{"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/function-fitting-based-on-kolmogorov-arnold","title":"Function Fitting Based on Kolmogorov-Arnold Theorem and Kernel Functions","arxiv_id":"2503.23038","date":"2025-03-29","proceeding":null,"authors":["Jianpeng Liu","Qizhi Pan"],"abstract":"This paper proposes a unified theoretical framework based on the Kolmogorov-Arnold representation theorem and kernel methods. By analyzing the mathematical relationship among kernels, B-spline basis functions in Kolmogorov-Arnold Networks (KANs) and the inner product operation in self-attention mechanisms, we establish a kernel-based feature fitting framework that unifies the two models as linear combinations of kernel functions. Under this framework, we propose a low-rank Pseudo-Multi-Head Self-Attention module (Pseudo-MHSA), which reduces the parameter count of traditional MHSA by nearly 50\\%. Furthermore, we design a Gaussian kernel multi-head self-attention variant (Gaussian-MHSA) to validate the effectiveness of nonlinear kernel functions in feature extraction. Experiments on the CIFAR-10 dataset demonstrate that Pseudo-MHSA model achieves performance comparable to the ViT model of the same dimensionality under the MAE framework and visualization analysis reveals their similarity of multi-head distribution patterns. Our code is publicly available.","url_abs":"https://arxiv.org/abs/2503.23038v1","url_pdf":"https://arxiv.org/pdf/2503.23038v1.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":"function-fitting-based-on-kolmogorov-arnold","repo_url":"https://github.com/cfrslyr/Experiments","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"kolmogorov-arnold-networks","task_name":"Kolmogorov-Arnold Networks"}],"methods":[{"method_slug":"mae","method_name":"MAE"}],"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}