Likelihood Landscapes: A Unifying Principle Behind Many Adversarial Defenses

TL;DR

This paper investigates how various adversarial defense techniques influence the likelihood landscape of neural networks, revealing that many defenses flatten this landscape, which correlates with increased robustness.

Contribution

It introduces a visualization method for the likelihood landscape and a measure of its flatness, linking defense effectiveness to landscape geometry.

Findings

Defense techniques often flatten the likelihood landscape.

Flattening correlates with improved adversarial robustness.

Regularizing for flat landscapes enhances defense effectiveness.

Abstract

Convolutional Neural Networks have been shown to be vulnerable to adversarial examples, which are known to locate in subspaces close to where normal data lies but are not naturally occurring and of low probability. In this work, we investigate the potential effect defense techniques have on the geometry of the likelihood landscape - likelihood of the input images under the trained model. We first propose a way to visualize the likelihood landscape leveraging an energy-based model interpretation of discriminative classifiers. Then we introduce a measure to quantify the flatness of the likelihood landscape. We observe that a subset of adversarial defense techniques results in a similar effect of flattening the likelihood landscape. We further explore directly regularizing towards a flat landscape for adversarial robustness.