PurSAMERE: Reliable Adversarial Purification via Sharpness-Aware Minimization of Expected Reconstruction Error

TL;DR

PurSAMERE introduces a deterministic purification technique that enhances adversarial robustness by guiding inputs toward data distribution modes using sharpness-aware minimization of expected reconstruction error, outperforming existing methods.

Contribution

The paper presents a novel deterministic purification method employing sharpness-aware minimization to improve adversarial robustness, addressing limitations of stochastic approaches.

Findings

Significant robustness gains against strong white-box attacks.

Effective purification guided by expected reconstruction error minimization.

Theoretical proof of recovery of local density maximizers in small-noise limit.

Abstract

We propose a novel deterministic purification method to improve adversarial robustness by mapping a potentially adversarial sample toward a nearby sample that lies close to a mode of the data distribution, where classifiers are more reliable. We design the method to be deterministic to ensure reliable test accuracy and to prevent the degradation of effective robustness observed in stochastic purification approaches when the adversary has full knowledge of the system and its randomness. We employ a score model trained by minimizing the expected reconstruction error of noise-corrupted data, thereby learning the structural characteristics of the input data distribution. Given a potentially adversarial input, the method searches within its local neighborhood for a purified sample that minimizes the expected reconstruction error under noise corruption and then feeds this purified sample to the classifier. During purification, sharpness-aware minimization is used to guide the purified samples toward flat regions of the expected reconstruction error landscape, thereby enhancing robustness. We further show that, as the noise level decreases, minimizing the expected reconstruction error biases the purified sample toward local maximizers of the Gaussian-smoothed density; under additional local assumptions on the score model, we prove recovery of a local maximizer in the small-noise limit. Experimental results demonstrate significant gains in adversarial robustness over state-of-the-art methods under strong deterministic white-box attacks.