There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, high codimension in the ambient space of the data manifolds of interest, and that the structure of machine learning models may encourage classifiers to develop decision boundaries close to data points. This article proposes a new framework for studying adversarial examples that does not depend directly on the distance to the decision boundary. Similarly to the smoothed classifier literature, we define a (natural or adversarial) data point to be $(\gamma,\sigma)$-stable if the probability of the same classification is at least $\gamma$ for points sampled in a Gaussian neighborhood of the point with a given standard deviation $\sigma$. We focus on studying the differences between persistence metrics along interpolants of natural and adversarial points. We show that adversarial examples have significantly lower persistence than natural examples for large neural networks in the context of the MNIST and ImageNet datasets. We connect this lack of persistence with decision boundary geometry by measuring angles of interpolants with respect to decision boundaries. Finally, we connect this approach with robustness by developing a manifold alignment gradient metric and demonstrating the increase in robustness that can be achieved when training with the addition of this metric.

提出了一个新的研究框架来研究对抗性示例，通过测量插值点与决策边界的角度，显示出对抗性示例在MNIST和ImageNet数据集的大神经网络中具有比自然示例更低的持久性，并通过开发流形对齐梯度度量与鲁棒性的联系，证明了加入这个度量时可以增强的鲁棒性。

持久分类：数据稳定性和对抗样本的新方法