8 accepted papers
We introduce an approach for training variational autoencoders (VAEs) that are certifiably robust to adversarial attack. Specifically, we first derive actionable bounds on the minimal size of an input perturbation required to change a VAE’s reconstruction by more than an allowed amount, with these b…
In this work we study Variational Autoencoders (VAEs) from the perspective of harmonic analysis. By viewing a VAE’s latent space as a Gaussian Space, a variety of measure space, we derive a series of results that show that the encoder variance of a VAE controls the frequency content of the functions…
Gaussian noise injections (GNIs) are a family of simple and widely-used regularisation methods for training neural networks, where one injects additive or multiplicative Gaussian noise to the network activations at every iteration of the optimisation algorithm, which is typically chosen as stochasti…
Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account in order to obtain meaningful generalization bounds, it is…
Variational autoencoders (VAEs) have recently been shown to be vulnerable to adversarial attacks, wherein they are fooled into reconstructing a chosen target image. However, how to defend against such attacks remains an open problem. We make significant advances in addressing this issue by introduci…
Separating high-dimensional data like images into independent latent factors, i.e independent component analysis (ICA), remains an open research problem. As we show, existing probabilistic deep generative models (DGMs), which are tailor-made for image data, underperform on non-linear ICA tasks. To a…
We make inroads into understanding the robustness of Variational Autoencoders (VAEs) to adversarial attacks and other input perturbations. While previous work has developed algorithmic approaches to attacking and defending VAEs, there remains a lack of formalization for what it means for a VAE to be…
We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive…