Robustness Certificates Against Adversarial Examples for ReLU Networks
This work addresses the robustness issue in neural networks for security-critical applications, offering incremental improvements in certification efficiency.
The paper tackles the problem of neural networks being vulnerable to adversarial perturbations by proposing two attack-agnostic robustness certificates for ReLU networks, which provide lower bounds on the distance to decision boundaries and are faster to compute than existing methods, with numerical results shown on MNIST.
While neural networks have achieved high performance in different learning tasks, their accuracy drops significantly in the presence of small adversarial perturbations to inputs. Defenses based on regularization and adversarial training are often followed by new attacks to defeat them. In this paper, we propose attack-agnostic robustness certificates for a multi-label classification problem using a deep ReLU network. Although computing the exact distance of a given input sample to the classification decision boundary requires solving a non-convex optimization, we characterize two lower bounds for such distances, namely the simplex certificate and the decision boundary certificate. These robustness certificates leverage the piece-wise linear structure of ReLU networks and use the fact that in a polyhedron around a given sample, the prediction function is linear. In particular, the proposed simplex certificate has a closed-form, is differentiable and is an order of magnitude faster to compute than the existing methods even for deep networks. In addition to theoretical bounds, we provide numerical results for our certificates over MNIST and compare them with some existing upper bounds.