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A Branch and Bound Framework for Stronger Adversarial Attacks of ReLU Networks

Strong adversarial attacks are important for evaluating the true robustness of deep neural networks. Most existing attacks find adversarial examples via searching in the input space, e.g., using gradient descent. In this work, we formulate an adversarial attack using a branch-and-bound (BaB) procedure on ReLU neural networks and search adversarial examples in the activation space corresponding to binary variables in a mixed integer programming (MIP) formulation. This attack formulation can be used to tackle hard instances where none of the existing adversarial attacks can succeed. Existing attacks using this formulation rely on generic solvers which cannot exploit the structure of neural networks and also cannot utilize GPU acceleration, so they are mostly limited to small networks and easy problem instances. To improve its scalability and practicability, we propose a top-down beam-search approach to quickly identify the subspace that may contain adversarial examples. The search utilizes the bound propagation based neural network verifiers on GPUs to rapidly evaluate a large number of searching regions, which is not possible in generic MIP solvers. Moreover, we exploit the fact that good candidates of adversarial examples can be easily found via gradient based attacks, and build an adversarial candidates pool to further guide the search in activation space via diving techniques. Additionally, any candidate adversarial examples found during the process are refined using a bottom-up large neighbourhood search (LNS) guided by the candidates pool. Our adversarial attack framework, BaB-Attack, opens up a new opportunity for designing novel adversarial attacks not limited to searching the input space, and enables us to borrow techniques from integer programming theory and neural network verification to build stronger attacks. In experiments, we can successfully generate adversarial examples for hard input instances where existing strong adversarial attacks fail, and outperform off-the-shelf MIP solver based attacks in both success rates and efficiency. Our results further close the gap between the upper bound of robust accuracy obtained by attacks and the lower bound obtained by verification.

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