{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:XGWX4WI3KREBTXEI2ZH3OKUYK2","short_pith_number":"pith:XGWX4WI3","canonical_record":{"source":{"id":"2304.02976","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2023-04-06T10:02:54Z","cross_cats_sorted":["cs.LG","cs.SY"],"title_canon_sha256":"ecdf6ee170055f24fe13ef9e540feb58fb0696b61e6bb0933ddaa5ef090b9ff3","abstract_canon_sha256":"9a1fa74e855ef80cb1a13e8e0f45de0372d83c71bccc554f17696b34cee518b7"},"schema_version":"1.0"},"canonical_sha256":"b9ad7e591b544819dc88d64fb72a98568e507f18d046f1a4b6cf223687ca3406","source":{"kind":"arxiv","id":"2304.02976","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.02976","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"arxiv_version","alias_value":"2304.02976v2","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.02976","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"pith_short_12","alias_value":"XGWX4WI3KREB","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"pith_short_16","alias_value":"XGWX4WI3KREBTXEI","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"pith_short_8","alias_value":"XGWX4WI3","created_at":"2026-07-05T06:50:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:XGWX4WI3KREBTXEI2ZH3OKUYK2","target":"record","payload":{"canonical_record":{"source":{"id":"2304.02976","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2023-04-06T10:02:54Z","cross_cats_sorted":["cs.LG","cs.SY"],"title_canon_sha256":"ecdf6ee170055f24fe13ef9e540feb58fb0696b61e6bb0933ddaa5ef090b9ff3","abstract_canon_sha256":"9a1fa74e855ef80cb1a13e8e0f45de0372d83c71bccc554f17696b34cee518b7"},"schema_version":"1.0"},"canonical_sha256":"b9ad7e591b544819dc88d64fb72a98568e507f18d046f1a4b6cf223687ca3406","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:50:54.463942Z","signature_b64":"6929QT/sL5+tYecNiXkGTqiy3OH8+R9ghxNuToK4D7Yb028ePTVnFSPuCTW7XJ9gec9SRFzCohjBMorBX3h9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9ad7e591b544819dc88d64fb72a98568e507f18d046f1a4b6cf223687ca3406","last_reissued_at":"2026-07-05T06:50:54.463463Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:50:54.463463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.02976","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:50:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCIrBj0nzlLzgXuC9P0RXnHISjVYSwPD4iwc85jFIBrx+85YrEk+U98Zh0QwmWeyXG+XxOKDLgA6G2yTX4mXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:38:10.007905Z"},"content_sha256":"98c7f475bec24b1065538991efa604e18608d7f10218cc5f31447d62788cc503","schema_version":"1.0","event_id":"sha256:98c7f475bec24b1065538991efa604e18608d7f10218cc5f31447d62788cc503"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:XGWX4WI3KREBTXEI2ZH3OKUYK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.SY"],"primary_cat":"eess.SY","authors_text":"Clara Luc\\'ia Galimberti, Daniele Martinelli, Giancarlo Ferrari-Trecate, Ian R. Manchester, Luca Furieri","submitted_at":"2023-04-06T10:02:54Z","abstract_excerpt":"In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Recurrent Equilibrium Networks (RENs). We show how to endow our proposed NodeRENs with contractivity and dissipativity -- crucial properties for robust learning and control. Most importantly, as for RENs, we derive parametrizations of contractive and dissipative NodeRENs which are unconstrained, hence enabling their learning for a large number o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.02976","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.02976/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:50:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w04l6AJh2SVFjTd7A2gZgjvLMKGAYCzwT6Rp88aVWQ5gRPJzRdCSWSIikcFmaJTgdPso5at5ITKB3s6hTutyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:38:10.008480Z"},"content_sha256":"bd786681314ddee2d2269565eb7593f8dc9533f1cdd2e789f8b704dc2676a987","schema_version":"1.0","event_id":"sha256:bd786681314ddee2d2269565eb7593f8dc9533f1cdd2e789f8b704dc2676a987"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XGWX4WI3KREBTXEI2ZH3OKUYK2/bundle.json","state_url":"https://pith.science/pith/XGWX4WI3KREBTXEI2ZH3OKUYK