LipSim: A Provably Robust Perceptual Similarity Metric

TL;DR

This paper introduces LipSim, a new perceptual similarity metric that is provably robust against adversarial attacks by using Lipschitz neural networks, improving reliability in visual similarity assessments.

Contribution

The paper proposes LipSim, a novel perceptual similarity metric based on 1-Lipschitz neural networks, with provable robustness guarantees against adversarial perturbations.

Findings

LipSim outperforms existing metrics in natural and certified scores.

LipSim provides robustness certificates for all perturbations within an $ ext{l}_2$ ball.

Experimental results demonstrate LipSim's effectiveness in image retrieval tasks.

Abstract

Recent years have seen growing interest in developing and applying perceptual similarity metrics. Research has shown the superiority of perceptual metrics over pixel-wise metrics in aligning with human perception and serving as a proxy for the human visual system. On the other hand, as perceptual metrics rely on neural networks, there is a growing concern regarding their resilience, given the established vulnerability of neural networks to adversarial attacks. It is indeed logical to infer that perceptual metrics may inherit both the strengths and shortcomings of neural networks. In this work, we demonstrate the vulnerability of state-of-the-art perceptual similarity metrics based on an ensemble of ViT-based feature extractors to adversarial attacks. We then propose a framework to train a robust perceptual similarity metric called LipSim (Lipschitz Similarity Metric) with provable guarantees. By leveraging 1-Lipschitz neural networks as the backbone, LipSim provides guarded areas around each data point and certificates for all perturbations within an $\ell_2$ ball. Finally, a comprehensive set of experiments shows the performance of LipSim in terms of natural and certified scores and on the image retrieval application. The code is available at https://github.com/SaraGhazanfari/LipSim.