{"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-across-scales-a-multiscale-method","title":"Learning across scales - A multiscale method for Convolution Neural Networks","arxiv_id":"1703.02009","date":"2017-03-06","proceeding":null,"authors":["Eldad Haber","Lars Ruthotto","Elliot Holtham","Seong-Hwan Jun"],"abstract":"In this work we establish the relation between optimal control and training\ndeep Convolution Neural Networks (CNNs). We show that the forward propagation\nin CNNs can be interpreted as a time-dependent nonlinear differential equation\nand learning as controlling the parameters of the differential equation such\nthat the network approximates the data-label relation for given training data.\nUsing this continuous interpretation we derive two new methods to scale CNNs\nwith respect to two different dimensions. The first class of multiscale methods\nconnects low-resolution and high-resolution data through prolongation and\nrestriction of CNN parameters. We demonstrate that this enables classifying\nhigh-resolution images using CNNs trained with low-resolution images and vice\nversa and warm-starting the learning process. The second class of multiscale\nmethods connects shallow and deep networks and leads to new training strategies\nthat gradually increase the depths of the CNN while re-using parameters for\ninitializations.","url_abs":"http://arxiv.org/abs/1703.02009v2","url_pdf":"http://arxiv.org/pdf/1703.02009v2.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-across-scales-a-multiscale-method","repo_url":"https://github.com/xtractopen/meganet.m","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":null,"task_name":"Relation"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}