{"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/kafnets-kernel-based-non-parametric","title":"Kafnets: kernel-based non-parametric activation functions for neural networks","arxiv_id":"1707.04035","date":"2017-07-13","proceeding":null,"authors":["Simone Scardapane","Steven Van Vaerenbergh","Simone Totaro","Aurelio Uncini"],"abstract":"Neural networks are generally built by interleaving (adaptable) linear layers\nwith (fixed) nonlinear activation functions. To increase their flexibility,\nseveral authors have proposed methods for adapting the activation functions\nthemselves, endowing them with varying degrees of flexibility. None of these\napproaches, however, have gained wide acceptance in practice, and research in\nthis topic remains open. In this paper, we introduce a novel family of flexible\nactivation functions that are based on an inexpensive kernel expansion at every\nneuron. Leveraging over several properties of kernel-based models, we propose\nmultiple variations for designing and initializing these kernel activation\nfunctions (KAFs), including a multidimensional scheme allowing to nonlinearly\ncombine information from different paths in the network. The resulting KAFs can\napproximate any mapping defined over a subset of the real line, either convex\nor nonconvex. Furthermore, they are smooth over their entire domain, linear in\ntheir parameters, and they can be regularized using any known scheme, including\nthe use of $\\ell_1$ penalties to enforce sparseness. To the best of our\nknowledge, no other known model satisfies all these properties simultaneously.\nIn addition, we provide a relatively complete overview on alternative\ntechniques for adapting the activation functions, which is currently lacking in\nthe literature. A large set of experiments validates our proposal.","url_abs":"http://arxiv.org/abs/1707.04035v2","url_pdf":"http://arxiv.org/pdf/1707.04035v2.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":"kafnets-kernel-based-non-parametric","repo_url":"https://github.com/ispamm/kernel-activation-functions","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"kafnets-kernel-based-non-parametric","repo_url":"https://github.com/shruti-jadon/Siamese-Network-for-One-shot-Learning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"kaf","method_name":"KAF"}],"datasets_introduced":[],"methods_introduced":[{"slug":"kaf","name":"KAF","full_name":"Kernel Activation Function"}],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}