Title: Efficient Training of Robust and Verifiable Neural Networks. Abstract: Recent works have developed several methods of defending neural networks against adversarial attacks with certified guarantees. We propose that many common certified defenses can be viewed under a unified framework of regularization. This unified framework provides a technique for comparing different certified defenses with respect to robust generalization. In addition, we develop a new regularizer that is both more efficient than existing certified defenses and can be used to train networks with higher certified accuracy. Our regularizer also extends to an L0 threat model and ensemble models. Through experiments on MNIST, CIFAR-10 and GTSRB, we demonstrate improvements in training speed and certified accuracy compared to state-of-the-art certified defenses.