Structural Robustness for Deep Learning Architectures

TL;DR

This paper introduces a formal, localized measure of robustness for deep networks, compares it with existing metrics, and evaluates its effectiveness through experiments on vision datasets.

Contribution

It proposes a new formal definition of robustness as a localized Lipschitz constant and analyzes its relation to existing robustness measures.

Findings

The new robustness metric correlates with network vulnerability.

Experimental results demonstrate the metric's usefulness in vision tasks.

Comparison shows advantages over traditional robustness measures.

Abstract

Deep Networks have been shown to provide state-of-the-art performance in many machine learning challenges. Unfortunately, they are susceptible to various types of noise, including adversarial attacks and corrupted inputs. In this work we introduce a formal definition of robustness which can be viewed as a localized Lipschitz constant of the network function, quantified in the domain of the data to be classified. We compare this notion of robustness to existing ones, and study its connections with methods in the literature. We evaluate this metric by performing experiments on various competitive vision datasets.