{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:X5FYLP26B4OXSOAGTZEMIBGRU3","short_pith_number":"pith:X5FYLP26","schema_version":"1.0","canonical_sha256":"bf4b85bf5e0f1d7938069e48c404d1a6f2bcd58a93e941bc47a444262f09331c","source":{"kind":"arxiv","id":"1609.04112","version":2},"attestation_state":"computed","paper":{"title":"Understanding Convolutional Neural Networks with A Mathematical Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"C.-C. Jay Kuo","submitted_at":"2016-09-14T02:17:09Z","abstract_excerpt":"This work attempts to address two fundamental questions about the structure of the convolutional neural networks (CNN): 1) why a non-linear activation function is essential at the filter output of every convolutional layer? 2) what is the advantage of the two-layer cascade system over the one-layer system? A mathematical model called the \"REctified-COrrelations on a Sphere\" (RECOS) is proposed to answer these two questions. After the CNN training process, the converged filter weights define a set of anchor vectors in the RECOS model. Anchor vectors represent the frequently occurring patterns ("},"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":"1609.04112","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-09-14T02:17:09Z","cross_cats_sorted":[],"title_canon_sha256":"27188058a84c5ea1f4b075f788fe6cda3de5ae299b05a54e41c7a2abe5097f33","abstract_canon_sha256":"83e9fc13c6939f4c825e1bd5d00d162482607711dbb7445bcf0685edebb7244b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:18.999771Z","signature_b64":"YLId1lapvfzXbNfKH3Fk8OebyhJ74cnA3R2uD8jgLJdKeBxujoMBOZkV6A99WL+Mcm04Mg+EnibyMKz3/JZnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf4b85bf5e0f1d7938069e48c404d1a6f2bcd58a93e941bc47a444262f09331c","last_reissued_at":"2026-05-18T01:00:18.999146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:18.999146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Understanding Convolutional Neural Networks with A Mathematical Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"C.-C. Jay Kuo","submitted_at":"2016-09-14T02:17:09Z","abstract_excerpt":"This work attempts to address two fundamental questions about the structure of the convolutional neural networks (CNN): 1) why a non-linear activation function is essential at the filter output of every convolutional layer? 2) what is the advantage of the two-layer cascade system over the one-layer system? A mathematical model called the \"REctified-COrrelations on a Sphere\" (RECOS) is proposed to answer these two questions. After the CNN training process, the converged filter weights define a set of anchor vectors in the RECOS model. Anchor vectors represent the frequently occurring patterns ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04112","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":""},"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":"1609.04112","created_at":"2026-05-18T01:00:18.999227+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04112v2","created_at":"2026-05-18T01:00:18.999227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04112","created_at":"2026-05-18T01:00:18.999227+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5FYLP26B4OX","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5FYLP26B4OXSOAG","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5FYLP26","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3","json":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3.json","graph_json":"https://pith.science/api/pith-number/X5FYLP26B4OXSOAGTZEMIBGRU3/graph.json","events_json":"https://pith.science/api/pith-number/X5FYLP26B4OXSOAGTZEMIBGRU3/events.json","paper":"https://pith.science/paper/X5FYLP26"},"agent_actions":{"view_html":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3","download_json":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3.json","view_paper":"https://pith.science/paper/X5FYLP26","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04112&json=true","fetch_graph":"https://pith.science/api/pith-number/X5FYLP26B4OXSOAGTZEMIBGRU3/graph.json","fetch_events":"https://pith.science/api/pith-number/X5FYLP26B4OXSOAGTZEMIBGRU3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3/action/storage_attestation","attest_author":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3/action/author_attestation","sign_citation":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3/action/citation_signature","submit_replication":"https://pith.science/pith/X5FYLP26B4OXSOAGTZEMIBGRU3/action/replication_record"}},"created_at":"2026-05-18T01:00:18.999227+00:00","updated_at":"2026-05-18T01:00:18.999227+00:00"}