English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

U-Net architectures are ubiquitous in state-of-the-art deep learning, howevertheir regularisation properties and relationship to wavelets are understudied.In this paper, we formulate a multi-resolution framework which identifiesU-Nets as finite-dimensional truncations of models on an infinite-dimensionalfunction space. We provide theoretical results which prove that average poolingcorresponds to projection within the space of square-integrable functions andshow that U-Nets with average pooling implicitly learn a Haar wavelet basisrepresentation of the data. We then leverage our framework to identifystate-of-the-art hierarchical VAEs (HVAEs), which have a U-Net architecture, asa type of two-step forward Euler discretisation of multi-resolution diffusionprocesses which flow from a point mass, introducing sampling instabilities. Wealso demonstrate that HVAEs learn a representation of time which allows forimproved parameter efficiency through weight-sharing. We use this observationto achieve state-of-the-art HVAE performance with half the number of parametersof existing models, exploiting the properties of our continuous-timeformulation.

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