{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2QW6CKQL4JO54ZS4O7N5GGDBTH","short_pith_number":"pith:2QW6CKQL","schema_version":"1.0","canonical_sha256":"d42de12a0be25dde665c77dbd3186199c7a84c88aa92b1957948b279b9acaff6","source":{"kind":"arxiv","id":"2501.18959","version":2},"attestation_state":"computed","paper":{"title":"Enhancing Neural Function Approximation: The XNet Outperforming KAN","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Xiaotao Zheng, Xin Li, Zhihong Xia","submitted_at":"2025-01-31T08:33:10Z","abstract_excerpt":"XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we show that the Cauchy activation functions used in XNet can achieve arbitrary-order polynomial convergence, fundamentally outperforming traditional MLPs and Kolmogorov-Arnold Networks (KANs) that rely on increased depth or B-spline activations. Our extensive experiments on function approximation, PDE solving, and reinforcement learning demonstrate XNet's superior performance - reducing approximation error by up to 50"},"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":"2501.18959","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-31T08:33:10Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"8c23572bd65ee7c21fee4405ee69bb0afb1a44930cb870fef27073355ea19ac7","abstract_canon_sha256":"215d98d9e61bd8a277cd36c9e4dd311bfdafaf74dfc292fa10dd0fc853d1bc5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:08.369131Z","signature_b64":"e8zzuigG4DQhj7y0S56sHFphPkc1wjsHRz7ulkBaJeJbz6XWSbA8KwNg2PReNAh03gpnSVO9UsIJxxfR5oyNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d42de12a0be25dde665c77dbd3186199c7a84c88aa92b1957948b279b9acaff6","last_reissued_at":"2026-07-05T10:14:08.368649Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:08.368649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enhancing Neural Function Approximation: The XNet Outperforming KAN","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Xiaotao Zheng, Xin Li, Zhihong Xia","submitted_at":"2025-01-31T08:33:10Z","abstract_excerpt":"XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we show that the Cauchy activation functions used in XNet can achieve arbitrary-order polynomial convergence, fundamentally outperforming traditional MLPs and Kolmogorov-Arnold Networks (KANs) that rely on increased depth or B-spline activations. Our extensive experiments on function approximation, PDE solving, and reinforcement learning demonstrate XNet's superior performance - reducing approximation error by up to 50"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18959","kind":"arxiv","version":2},"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/2501.18959/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":"2501.18959","created_at":"2026-07-05T10:14:08.368709+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.18959v2","created_at":"2026-07-05T10:14:08.368709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18959","created_at":"2026-07-05T10:14:08.368709+00:00"},{"alias_kind":"pith_short_12","alias_value":"2QW6CKQL4JO5","created_at":"2026-07-05T10:14:08.368709+00:00"},{"alias_kind":"pith_short_16","alias_value":"2QW6CKQL4JO54ZS4","created_at":"2026-07-05T10:14:08.368709+00:00"},{"alias_kind":"pith_short_8","alias_value":"2QW6CKQL","created_at":"2026-07-05T10:14:08.368709+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2502.06238","citing_title":"XNet-Enhanced Deep BSDE Method and Numerical Analysis","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH","json":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH.json","graph_json":"https://pith.science/api/pith-number/2QW6CKQL4JO54ZS4O7N5GGDBTH/graph.json","events_json":"https://pith.science/api/pith-number/2QW6CKQL4JO54ZS4O7N5GGDBTH/events.json","paper":"https://pith.science/paper/2QW6CKQL"},"agent_actions":{"view_html":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH","download_json":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH.json","view_paper":"https://pith.science/paper/2QW6CKQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.18959&json=true","fetch_graph":"https://pith.science/api/pith-number/2QW6CKQL4JO54ZS4O7N5GGDBTH/graph.json","fetch_events":"https://pith.science/api/pith-number/2QW6CKQL4JO54ZS4O7N5GGDBTH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH/action/storage_attestation","attest_author":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH/action/author_attestation","sign_citation":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH/action/citation_signature","submit_replication":"https://pith.science/pith/2QW6CKQL4JO54ZS4O7N5GGDBTH/action/replication_record"}},"created_at":"2026-07-05T10:14:08.368709+00:00","updated_at":"2026-07-05T10:14:08.368709+00:00"}