{"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/complex-valued-neural-networks-with-non","title":"Complex-valued Neural Networks with Non-parametric Activation Functions","arxiv_id":"1802.08026","date":"2018-02-22","proceeding":null,"authors":["Simone Scardapane","Steven Van Vaerenbergh","Amir Hussain","Aurelio Uncini"],"abstract":"Complex-valued neural networks (CVNNs) are a powerful modeling tool for\ndomains where data can be naturally interpreted in terms of complex numbers.\nHowever, several analytical properties of the complex domain (e.g.,\nholomorphicity) make the design of CVNNs a more challenging task than their\nreal counterpart. In this paper, we consider the problem of flexible activation\nfunctions (AFs) in the complex domain, i.e., AFs endowed with sufficient\ndegrees of freedom to adapt their shape given the training data. While this\nproblem has received considerable attention in the real case, a very limited\nliterature exists for CVNNs, where most activation functions are generally\ndeveloped in a split fashion (i.e., by considering the real and imaginary parts\nof the activation separately) or with simple phase-amplitude techniques.\nLeveraging over the recently proposed kernel activation functions (KAFs), and\nrelated advances in the design of complex-valued kernels, we propose the first\nfully complex, non-parametric activation function for CVNNs, which is based on\na kernel expansion with a fixed dictionary that can be implemented efficiently\non vectorized hardware. Several experiments on common use cases, including\nprediction and channel equalization, validate our proposal when compared to\nreal-valued neural networks and CVNNs with fixed activation functions.","url_abs":"http://arxiv.org/abs/1802.08026v1","url_pdf":"http://arxiv.org/pdf/1802.08026v1.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":"complex-valued-neural-networks-with-non","repo_url":"https://github.com/omrijsharon/torchlex","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"complex-valued-neural-networks-with-non","repo_url":"https://github.com/ypeleg/komplex","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"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}