Title: Robustness Guarantees for Adversarially Trained Neural Networks. Abstract: We study robust adversarial training of two-layer neural networks with Leaky ReLU activation function as a bi-level optimization problem. In particular, for the inner-loop that implements the PGD attack, we propose maximizing a lower bound on the 0/1-loss by reflecting a surrogate loss about the origin. This allows us to give a convergence guarantee for the inner-loop PGD attack and precise iteration complexity results for end-to-end adversarial training, which hold for any width and initialization in a realizable setting.