  Neural networks are vulnerable to adversarial attacks, i.e., small input
perturbations can significantly affect the outputs of a neural network. In
safety-critical environments, the inputs often contain noisy sensor data;
hence, in this case, neural networks that are robust against input
perturbations are required. To ensure safety, the robustness of a neural
network must be formally verified. However, training and formally verifying
robust neural networks is challenging. We address both of these challenges by
employing, for the first time, an end-to-end set-based training procedure that
trains robust neural networks for formal verification. Our training procedure
trains neural networks, which can be easily verified using simple
polynomial-time verification algorithms. Moreover, our extensive evaluation
demonstrates that our set-based training procedure effectively trains robust
neural networks, which are easier to verify. Set-based trained neural networks
consistently match or outperform those trained with state-of-the-art robust
training approaches.
