Global Robustness Evaluation of Deep Neural Networks with Provable Guarantees for the $L_0$ Norm
This work addresses the need for reliable safety assurances in critical systems using DNNs, offering a novel approach with provable convergence, though it is incremental in building on existing robustness evaluation methods.
The paper tackles the problem of providing provable guarantees for the robustness of deep neural networks against adversarial perturbations under the L0 norm, by proposing an anytime, tensor-based method that computes lower and upper bounds on global robustness, demonstrating its utility in various applications such as ImageNet evaluations and competitive attacks.
Deployment of deep neural networks (DNNs) in safety- or security-critical systems requires provable guarantees on their correct behaviour. A common requirement is robustness to adversarial perturbations in a neighbourhood around an input. In this paper we focus on the $L_0$ norm and aim to compute, for a trained DNN and an input, the maximal radius of a safe norm ball around the input within which there are no adversarial examples. Then we define global robustness as an expectation of the maximal safe radius over a test data set. We first show that the problem is NP-hard, and then propose an approximate approach to iteratively compute lower and upper bounds on the network's robustness. The approach is \emph{anytime}, i.e., it returns intermediate bounds and robustness estimates that are gradually, but strictly, improved as the computation proceeds; \emph{tensor-based}, i.e., the computation is conducted over a set of inputs simultaneously, instead of one by one, to enable efficient GPU computation; and has \emph{provable guarantees}, i.e., both the bounds and the robustness estimates can converge to their optimal values. Finally, we demonstrate the utility of the proposed approach in practice to compute tight bounds by applying and adapting the anytime algorithm to a set of challenging problems, including global robustness evaluation, competitive $L_0$ attacks, test case generation for DNNs, and local robustness evaluation on large-scale ImageNet DNNs. We release the code of all case studies via GitHub.