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- W4322096543 abstract "We investigate the geometric complexity of decision boundaries for robust training compared to standard training. By considering the local geometry of nearest neighbour sets, we study them in a model-agnostic way and theoretically derive a lower-bound $$R^*in mathbb {R}$$ on the perturbation magnitude $$delta in mathbb {R}$$ for which robust training provably requires a geometrically more complex decision boundary than accurate training. We show that state-of-the-art robust models learn more complex decision boundaries than their non-robust counterparts, confirming previous hypotheses. Then, we compute $$R^*$$ for common image benchmarks and find that it also empirically serves as an upper bound over which label noise is introduced. We demonstrate for deep neural network classifiers that perturbation magnitudes $$delta ge R^*$$ lead to reduced robustness and generalization performance. Therefore, $$R^*$$ bounds the maximum feasible perturbation magnitude for norm-bounded robust training and data augmentation. Finally, we show that $$R^*< 0.5R$$ for common benchmarks, where R is a distribution’s minimum nearest neighbour distance. Thus, we improve previous work on determining a distribution’s maximum robust radius." @default.
- W4322096543 created "2023-02-26" @default.
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- W4322096543 date "2023-01-01" @default.
- W4322096543 modified "2023-09-25" @default.
- W4322096543 title "Comparing Complexities of Decision Boundaries for Robust Training: A Universal Approach" @default.
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- W4322096543 doi "https://doi.org/10.1007/978-3-031-26351-4_38" @default.
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