{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DW6MUH3EO5NEEOFGARX5OSD7GR","short_pith_number":"pith:DW6MUH3E","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"},"canonical_sha256":"1dbcca1f64775a4238a6046fd7487f344e823b271200f90865bdd02e3b9310af","source":{"kind":"arxiv","id":"1811.09885","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09885","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09885v1","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09885","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"DW6MUH3EO5NE","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DW6MUH3EO5NEEOFG","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DW6MUH3E","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DW6MUH3EO5NEEOFGARX5OSD7GR","target":"record","payload":{"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"},"canonical_sha256":"1dbcca1f64775a4238a6046fd7487f344e823b271200f90865bdd02e3b9310af","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"},"source_kind":"arxiv","source_id":"1811.09885","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CogBJpz12wLmGQfrtDf7nhGyDBdNlOdGusFsYNEsBs3/WS4cNq4AGEt3JAyq7tsij/KHF8D6rhXXbIXKr8nNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T13:35:57.906873Z"},"content_sha256":"c280e3efea8525ef164b93274cbdbae5f7b606c5aca2fabc4f5a550be9244f1d","schema_version":"1.0","event_id":"sha256:c280e3efea8525ef164b93274cbdbae5f7b606c5aca2fabc4f5a550be9244f1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DW6MUH3EO5NEEOFGARX5OSD7GR","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l47L0/BY7dn56RHnO4gppDrnXZITGu7ndMP8WGgU+d/dJbtO+aB1B11ritJahRVy6nYFiWJEoKdJTcbZos39Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T13:35:57.907304Z"},"content_sha256":"d5b558eb15b8d246a6fe5227b177d64167ef0ef2be349f3e63d7d1525e686db1","schema_version":"1.0","event_id":"sha256:d5b558eb15b8d246a6fe5227b177d64167ef0ef2be349f3e63d7d1525e686db1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/bundle.json","state_url":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T13:35:57Z","links":{"resolver":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR","bundle":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/bundle.json","state":"https://pith.science/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DW6MUH3EO5NEEOFGARX5OSD7GR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DW6MUH3EO5NEEOFGARX5OSD7GR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"38a5cea918df204a16caa837b025f15230bfca6fb47af3ed8f2f276c559b07d4","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-11-24T19:43:22Z","title_canon_sha256":"1d415dc3705f89079a2ca9e604569b83b9b45907a54ef67d9b30c27e287a5bc6"},"schema_version":"1.0","source":{"id":"1811.09885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09885","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09885v1","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09885","created_at":"2026-05-17T23:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"DW6MUH3EO5NE","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DW6MUH3EO5NEEOFG","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DW6MUH3E","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:d5b558eb15b8d246a6fe5227b177d64167ef0ef2be349f3e63d7d1525e686db1","target":"graph","created_at":"2026-05-17T23:59:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Hayden Schaeffer, Linan Zhang","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-11-24T19:43:22Z","title":"Forward Stability of ResNet and Its Variants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09885","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c280e3efea8525ef164b93274cbdbae5f7b606c5aca2fabc4f5a550be9244f1d","target":"record","created_at":"2026-05-17T23:59:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"38a5cea918df204a16caa837b025f15230bfca6fb47af3ed8f2f276c559b07d4","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-11-24T19:43:22Z","title_canon_sha256":"1d415dc3705f89079a2ca9e604569b83b9b45907a54ef67d9b30c27e287a5bc6"},"schema_version":"1.0","source":{"id":"1811.09885","kind":"arxiv","version":1}},"canonical_sha256":"1dbcca1f64775a4238a6046fd7487f344e823b271200f90865bdd02e3b9310af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dbcca1f64775a4238a6046fd7487f344e823b271200f90865bdd02e3b9310af","first_computed_at":"2026-05-17T23:59:59.217418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:59.217418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"moX0liKTnoQsCR0a7FN+hK08r24GZo4fjcEejpw6Q1A/sXd+SY3OQdtEwrU+wC3pgnJqMgUBor+SwDtyrPYJAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:59.217880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c280e3efea8525ef164b93274cbdbae5f7b606c5aca2fabc4f5a550be9244f1d","sha256:d5b558eb15b8d246a6fe5227b177d64167ef0ef2be349f3e63d7d1525e686db1"],"state_sha256":"56caf51067a4b75cac2fbfab267b3b26dcde95d208c3cd643eeadb13dd957649"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J8Br0QWay+iwirpPcCA2CqqjL+GtpxvF3kmeYU69IdCW3uNjGaUCWSH/prii9MLndzhHenMyMBm2xhJQSbAmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T13:35:57.911512Z","bundle_sha256":"5aca69eed73630e9050f9160faa67b6c3ffea63536312fc0bc1d0cf3f764644f"}}