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Research map / Adversarial robustness and security / Certified and empirical robustness

On the Generalization Analysis of Adversarial Learning

ICML 2022 · Adversarial robustness and security › Certified and empirical robustness · approach: Provable robust learning guarantees

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Replace additive adversarial noise with general (non-additive) noise application functions in the adversarial generalization analysisAdversarial learning generalization bounds · Theoretical analysis (multi-class linear and neural networks)adversarial generalization bound scalingHelped
Scale of bound in number of classes K changed from O(sqrt(K)) or O(K) in prior work to O(log(K)) via covering-number analysisMulti-class linear classifiers under l-infinity additive attack · Theoretical analysis (K classes)dependence on number of classesHelped
Optimistic (local Rademacher) bounds for smooth robust-self-bounding losses, giving fast rates when empirical adversarial risk is zeroAdversarial deep learning with smooth margin loss · Theoretical analysisgeneralization rateHelped
Bound dependence on input dimension d for additive l-infinity attacks includes extra sqrt(d) factor from noise-set complexity, unlike prior boundsMulti-class linear classifiers under l-infinity additive attack · Theoretical analysisdependence on input dimensionHurt

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