{"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/continuous-generative-neural-networks","title":"Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spaces","arxiv_id":"2205.14627","date":"2022-05-29","proceeding":null,"authors":["Giovanni S. Alberti","Matteo Santacesaria","Silvia Sciutto"],"abstract":"In this work, we present and study Continuous Generative Neural Networks (CGNNs), namely, generative models in the continuous setting: the output of a CGNN belongs to an infinite-dimensional function space. The architecture is inspired by DCGAN, with one fully connected layer, several convolutional layers and nonlinear activation functions. In the continuous $L^2$ setting, the dimensions of the spaces of each layer are replaced by the scales of a multiresolution analysis of a compactly supported wavelet. We present conditions on the convolutional filters and on the nonlinearity that guarantee that a CGNN is injective. This theory finds applications to inverse problems, and allows for deriving Lipschitz stability estimates for (possibly nonlinear) infinite-dimensional inverse problems with unknowns belonging to the manifold generated by a CGNN. Several numerical simulations, including signal deblurring, illustrate and validate this approach.","url_abs":"https://arxiv.org/abs/2205.14627v3","url_pdf":"https://arxiv.org/pdf/2205.14627v3.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":"continuous-generative-neural-networks","repo_url":"https://github.com/contgenmod/continuous-generative-neural-network","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"deblurring","task_name":"Deblurring"},{"task_slug":"image-deblurring","task_name":"Image Deblurring"}],"methods":[{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"cgnn","method_name":"CGNN"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"dcgan","method_name":"DCGAN"},{"method_slug":"mpnn","method_name":"MPNN"},{"method_slug":"relu","method_name":"ReLU"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}