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• W2899434523 abstract "Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. We propose a geometric framework, drawing on tools from the manifold reconstruction literature, to analyze the high-dimensional geometry of adversarial examples. In particular, we highlight the importance of codimension: for low-dimensional data manifolds embedded in high-dimensional space there are many directions off the manifold in which to construct adversarial examples. Adversarial examples are a natural consequence of learning a decision boundary that classifies the low-dimensional data manifold well, but classifies points near the manifold incorrectly. Using our geometric framework we prove (1) a tradeoff between robustness under different norms, (2) that adversarial training in balls around the data is sample inefficient, and (3) sufficient sampling conditions under which nearest neighbor classifiers and ball-based adversarial training are robust." @default.
• W2899434523 created "2018-11-09" @default.
• W2899434523 creator A5022522148 @default.
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• W2899434523 date "2018-09-27" @default.
• W2899434523 modified "2023-09-27" @default.
• W2899434523 title "On the Geometry of Adversarial Examples." @default.
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• W2899434523 hasPublicationYear "2018" @default.
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