{"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/trainable-back-propagated-functional-transfer","title":"Trainable back-propagated functional transfer matrices","arxiv_id":"1710.10403","date":"2017-10-28","proceeding":null,"authors":["Cheng-Hao Cai","Yanyan Xu","Dengfeng Ke","Kaile Su","Jing Sun"],"abstract":"Connections between nodes of fully connected neural networks are usually\nrepresented by weight matrices. In this article, functional transfer matrices\nare introduced as alternatives to the weight matrices: Instead of using real\nweights, a functional transfer matrix uses real functions with trainable\nparameters to represent connections between nodes. Multiple functional transfer\nmatrices are then stacked together with bias vectors and activations to form\ndeep functional transfer neural networks. These neural networks can be trained\nwithin the framework of back-propagation, based on a revision of the delta\nrules and the error transmission rule for functional connections. In\nexperiments, it is demonstrated that the revised rules can be used to train a\nrange of functional connections: 20 different functions are applied to neural\nnetworks with up to 10 hidden layers, and most of them gain high test\naccuracies on the MNIST database. It is also demonstrated that a functional\ntransfer matrix with a memory function can roughly memorise a non-cyclical\nsequence of 400 digits.","url_abs":"http://arxiv.org/abs/1710.10403v1","url_pdf":"http://arxiv.org/pdf/1710.10403v1.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":"trainable-back-propagated-functional-transfer","repo_url":"https://github.com/cchrewrite/Functional-Transfer-Neural-Networks","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}