This paper is concerned with the robustness of VAEs to adversarial attacks. We highlight that conventional VAEs are brittle under attack but that methods recently introduced for disentanglement such as @math -TCVAE (, 2018) improve robustness, as demonstrated through a variety of previously proposed adversarial attacks ( (2016); Gondim- (2018); (2018)). This motivated us to develop Seatbelt-VAE, a new hierarchical disentangled VAE that is designed to be significantly more robust to adversarial attacks than existing approaches, while retaining high quality reconstructions.
To perform amortised variational inference one introduces a recognition network, which can be any directed acyclic graph where each node, each distribution over each @math , is Gaussian conditioned on its parents. This could be a chain, as in @cite_5 : Again, marginalising out intermediate @math layers, we see @math @math is a non-Gaussian, highly flexible, distribution.
@cite_5
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We marry ideas from deep neural networks and approximate Bayesian inference to derive a generalised class of deep, directed generative models, endowed with a new algorithm for scalable inference and learning. Our algorithm introduces a recognition model to represent an approximate posterior distribution and uses this for optimisation of a variational lower bound. We develop stochastic backpropagation - rules for gradient backpropagation through stochastic variables - and derive an algorithm that allows for joint optimisation of the parameters of both the generative and recognition models. We demonstrate on several real-world data sets that by using stochastic backpropagation and variational inference, we obtain models that are able to generate realistic samples of data, allow for accurate imputations of missing data, and provide a useful tool for high-dimensional data visualisation.