{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:P2WWTPFH3FS6E76KOXCYCUQS6S","short_pith_number":"pith:P2WWTPFH","schema_version":"1.0","canonical_sha256":"7ead69bca7d965e27fca75c5815212f4b2bb5cceee8c5bc789570e84d555533b","source":{"kind":"arxiv","id":"2406.07456","version":1},"attestation_state":"computed","paper":{"title":"fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Alireza Afzal Aghaei","submitted_at":"2024-06-11T17:01:45Z","abstract_excerpt":"Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs), which enhance speed, interpretability, and precision. This paper presents the Fractional Kolmogorov-Arnold Network (fKAN), a novel neural network architecture that incorporates the distinctive attributes of KANs with a trainable adaptive fractional-orthogonal Jacobi function as its basis function. By leveraging the unique mathematical properties of fractional Jacobi functions, including simple derivative formulas, non-polynomial behavior, and activity for both positive and nega"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2406.07456","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-11T17:01:45Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"866d5f3b91224d337dbc5a0e524aee50e6ce00d55d348ef19df3f23593408c85","abstract_canon_sha256":"c6dd2dc90313e44366e351e530815688dec510a47c68ac0e997fa42a0f9fa97d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:30:25.706890Z","signature_b64":"ypK1ukbYHno17NGT3i26n1Zqi1K9ET1sskeYzISFo4dEuZ2m7bQB7K1s0pA4DfClYbJ3Rm4ypQtqrnye6eiCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ead69bca7d965e27fca75c5815212f4b2bb5cceee8c5bc789570e84d555533b","last_reissued_at":"2026-07-05T08:30:25.706257Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:30:25.706257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Alireza Afzal Aghaei","submitted_at":"2024-06-11T17:01:45Z","abstract_excerpt":"Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs), which enhance speed, interpretability, and precision. This paper presents the Fractional Kolmogorov-Arnold Network (fKAN), a novel neural network architecture that incorporates the distinctive attributes of KANs with a trainable adaptive fractional-orthogonal Jacobi function as its basis function. By leveraging the unique mathematical properties of fractional Jacobi functions, including simple derivative formulas, non-polynomial behavior, and activity for both positive and nega"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.07456","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.07456/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2406.07456","created_at":"2026-07-05T08:30:25.706330+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.07456v1","created_at":"2026-07-05T08:30:25.706330+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.07456","created_at":"2026-07-05T08:30:25.706330+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2WWTPFH3FS6","created_at":"2026-07-05T08:30:25.706330+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2WWTPFH3FS6E76K","created_at":"2026-07-05T08:30:25.706330+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2WWTPFH","created_at":"2026-07-05T08:30:25.706330+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2410.04435","citing_title":"QKAN: quantum Kolmogorov-Arnold networks with applications in machine learning and multivariate state preparation","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2410.04096","citing_title":"Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2510.25781","citing_title":"A Practitioner's Guide to Kolmogorov-Arnold Networks","ref_index":134,"is_internal_anchor":false},{"citing_arxiv_id":"2604.23599","citing_title":"Partition-of-Unity Gaussian Kolmogorov-Arnold Networks","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21174","citing_title":"Scale-Parameter Selection in Gaussian Kolmogorov-Arnold Networks","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2604.16842","citing_title":"Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S","json":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S.json","graph_json":"https://pith.science/api/pith-number/P2WWTPFH3FS6E76KOXCYCUQS6S/graph.json","events_json":"https://pith.science/api/pith-number/P2WWTPFH3FS6E76KOXCYCUQS6S/events.json","paper":"https://pith.science/paper/P2WWTPFH"},"agent_actions":{"view_html":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S","download_json":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S.json","view_paper":"https://pith.science/paper/P2WWTPFH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.07456&json=true","fetch_graph":"https://pith.science/api/pith-number/P2WWTPFH3FS6E76KOXCYCUQS6S/graph.json","fetch_events":"https://pith.science/api/pith-number/P2WWTPFH3FS6E76KOXCYCUQS6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S/action/storage_attestation","attest_author":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S/action/author_attestation","sign_citation":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S/action/citation_signature","submit_replication":"https://pith.science/pith/P2WWTPFH3FS6E76KOXCYCUQS6S/action/replication_record"}},"created_at":"2026-07-05T08:30:25.706330+00:00","updated_at":"2026-07-05T08:30:25.706330+00:00"}