On Certifying Non-uniform Bound against Adversarial Attacks
This work addresses the need for more accurate robustness certification in neural networks, offering an incremental improvement over existing uniform-bound methods.
The paper tackles the problem of certifying robustness of neural networks against adversarial attacks by finding non-uniform bounds around data points, showing that these bounds have larger volumes than uniform bounds and provide a quantitative metric for feature robustness.
This work studies the robustness certification problem of neural network models, which aims to find certified adversary-free regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider non-uniform bounds and use it to study the decision boundary of neural network models. We formulate our target as an optimization problem with nonlinear constraints. Then, a framework applicable for general feedforward neural networks is proposed to bound the output logits so that the relaxed problem can be solved by the augmented Lagrangian method. Our experiments show the non-uniform bounds have larger volumes than uniform ones and the geometric similarity of the non-uniform bounds gives a quantitative, data-agnostic metric of input features' robustness. Further, compared with normal models, the robust models have even larger non-uniform bounds and better interpretability.