Persistent Classification: A New Approach to Stability of Data and Adversarial Examples
This work addresses adversarial robustness for machine learning models, offering a novel perspective on stability that could enhance security in applications like image recognition, though it is incremental relative to existing smoothed classifier approaches.
The paper tackles the problem of adversarial examples in classification by introducing a persistence-based framework to measure stability, showing that adversarial examples have significantly lower persistence than natural ones on MNIST and ImageNet datasets, and connecting this to decision boundary geometry to improve robustness.
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 $(γ,σ)$-stable if the probability of the same classification is at least $γ$ for points sampled in a Gaussian neighborhood of the point with a given standard deviation $σ$. 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.