The Double-Edged Sword of Implicit Bias: Generalization vs. Robustness in ReLU Networks

Understand

In this work, we study the implications of the implicit bias of gradient flow on generalization and adversarial robustness in ReLU networks.

• We focus on a setting where the data consists of clusters and the correlations between cluster means are small, and show that in two-layer ReLU networks gradient flow is biased towards solutions that generalize well, but are highly vulnerable to adversarial examples.
• Our results hold even in cases where the network has many more parameters than training examples.
• Despite the potential for harmful overfitting in such overparameterized settings, we prove that the implicit bias of gradient flow prevents it.