{"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/exploring-the-potential-of-polynomial-basis","title":"Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials","arxiv_id":"2406.02583","date":"2024-05-30","proceeding":null,"authors":["Seyd Teymoor Seydi"],"abstract":"This paper presents a comprehensive survey of 18 distinct polynomials and their potential applications in Kolmogorov-Arnold Network (KAN) models as an alternative to traditional spline-based methods. The polynomials are classified into various groups based on their mathematical properties, such as orthogonal polynomials, hypergeometric polynomials, q-polynomials, Fibonacci-related polynomials, combinatorial polynomials, and number-theoretic polynomials. The study aims to investigate the suitability of these polynomials as basis functions in KAN models for complex tasks like handwritten digit classification on the MNIST dataset. The performance metrics of the KAN models, including overall accuracy, Kappa, and F1 score, are evaluated and compared. The Gottlieb-KAN model achieves the highest performance across all metrics, suggesting its potential as a suitable choice for the given task. However, further analysis and tuning of these polynomials on more complex datasets are necessary to fully understand their capabilities in KAN models. The source code for the implementation of these KAN models is available at https://github.com/seydi1370/Basis_Functions .","url_abs":"https://arxiv.org/abs/2406.02583v2","url_pdf":"https://arxiv.org/pdf/2406.02583v2.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":"exploring-the-potential-of-polynomial-basis","repo_url":"https://github.com/seydi1370/basis_functions","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"kolmogorov-arnold-networks","task_name":"Kolmogorov-Arnold Networks"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2406.02583","atlas_url":"https://app.syntology.ai/?focus=2406.02583","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2406.02583"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/seydi1370/basis_functions","reach":{"status":"ok"}}],"summary":{"ran":11,"unverified":1},"by_repo_kind":{"official":{"samples":12,"ran":11,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":12,"samples":[{"code_sha256_prefix":"d946280151e1d04c","entry":"al_salam_carlitz","repo":"seydi1370/basis_functions","repo_kind":"official","path":"AlSalamCarlitz.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/AlSalamCarlitz.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"d946280151e1d04c"}},{"code_sha256_prefix":"d9bc9bc30258d55e","entry":"askey_wilson","repo":"seydi1370/basis_functions","repo_kind":"official","path":"AskeyWilson.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/AskeyWilson.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"d9bc9bc30258d55e"}},{"code_sha256_prefix":"6d1f2d1b6f4abedc","entry":"bannai_ito","repo":"seydi1370/basis_functions","repo_kind":"official","path":"BannaiIto.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/BannaiIto.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"6d1f2d1b6f4abedc"}},{"code_sha256_prefix":"a0f91b275c9c8a88","entry":"boas_buck","repo":"seydi1370/basis_functions","repo_kind":"official","path":"BoasBuck.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/BoasBuck.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a0f91b275c9c8a88"}},{"code_sha256_prefix":"a23effbb302583b5","entry":"boubaker","repo":"seydi1370/basis_functions","repo_kind":"official","path":"Boubaker.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/Boubaker.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"a23effbb302583b5"}},{"code_sha256_prefix":"37c4efb766082045","entry":"fermat","repo":"seydi1370/basis_functions","repo_kind":"official","path":"Fermat.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/Fermat.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"37c4efb766082045"}},{"code_sha256_prefix":"aa6bebe2aba001b2","entry":"gottlieb","repo":"seydi1370/basis_functions","repo_kind":"official","path":"Gottlieb.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/Gottlieb.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"aa6bebe2aba001b2"}},{"code_sha256_prefix":"fc634f7c6aa7732b","entry":"heptanacci","repo":"seydi1370/basis_functions","repo_kind":"official","path":"Heptanacci.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/Heptanacci.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"fc634f7c6aa7732b"}},{"code_sha256_prefix":"f305665a5793276e","entry":"hexanacci","repo":"seydi1370/basis_functions","repo_kind":"official","path":"Hexanacci.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/Hexanacci.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"f305665a5793276e"}},{"code_sha256_prefix":"ed35cd01dbaec4f3","entry":"meixner_pollaczek","repo":"seydi1370/basis_functions","repo_kind":"official","path":"MeixnerPollaczek.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/MeixnerPollaczek.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"ed35cd01dbaec4f3"}},{"code_sha256_prefix":"aeb1f1f578139674","entry":"narayana","repo":"seydi1370/basis_functions","repo_kind":"official","path":"Narayana.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/Narayana.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"aeb1f1f578139674"}},{"code_sha256_prefix":"d9c7379f3daf27ac","entry":"charlier","repo":"seydi1370/basis_functions","repo_kind":"official","path":"Charlier.py","file_url":"https://github.com/seydi1370/basis_functions/blob/HEAD/Charlier.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"d9c7379f3daf27ac"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}