{"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/learning-optimal-wavelet-bases-using-a-neural","title":"Learning optimal wavelet bases using a neural network approach","arxiv_id":"1706.03041","date":"2017-03-25","proceeding":null,"authors":["Andreas Søgaard"],"abstract":"A novel method for learning optimal, orthonormal wavelet bases for\nrepresenting 1- and 2D signals, based on parallels between the wavelet\ntransform and fully connected artificial neural networks, is described. The\nstructural similarities between these two concepts are reviewed and combined to\na \"wavenet\", allowing for the direct learning of optimal wavelet filter\ncoefficient through stochastic gradient descent with back-propagation over\nensembles of training inputs, where conditions on the filter coefficients for\nconstituting orthonormal wavelet bases are cast as quadratic regularisations\nterms. We describe the practical implementation of this method, and study its\nperformance for high-energy physics collision events for QCD $2 \\to 2$\nprocesses. It is shown that an optimal solution is found, even in a\nhigh-dimensional search space, and the implications of the result are\ndiscussed.","url_abs":"http://arxiv.org/abs/1706.03041v2","url_pdf":"http://arxiv.org/pdf/1706.03041v2.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":"learning-optimal-wavelet-bases-using-a-neural","repo_url":"https://github.com/asogaard/Wavenet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}