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Poster
A Unified Framework for U-Net Design and Analysis
Christopher Williams · Fabian Falck · George Deligiannidis · Chris C Holmes · Arnaud Doucet · Saifuddin Syed

Tue Dec 12 03:15 PM -- 05:15 PM (PST) @ Great Hall & Hall B1+B2 #526
in Poster Session 2 »

U-Nets are a go-to neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however their design and architecture is understudied. In this paper, we provide a framework for designing and analysing general U-Net architectures. We present theoretical results which characterise the role of the encoder and decoder in a U-Net, their high-resolution scaling limits and their conjugacy to ResNets via preconditioning. We propose Multi-ResNets, U-Nets with a simplified, wavelet-based encoder without learnable parameters. Further, we show how to design novel U-Net architectures which encode function constraints, natural bases, or the geometry of the data. In diffusion models, our framework enables us to identify that high-frequency information is dominated by noise exponentially faster, and show how U-Nets with average pooling exploit this. In our experiments, we demonstrate how Multi-ResNets achieve competitive and often superior performance compared to classical U-Nets in image segmentation, PDE surrogate modelling, and generative modelling with diffusion models. Our U-Net framework paves the way to study the theoretical properties of U-Nets and design natural, scalable neural architectures for a multitude of problems beyond the square.

Author Information

Christopher Williams (University of Oxford)
Fabian Falck (University of Oxford)
George Deligiannidis (Oxford)
Chris C Holmes (University of Oxford)
Arnaud Doucet (Oxford)
Saifuddin Syed (University of Oxford)

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