We present REGLO, a novel methodology for repairing pretrained neural networks to satisfy global robustness and individual fairness properties. A neural network is said to be globally robust with respect to a given input region if and only if all the input points in the region are locally robust. This notion of global robustness also captures the notion of individual fairness as a special case. We prove that any counterexample to a global robustness property must exhibit a corresponding large gradient. For ReLU networks, this result allows us to efficiently identify the linear regions that violate a given global robustness property. By formulating and solving a suitable robust convex optimization problem, REGLO then computes a minimal weight change that will provably repair these violating linear regions.

We present a novel methodology for neural network backdoor attacks. Unlike existing training-time attacks where the Trojaned network would respond to the Trojan trigger after training, our approach inserts a Trojan that will remain dormant until it is activated. The activation is realized through a specific perturbation to the network's weight parameters only known to the attacker. Our analysis and the experimental results demonstrate that dormant Trojaned networks can effectively evade detection by state-of-the-art backdoor detection methods.