{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:6VBO575FCLILAC23QHTJ6XSOLC","short_pith_number":"pith:6VBO575F","schema_version":"1.0","canonical_sha256":"f542eeffa512d0b00b5b81e69f5e4e58b21943fe98b2c0973ed0f33dfe25da3c","source":{"kind":"arxiv","id":"2407.19258","version":1},"attestation_state":"computed","paper":{"title":"Comprehensive Survey of Complex-Valued Neural Networks: Insights into Backpropagation and Activation Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"M. M. Hammad","submitted_at":"2024-07-27T13:47:16Z","abstract_excerpt":"Artificial neural networks (ANNs), particularly those employing deep learning models, have found widespread application in fields such as computer vision, signal processing, and wireless communications, where complex numbers are crucial. Despite the prevailing use of real-number implementations in current ANN frameworks, there is a growing interest in developing ANNs that utilize complex numbers. This paper presents a comprehensive survey of recent advancements in complex-valued neural networks (CVNNs), focusing on their activation functions (AFs) and learning algorithms. We delve into the ext"},"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":"2407.19258","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-07-27T13:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"0f4f80fd10f9ea5ec82c7398a7d6c828bc567f81016ddad1d1cb10aaa2121bec","abstract_canon_sha256":"3cf846b2591c14c674961956f728a934dcff6640a8bf03e43cf136a5fa238fd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:49:16.501459Z","signature_b64":"nnp0d36dZ4Bh7AaJckEbEeuN5kuQPzbBBJT6GqcDZl/MZ1PyrxoDzYfk3IPGTZUAGgjlADD/m+vEvi7tiEpwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f542eeffa512d0b00b5b81e69f5e4e58b21943fe98b2c0973ed0f33dfe25da3c","last_reissued_at":"2026-07-05T08:49:16.501089Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:49:16.501089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comprehensive Survey of Complex-Valued Neural Networks: Insights into Backpropagation and Activation Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"M. M. Hammad","submitted_at":"2024-07-27T13:47:16Z","abstract_excerpt":"Artificial neural networks (ANNs), particularly those employing deep learning models, have found widespread application in fields such as computer vision, signal processing, and wireless communications, where complex numbers are crucial. Despite the prevailing use of real-number implementations in current ANN frameworks, there is a growing interest in developing ANNs that utilize complex numbers. This paper presents a comprehensive survey of recent advancements in complex-valued neural networks (CVNNs), focusing on their activation functions (AFs) and learning algorithms. We delve into the ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19258","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/2407.19258/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":"2407.19258","created_at":"2026-07-05T08:49:16.501144+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.19258v1","created_at":"2026-07-05T08:49:16.501144+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.19258","created_at":"2026-07-05T08:49:16.501144+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VBO575FCLIL","created_at":"2026-07-05T08:49:16.501144+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VBO575FCLILAC23","created_at":"2026-07-05T08:49:16.501144+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VBO575F","created_at":"2026-07-05T08:49:16.501144+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.27134","citing_title":"Fast summation on rectangular cuboids with arbitrary periodicity in the DMK framework","ref_index":55,"is_internal_anchor":false},{"citing_arxiv_id":"2509.04154","citing_title":"Robust Filter Attention: Self-Attention as Precision-Weighted State Estimation","ref_index":36,"is_internal_anchor":false},{"citing_arxiv_id":"2604.02615","citing_title":"Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC","json":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC.json","graph_json":"https://pith.science/api/pith-number/6VBO575FCLILAC23QHTJ6XSOLC/graph.json","events_json":"https://pith.science/api/pith-number/6VBO575FCLILAC23QHTJ6XSOLC/events.json","paper":"https://pith.science/paper/6VBO575F"},"agent_actions":{"view_html":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC","download_json":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC.json","view_paper":"https://pith.science/paper/6VBO575F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.19258&json=true","fetch_graph":"https://pith.science/api/pith-number/6VBO575FCLILAC23QHTJ6XSOLC/graph.json","fetch_events":"https://pith.science/api/pith-number/6VBO575FCLILAC23QHTJ6XSOLC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC/action/storage_attestation","attest_author":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC/action/author_attestation","sign_citation":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC/action/citation_signature","submit_replication":"https://pith.science/pith/6VBO575FCLILAC23QHTJ6XSOLC/action/replication_record"}},"created_at":"2026-07-05T08:49:16.501144+00:00","updated_at":"2026-07-05T08:49:16.501144+00:00"}