{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:6HT4NIWUV3TRW5GUNKYQKT52IC","short_pith_number":"pith:6HT4NIWU","schema_version":"1.0","canonical_sha256":"f1e7c6a2d4aee71b74d46ab1054fba40b7888be2fb23cf24d7d8b7695619fb97","source":{"kind":"arxiv","id":"2410.00435","version":4},"attestation_state":"computed","paper":{"title":"Incorporating Arbitrary Matrix Group Equivariance into KANs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Lexiang Hu, Yisen Wang, Zhouchen Lin","submitted_at":"2024-10-01T06:34:58Z","abstract_excerpt":"Kolmogorov-Arnold Networks (KANs) have seen great success in scientific domains thanks to spline activation functions, becoming an alternative to Multi-Layer Perceptrons (MLPs). However, spline functions may not respect symmetry in tasks, which is crucial prior knowledge in machine learning. In this paper, we propose Equivariant Kolmogorov-Arnold Networks (EKAN), a method for incorporating arbitrary matrix group equivariance into KANs, aiming to broaden their applicability to more fields. We first construct gated spline basis functions, which form the EKAN layer together with equivariant linea"},"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":"2410.00435","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-01T06:34:58Z","cross_cats_sorted":[],"title_canon_sha256":"740dd1b65a5f5855af81353b3f73e499a79d0c591588293761c5fc31172cdbd8","abstract_canon_sha256":"9f5654a26b0423d6128e5e3ff42637b8f7a838c3504b37dfdf05a38f026a7601"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:54:28.539100Z","signature_b64":"f2P7RiM7uezwYOE2eyuBixfalXHVK3s2mhV5rG2cFqIEDzbltz+dmQFeADumWNj0EMgPkZ4P31JB4CmyagDyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1e7c6a2d4aee71b74d46ab1054fba40b7888be2fb23cf24d7d8b7695619fb97","last_reissued_at":"2026-07-05T11:54:28.538665Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:54:28.538665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incorporating Arbitrary Matrix Group Equivariance into KANs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Lexiang Hu, Yisen Wang, Zhouchen Lin","submitted_at":"2024-10-01T06:34:58Z","abstract_excerpt":"Kolmogorov-Arnold Networks (KANs) have seen great success in scientific domains thanks to spline activation functions, becoming an alternative to Multi-Layer Perceptrons (MLPs). However, spline functions may not respect symmetry in tasks, which is crucial prior knowledge in machine learning. In this paper, we propose Equivariant Kolmogorov-Arnold Networks (EKAN), a method for incorporating arbitrary matrix group equivariance into KANs, aiming to broaden their applicability to more fields. We first construct gated spline basis functions, which form the EKAN layer together with equivariant linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00435","kind":"arxiv","version":4},"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/2410.00435/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":"2410.00435","created_at":"2026-07-05T11:54:28.538721+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.00435v4","created_at":"2026-07-05T11:54:28.538721+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.00435","created_at":"2026-07-05T11:54:28.538721+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HT4NIWUV3TR","created_at":"2026-07-05T11:54:28.538721+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HT4NIWUV3TRW5GU","created_at":"2026-07-05T11:54:28.538721+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HT4NIWU","created_at":"2026-07-05T11:54:28.538721+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.07176","citing_title":"MatrixKAN: Parallelized Kolmogorov-Arnold Network","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC","json":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC.json","graph_json":"https://pith.science/api/pith-number/6HT4NIWUV3TRW5GUNKYQKT52IC/graph.json","events_json":"https://pith.science/api/pith-number/6HT4NIWUV3TRW5GUNKYQKT52IC/events.json","paper":"https://pith.science/paper/6HT4NIWU"},"agent_actions":{"view_html":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC","download_json":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC.json","view_paper":"https://pith.science/paper/6HT4NIWU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.00435&json=true","fetch_graph":"https://pith.science/api/pith-number/6HT4NIWUV3TRW5GUNKYQKT52IC/graph.json","fetch_events":"https://pith.science/api/pith-number/6HT4NIWUV3TRW5GUNKYQKT52IC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC/action/storage_attestation","attest_author":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC/action/author_attestation","sign_citation":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC/action/citation_signature","submit_replication":"https://pith.science/pith/6HT4NIWUV3TRW5GUNKYQKT52IC/action/replication_record"}},"created_at":"2026-07-05T11:54:28.538721+00:00","updated_at":"2026-07-05T11:54:28.538721+00:00"}