Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality

TL;DR

This paper uses Local Intrinsic Dimensionality to characterize and distinguish adversarial regions in deep neural networks, providing insights that could improve detection and understanding of adversarial attacks.

Contribution

It introduces LID as a novel metric to analyze adversarial subspaces and demonstrates its effectiveness in detecting adversarial examples across multiple attack strategies.

Findings

LID can effectively distinguish adversarial examples from normal data.

LID outperforms several state-of-the-art detection methods.

Analysis suggests new directions for adversarial defense and attack development.

Abstract

Deep Neural Networks (DNNs) have recently been shown to be vulnerable against adversarial examples, which are carefully crafted instances that can mislead DNNs to make errors during prediction. To better understand such attacks, a characterization is needed of the properties of regions (the so-called 'adversarial subspaces') in which adversarial examples lie. We tackle this challenge by characterizing the dimensional properties of adversarial regions, via the use of Local Intrinsic Dimensionality (LID). LID assesses the space-filling capability of the region surrounding a reference example, based on the distance distribution of the example to its neighbors. We first provide explanations about how adversarial perturbation can affect the LID characteristic of adversarial regions, and then show empirically that LID characteristics can facilitate the distinction of adversarial examples generated using state-of-the-art attacks. As a proof-of-concept, we show that a potential application of LID is to distinguish adversarial examples, and the preliminary results show that it can outperform several state-of-the-art detection measures by large margins for five attack strategies considered in this paper across three benchmark datasets. Our analysis of the LID characteristic for adversarial regions not only motivates new directions of effective adversarial defense, but also opens up more challenges for developing new attacks to better understand the vulnerabilities of DNNs.