End-To-End Set-Based Training for Neural Network Verification
Lukas Koller Tobias Ladner Matthias Althoff
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.