite samples. Our analysis allows us to identify new tradeoffs between approximation (as measured via test error) and robustness, whereby robustness can only get worse when test error improves, and vice versa. We also show how linearized lazy training regimes can worsen robustness, due to improperly scaled random initialization. Our theoretical results are illustrated with numerical experiments.