{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:55FSENDAPDY3SR7FWVT4W4MOE3","short_pith_number":"pith:55FSENDA","schema_version":"1.0","canonical_sha256":"ef4b22346078f1b947e5b567cb718e26dd404ed36531911fce95f2a911973f0a","source":{"kind":"arxiv","id":"1806.03751","version":3},"attestation_state":"computed","paper":{"title":"State Space Representations of Deep Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.NE","authors_text":"Asok Ray, Michael Hauser, Samer Saab Jr, Sean Gunn","submitted_at":"2018-06-11T00:26:13Z","abstract_excerpt":"This paper deals with neural networks as dynamical systems governed by differential or difference equations. It shows that the introduction of skip connections into network architectures, such as residual networks and dense networks, turns a system of static equations into a system of dynamical equations with varying levels of smoothness on the layer-wise transformations. Closed form solutions for the state space representations of general dense networks, as well as $k^{th}$ order smooth networks, are found in general settings. Furthermore, it is shown that imposing $k^{th}$ order smoothness o"},"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":"1806.03751","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2018-06-11T00:26:13Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"2de7d238b7e616bfa43a16e851997849e19885e394941af23619085a44894c27","abstract_canon_sha256":"657741c5016fbfa335dd0a9880ccbd5a989c9386ae5ea66f7d632b5328d179fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:59.126069Z","signature_b64":"dyBL1RD0yOrXujXc8uONxaLLI9kYHwguUqUtU1oVJDMBSx5qBq6+IaeRVYsbpR4kxEIYJkg6XCFr/jpHsMJoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef4b22346078f1b947e5b567cb718e26dd404ed36531911fce95f2a911973f0a","last_reissued_at":"2026-05-17T23:52:59.125534Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:59.125534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"State Space Representations of Deep Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.NE","authors_text":"Asok Ray, Michael Hauser, Samer Saab Jr, Sean Gunn","submitted_at":"2018-06-11T00:26:13Z","abstract_excerpt":"This paper deals with neural networks as dynamical systems governed by differential or difference equations. It shows that the introduction of skip connections into network architectures, such as residual networks and dense networks, turns a system of static equations into a system of dynamical equations with varying levels of smoothness on the layer-wise transformations. Closed form solutions for the state space representations of general dense networks, as well as $k^{th}$ order smooth networks, are found in general settings. Furthermore, it is shown that imposing $k^{th}$ order smoothness o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03751","kind":"arxiv","version":3},"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":"1806.03751","created_at":"2026-05-17T23:52:59.125616+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.03751v3","created_at":"2026-05-17T23:52:59.125616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03751","created_at":"2026-05-17T23:52:59.125616+00:00"},{"alias_kind":"pith_short_12","alias_value":"55FSENDAPDY3","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"55FSENDAPDY3SR7F","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"55FSENDA","created_at":"2026-05-18T12:32:05.422762+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/55FSENDAPDY3SR7FWVT4W4MOE3","json":"https://pith.science/pith/55FSENDAPDY3SR7FWVT4W4MOE3.json","graph_json":"https://pith.science/api/pith-number/55FSENDAPDY3SR7FWVT4W4MOE3/graph.json","events_json":"https://pith.science/api/pith-number/55FSENDAPDY3SR7FWVT4W4MOE3/events.json","paper":"https://pith.science/paper/55FSENDA"},"agent_actions":{"view_html":"https://pith.science/pith/55FSENDAPDY3SR7FWVT4W4MOE3","download_json":"https://pith.science/pith/55FSENDAPDY3SR7FWVT4W4MOE3.json","view_paper":"https://pith.science/paper/55FSENDA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.03751&json=true","fetch_graph":"https://pith.science/api/pith-number/55FSENDAPDY3SR7FWVT4W4MOE3/graph.json","fetch_events":"https://pith.science/api/pith-number/55FSENDAPDY3SR7FWVT4W4MOE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/55FSENDAPDY3SR7FWVT4W4MOE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/55FSENDAPDY3SR7FWVT4W4MOE3/action/storage_attestation","attest_author":"https://pith.science/pith/55FSENDAPDY3SR7FWVT4W4MOE3/action/author_attestation","sign_citation":"https://pith.science/pith/55FSENDAPDY3SR7FWVT4W4MOE3/action/citation_signature","submit_replication":"https://pith.science/pith/55FSENDAPDY3SR7FWVT4W4MOE3/action/replication_record"}},"created_at":"2026-05-17T23:52:59.125616+00:00","updated_at":"2026-05-17T23:52:59.125616+00:00"}