{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DW6MUH3EO5NEEOFGARX5OSD7GR","short_pith_number":"pith:DW6MUH3E","schema_version":"1.0","canonical_sha256":"1dbcca1f64775a4238a6046fd7487f344e823b271200f90865bdd02e3b9310af","source":{"kind":"arxiv","id":"1811.09885","version":1},"attestation_state":"computed","paper":{"title":"Forward Stability of ResNet and Its Variants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.CV","authors_text":"Hayden Schaeffer, Linan Zhang","submitted_at":"2018-11-24T19:43:22Z","abstract_excerpt":"The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work has been on establishing connections between ResNets and continuous-time optimal control problems. In this work, we show that the post-activation ResNet is related to an optimal control problem with differential inclusions, and provide continuous-time stability results for the differential inclusion associated with ResNet. Motivated by the stability conditions"},"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":"1811.09885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-11-24T19:43:22Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"1d415dc3705f89079a2ca9e604569b83b9b45907a54ef67d9b30c27e287a5bc6","abstract_canon_sha256":"38a5cea918df204a16caa837b025f15230bfca6fb47af3ed8f2f276c559b07d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:59.217880Z","signature_b64":"moX0liKTnoQsCR0a7FN+hK08r24GZo4fjcEejpw6Q1A/sXd+SY3OQdtEwrU+wC3pgnJqMgUBor+SwDtyrPYJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dbcca1f64775a4238a6046fd7487f344e823b271200f90865bdd02e3b9310af","last_reissued_at":"2026-05-17T23:59:59.217418Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:59.217418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forward Stability of ResNet and Its Variants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.CV","authors_text":"Hayden Schaeffer, Linan Zhang","submitted_at":"2018-11-24T19:43:22Z","abstract_excerpt":"The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work has been on establishing connections between ResNets and continuous-time optimal control problems. In this work, we show that the post-activation ResNet is related to an optimal control problem with differential inclusions, and provide continuous-time stability results for the differential inclusion associated with ResNet. Motivated by the stability conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09885","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":""},"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":"1811.09885","created_at":"2026-05-17T23:59:59.217490+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.09885v1","created_at":"2026-05-17T23:59:59.217490+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09885","created_at":"2026-05-17T23:59:59.217490+00:00"},{"alias_kind":"pith_short_12","alias_value":"DW6MUH3EO5NE","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DW6MUH3EO5NEEOFG","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DW6MUH3E","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.09853","citing_title":"Understand the Effectiveness of Shortcuts through the Lens of DCA","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR","json":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR.json","graph_json":"https://pith.science/api/pith-number/DW6MUH3EO5NEEOFGARX5OSD7GR/graph.json","events_json":"https://pith.science/api/pith-number/DW6MUH3EO5NEEOFGARX5OSD7GR/events.json","paper":"https://pith.science/paper/DW6MUH3E"},"agent_actions":{"view_html":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR","download_json":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR.json","view_paper":"https://pith.science/paper/DW6MUH3E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.09885&json=true","fetch_graph":"https://pith.science/api/pith-number/DW6MUH3EO5NEEOFGARX5OSD7GR/graph.json","fetch_events":"https://pith.science/api/pith-number/DW6MUH3EO5NEEOFGARX5OSD7GR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/action/storage_attestation","attest_author":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/action/author_attestation","sign_citation":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/action/citation_signature","submit_replication":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/action/replication_record"}},"created_at":"2026-05-17T23:59:59.217490+00:00","updated_at":"2026-05-17T23:59:59.217490+00:00"}