{"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/fc-kan-function-combinations-in-kolmogorov","title":"FC-KAN: Function Combinations in Kolmogorov-Arnold Networks","arxiv_id":"2409.01763","date":"2024-09-03","proceeding":null,"authors":["Hoang-Thang Ta","Duy-Quy Thai","Abu Bakar Siddiqur Rahman","Grigori Sidorov","Alexander Gelbukh"],"abstract":"In this paper, we introduce FC-KAN, a Kolmogorov-Arnold Network (KAN) that leverages combinations of popular mathematical functions such as B-splines, wavelets, and radial basis functions on low-dimensional data through element-wise operations. We explore several methods for combining the outputs of these functions, including sum, element-wise product, the addition of sum and element-wise product, representations of quadratic and cubic functions, concatenation, linear transformation of the concatenated output, and others. In our experiments, we compare FC-KAN with a multi-layer perceptron network (MLP) and other existing KANs, such as BSRBF-KAN, EfficientKAN, FastKAN, and FasterKAN, on the MNIST and Fashion-MNIST datasets. Two variants of FC-KAN, which use a combination of outputs from B-splines and Difference of Gaussians (DoG) and from B-splines and linear transformations in the form of a quadratic function, outperformed overall other models on the average of 5 independent training runs. We expect that FC-KAN can leverage function combinations to design future KANs. Our repository is publicly available at: https://github.com/hoangthangta/FC_KAN.","url_abs":"https://arxiv.org/abs/2409.01763v3","url_pdf":"https://arxiv.org/pdf/2409.01763v3.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":"fc-kan-function-combinations-in-kolmogorov","repo_url":"https://github.com/hoangthangta/fc_kan","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"fc-kan-function-combinations-in-kolmogorov","repo_url":"https://github.com/hoangthangta/all-kan","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"kolmogorov-arnold-networks","task_name":"Kolmogorov-Arnold Networks"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}