Matthew Willetts — accepted AI-conference papers

2022

A Multi-Resolution Framework for U-Nets with Applications to Hierarchical VAEs

Fabian Falck, Christopher Williams, Dominic Danks, George Deligiannidis, Christopher Yau, Christopher C. Holmes +2

NeurIPS 2022accept

U-Net architectures are ubiquitous in state-of-the-art deep learning, however their regularisation properties and relationship to wavelets are understudied. In this paper, we formulate a multi-resolution framework which identifies U-Nets as finite-dimensional truncations of models on an infinite-dim…

Cited by 10 Source ↗PDF ↗Scholar ↗

2022

Certifiably Robust Variational Autoencoders

Ben Barrett, Alexander Camuto, Matthew Willetts, Tom Rainforth

AISTATS 2022poster

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…

Cited by 21 Source ↗PDF ↗Scholar ↗

2022

Variational Autoencoders: A Harmonic Perspective

Alexander Camuto, Matthew Willetts

AISTATS 2022poster

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…

Cited by 2 Source ↗PDF ↗Scholar ↗

2021

Learning Bijective Feature Maps for Linear ICA

Alexander Camuto, Matthew Willetts, Chris Holmes, Brooks Paige, Stephen Roberts

AISTATS 2021poster

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…

Cited by 2 Source ↗PDF ↗Scholar ↗

2021

Multi-Facet Clustering Variational Autoencoders

Fabian Falck, Haoting Zhang, Matthew Willetts, George Nicholson, Christopher Yau, Christopher C. Holmes

NeurIPS 2021poster

Work in deep clustering focuses on finding a single partition of data. However, high-dimensional data, such as images, typically feature multiple interesting characteristics one could cluster over. For example, images of objects against a background could be clustered over the shape of the object an…

Cited by 48 Source ↗PDF ↗code ↗Scholar ↗

2021

Towards a Theoretical Understanding of the Robustness of Variational Autoencoders

Alexander Camuto, Matthew Willetts, Stephen Roberts, Chris Holmes, Tom Rainforth

AISTATS 2021poster

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…

Cited by 44 Source ↗PDF ↗Scholar ↗

2020

Explicit Regularisation in Gaussian Noise Injections

Alexander Camuto, Matthew Willetts, Umut Simsekli, Stephen J. Roberts, Chris C Holmes

NeurIPS 2020poster

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…

Cited by 78 Source ↗PDF ↗Scholar ↗