We explore the concept of co-design in the context of neural network verification. Specifically, we aim to train deep neural networks that not only are robust to adversarial perturbations but also whose robustness can be verified more easily. To this end, we identify two properties of network models - weight sparsity and so-called ReLU stability - that turn out to significantly impact the complexity of the corresponding verification task. We demonstrate that improving weight sparsity alone already enables us to turn computationally intractable verification problems into tractable ones. Then, improving ReLU stability leads to an additional 4-13x speedup in verification times. An important feature of our methodology is its "universality," in the sense that it can be used with a broad range of training procedures and verification approaches.

We develop methods to train deep neural models that are both robust to adversarial perturbations and whose robustness is significantly easier to verify. The paper presents several ways to regularize plain ReLU networks to opimize the adversarial robustness, provable adversarial robustness, and the verification speed. This paper proposes methods to train robust neural networks that can be verified faster, using pruning methods to encourage weight sparsity and regularization to encourage ReLU stability.