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ABSTRACT There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high‐dimensionality of the data, the 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 for points sampled in a Gaussian neighborhood of the point with a given standard deviation . 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. 

Variety of Big data is a significant impediment for anyone who wants to search inside a large-scale structured dataset. For example, there are millions of tables available on the Web, but the most relevant search result does not necessarily match the keyword-query exactly due to a variety of ways to represent the same information. Here we describe Hybrid.AI, a learning search engine for large-scale structured data that uses automatically generated machine learning classifiers and Unified Famous Objects (UFOs) to return the most relevant search results from a large-scale Web tables corpora. We evaluate it over this corpora, collecting 99 queries and their results from users, and observe significant relevance gain.