{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-unified-framework-for-u-net-design-and-1","title":"A Unified Framework for U-Net Design and Analysis","arxiv_id":"2305.19638","date":"2023-05-31","proceeding":"NeurIPS 2023 11","authors":["Christopher Williams","Fabian Falck","George Deligiannidis","Chris Holmes","Arnaud Doucet","Saifuddin Syed"],"abstract":"U-Nets are a go-to, state-of-the-art 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.","url_abs":"https://arxiv.org/abs/2305.19638v2","url_pdf":"https://arxiv.org/pdf/2305.19638v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-unified-framework-for-u-net-design-and-1","repo_url":"https://github.com/fabianfalck/unet-design","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"decoder","task_name":"Decoder"},{"task_slug":"image-segmentation","task_name":"Image Segmentation"},{"task_slug":"semantic-segmentation","task_name":"Semantic Segmentation"}],"methods":[{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"concatenated-skip-connection","method_name":"Concatenated Skip Connection"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"diffusion","method_name":"Diffusion"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"u-net","method_name":"U-Net"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2305.19638","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2305.19638"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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