Deep neural networks (DNNs) are known to be vulnerable to adversarial
geometric transformation. This paper aims to verify the robustness of
large-scale DNNs against the combination of multiple geometric transformations
with a provable guarantee. Given a set of transformations (e.g., rotation,
scaling, etc.), we develop GeoRobust, a black-box robustness analyser built
upon a novel global optimisation strategy, for locating the worst-case
combination of transformations that affect and even alter a network's output.
GeoRobust can provide provable guarantees on finding the worst-case combination
based on recent advances in Lipschitzian theory. Due to its black-box nature,
GeoRobust can be deployed on large-scale DNNs regardless of their
architectures, activation functions, and the number of neurons. In practice,
GeoRobust can locate the worst-case geometric transformation with high
precision for the ResNet50 model on ImageNet in a few seconds on average. We
examined 18 ImageNet classifiers, including the ResNet family and vision
transformers, and found a positive correlation between the geometric robustness
of the networks and the parameter numbers. We also observe that increasing the
depth of DNN is more beneficial than increasing its width in terms of improving
its geometric robustness. Our tool GeoRobust is available at
this https URL.

研究通过 GeoRobust 在深度神经网络上实现几何变换的鲁棒性分析，并提供了基于 Lipschitz 理论的最坏情况变换证明保证。我们还发现，在 ImageNet 分类器上，增加深度比增加宽度更有益于提高网络的几何鲁棒性。