{"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/normalization-equivariant-neural-networks","title":"Normalization-Equivariant Neural Networks with Application to Image Denoising","arxiv_id":"2306.05037","date":"2023-06-08","proceeding":"NeurIPS 2023 11","authors":["Sébastien Herbreteau","Emmanuel Moebel","Charles Kervrann"],"abstract":"In many information processing systems, it may be desirable to ensure that any change of the input, whether by shifting or scaling, results in a corresponding change in the system response. While deep neural networks are gradually replacing all traditional automatic processing methods, they surprisingly do not guarantee such normalization-equivariance (scale + shift) property, which can be detrimental in many applications. To address this issue, we propose a methodology for adapting existing neural networks so that normalization-equivariance holds by design. Our main claim is that not only ordinary convolutional layers, but also all activation functions, including the ReLU (rectified linear unit), which are applied element-wise to the pre-activated neurons, should be completely removed from neural networks and replaced by better conditioned alternatives. To this end, we introduce affine-constrained convolutions and channel-wise sort pooling layers as surrogates and show that these two architectural modifications do preserve normalization-equivariance without loss of performance. Experimental results in image denoising show that normalization-equivariant neural networks, in addition to their better conditioning, also provide much better generalization across noise levels.","url_abs":"https://arxiv.org/abs/2306.05037v2","url_pdf":"https://arxiv.org/pdf/2306.05037v2.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":"normalization-equivariant-neural-networks","repo_url":"https://github.com/sherbret/normalization_equivariant_nn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"image-denoising","task_name":"Image Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2306.05037","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}