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XGWX4WI3KREBTXEI2ZH3OKUYK2/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":"2026-08-14T23:38:10Z","links":{"resolver":"https://pith.science/pith/XGWX4WI3KREBTXEI2ZH3OKUYK2","bundle":"https://pith.science/pith/XGWX4WI3KREBTXEI2ZH3OKUYK2/bundle.json","state":"https://pith.science/pith/XGWX4WI3KREBTXEI2ZH3OKUYK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XGWX4WI3KREBTXEI2ZH3OKUYK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:XGWX4WI3KREBTXEI2ZH3OKUYK2","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":"9a1fa74e855ef80cb1a13e8e0f45de0372d83c71bccc554f17696b34cee518b7","cross_cats_sorted":["cs.LG","cs.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2023-04-06T10:02:54Z","title_canon_sha256":"ecdf6ee170055f24fe13ef9e540feb58fb0696b61e6bb0933ddaa5ef090b9ff3"},"schema_version":"1.0","source":{"id":"2304.02976","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.02976","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"arxiv_version","alias_value":"2304.02976v2","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.02976","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"pith_short_12","alias_value":"XGWX4WI3KREB","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"pith_short_16","alias_value":"XGWX4WI3KREBTXEI","created_at":"2026-07-05T06:50:54Z"},{"alias_kind":"pith_short_8","alias_value":"XGWX4WI3","created_at":"2026-07-05T06:50:54Z"}],"graph_snapshots":[{"event_id":"sha256:bd786681314ddee2d2269565eb7593f8dc9533f1cdd2e789f8b704dc2676a987","target":"graph","created_at":"2026-07-05T06:50:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2304.02976/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Recurrent Equilibrium Networks (RENs). We show how to endow our proposed NodeRENs with contractivity and dissipativity -- crucial properties for robust learning and control. Most importantly, as for RENs, we derive parametrizations of contractive and dissipative NodeRENs which are unconstrained, hence enabling their learning for a large number o","authors_text":"Clara Luc\\'ia Galimberti, Daniele Martinelli, Giancarlo Ferrari-Trecate, Ian R. Manchester, Luca Furieri","cross_cats":["cs.LG","cs.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2023-04-06T10:02:54Z","title":"Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.02976","kind":"arxiv","version":2},"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":"sha256:98c7f475bec24b1065538991efa604e18608d7f10218cc5f31447d62788cc503","target":"record","created_at":"2026-07-05T06:50:54Z","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":"9a1fa74e855ef80cb1a13e8e0f45de0372d83c71bccc554f17696b34cee518b7","cross_cats_sorted":["cs.LG","cs.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"eess.SY","submitted_at":"2023-04-06T10:02:54Z","title_canon_sha256":"ecdf6ee170055f24fe13ef9e540feb58fb0696b61e6bb0933ddaa5ef090b9ff3"},"schema_version":"1.0","source":{"id":"2304.02976","kind":"arxiv","version":2}},"canonical_sha256":"b9ad7e591b544819dc88d64fb72a98568e507f18d046f1a4b6cf223687ca3406","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9ad7e591b544819dc88d64fb72a98568e507f18d046f1a4b6cf223687ca3406","first_computed_at":"2026-07-05T06:50:54.463463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:50:54.463463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6929QT/sL5+tYecNiXkGTqiy3OH8+R9ghxNuToK4D7Yb028ePTVnFSPuCTW7XJ9gec9SRFzCohjBMorBX3h9DA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:50:54.463942Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.02976","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98c7f475bec24b1065538991efa604e18608d7f10218cc5f31447d62788cc503","sha256:bd786681314ddee2d2269565eb7593f8dc9533f1cdd2e789f8b704dc2676a987"],"state_sha256":"71e97ff5b9756b50f4d629b9fa9db8e81988238273cc067a71a13f1a37127d50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LlkqCbZAH01infk8vYYCit6a9T4nifTymVRIngDMwqNVol01zcVe8xq5aFz/nL2s099TZ1fyyeLSmy636iWHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T23:38:10.013827Z","bundle_sha256":"961f5e7c7976d3d58704f7d58aca015d2fdb30365bf1079a21741c05a9fab65e"}}