Title: Composite Adversarial Training for Multiple Adversarial Perturbations and Beyond. Abstract: One intriguing property of deep neural networks (DNNs) is their vulnerability to adversarial perturbations. Despite the plethora of work on defending against individual perturbation models, improving DNN robustness against the combinations of multiple perturbations is still fairly under-studied. In this paper, we propose \underline{c}omposite \underline{a}dversarial \underline{t}raining (CAT), a novel training method that flexibly integrates and optimizes multiple adversarial losses, leading to significant robustness improvement with respect to individual perturbations as well as their ``compositions''. Through empirical evaluation on benchmark datasets and models, we show that CAT outperforms existing adversarial training methods by large margins in defending against the compositions of pixel perturbations and spatial transformations, two major classes of adversarial perturbation models, while incurring limited impact on clean inputs.