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In this work, we study the implications of the implicit bias of gradient flowon generalization and adversarial robustness in ReLU networks. We focus on asetting where the data consists of clusters and the correlations betweencluster means are small, and show that in two-layer ReLU networks gradient flowis biased towards solutions that generalize well, but are highly vulnerable toadversarial examples. Our results hold even in cases where the network has manymore parameters than training examples. Despite the potential for harmfuloverfitting in such overparameterized settings, we prove that the implicit biasof gradient flow prevents it. However, the implicit bias also leads tonon-robust solutions (susceptible to small adversarial $\ell_2$-perturbations),even though robust networks that fit the data exist.

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