We investigate the HSIC (Hilbert-Schmidt independence criterion) bottleneck\nas a regularizer for learning an adversarially robust deep neural network\nclassifier. In addition to the usual cross-entropy loss, we add regularization\nterms for every intermediate layer to ensure that the latent representations\nretain useful information for output prediction while reducing redundant\ninformation. We show that the HSIC bottleneck enhances robustness to\nadversarial attacks both theoretically and experimentally. In particular, we\nprove that the HSIC bottleneck regularizer reduces the sensitivity of the\nclassifier to adversarial examples. Our experiments on multiple benchmark\ndatasets and architectures demonstrate that incorporating an HSIC bottleneck\nregularizer attains competitive natural accuracy and improves adversarial\nrobustness, both with and without adversarial examples during training. Our\ncode and adversarially robust models are publicly available.\n