CS Events

Qualifying Exam

A Manifold View of Adversarial Risk

 

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Wednesday, November 02, 2022, 12:00pm - 01:00pm

 

Speaker: Wenjia Zhang

Location : https://rutgers.zoom.us/j/93084168396?pwd=OFZZeHJOYWlydEEyRDZmdW40aitQdz09

Committee

Prof. Dimitris Metaxas

Dr. Hao Wang

Prof. Konstantinos Michmizos.

Prof. Xiong Fan

Event Type: Qualifying Exam

Abstract: The adversarial risk of a machine learning model has been widely studied. Most previous works assume that the data lies in the whole ambient space. We propose to take a new angle and take the manifold assumption into consideration. Assuming data lies in a manifold, we investigate two new types of adversarial risk, the normal adversarial risk due to perturbation along normal direction, and the in-manifold adversarial risk due to perturbation within the manifold. We prove that the classic adversarial risk can be bounded from both sides using the normal and in-manifold adversarial risks. We also show with a surprisingly pessimistic case that the standard adversarial risk can be nonzero even when both normal and in-manifold risks are zero. We finalize the paper with empirical studies supporting our theoretical results. Our results suggest the possibility of improving the robustness of a classifier by only focusing on the normal adversarial risk.

Organization

Rutgers