Neural networks are vulnerable to adversarial attacks, i.e., small input
perturbations can result in substantially different outputs of a neural
network. Safety-critical environments require neural networks that are robust
against input perturbations. However, training and formally verifying robust
neural networks is challenging. We address this challenge by employing, for the
first time, a end-to-end set-based training procedure that trains robust neural
networks for formal verification. Our training procedure drastically simplifies
the subsequent formal robustness verification of the trained neural network.
While previous research has predominantly focused on augmenting neural network
training with adversarial attacks, our approach leverages set-based computing
to train neural networks with entire sets of perturbed inputs. Moreover, we
demonstrate that our set-based training procedure effectively trains robust
neural networks, which are easier to verify. In many cases, set-based trained
neural networks outperform neural networks trained with state-of-the-art
adversarial attacks.

神经网络在对抗攻击中容易受到干扰，训练和验证稳健的神经网络是有挑战的，而本论文通过采用端到端的基于集合的训练方法来解决这个问题，该方法使得训练和验证神经网络的稳健性更加简单有效。此外，通过使用集合训练的方法，可以在很多情况下比使用最先进的对抗攻击训练的神经网络表现更好。