Adversarial robustness of VAEs through the lens of local geometry
This work addresses adversarial robustness in unsupervised learning for VAEs, providing incremental improvements through geometric analysis and training techniques.
The paper tackles the vulnerability of variational autoencoders (VAEs) to adversarial attacks by analyzing local geometry via the pullback metric tensor, showing that optimal attacks exploit directional bias in this tensor and proposing robustness scores that correlate with β-VAE parameters. It demonstrates that mixup training can improve robustness while maintaining reconstruction quality, offering an alternative to increasing β which degrades reconstructions.
In an unsupervised attack on variational autoencoders (VAEs), an adversary finds a small perturbation in an input sample that significantly changes its latent space encoding, thereby compromising the reconstruction for a fixed decoder. A known reason for such vulnerability is the distortions in the latent space resulting from a mismatch between approximated latent posterior and a prior distribution. Consequently, a slight change in an input sample can move its encoding to a low/zero density region in the latent space resulting in an unconstrained generation. This paper demonstrates that an optimal way for an adversary to attack VAEs is to exploit a directional bias of a stochastic pullback metric tensor induced by the encoder and decoder networks. The pullback metric tensor of an encoder measures the change in infinitesimal latent volume from an input to a latent space. Thus, it can be viewed as a lens to analyse the effect of input perturbations leading to latent space distortions. We propose robustness evaluation scores using the eigenspectrum of a pullback metric tensor. Moreover, we empirically show that the scores correlate with the robustness parameter $β$ of the $β-$VAE. Since increasing $β$ also degrades reconstruction quality, we demonstrate a simple alternative using \textit{mixup} training to fill the empty regions in the latent space, thus improving robustness with improved reconstruction.