  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.
