{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:OS3K4GCJG5GSFLEW24DVH2EVF2","short_pith_number":"pith:OS3K4GCJ","schema_version":"1.0","canonical_sha256":"74b6ae1849374d22ac96d70753e8952eb7503af82e9bbc5246269c4411fffb79","source":{"kind":"arxiv","id":"2006.12070","version":3},"attestation_state":"computed","paper":{"title":"Lipschitz Recurrent Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alejandro Queiruga, Liam Hodgkinson, Michael W. Mahoney, N.Benjamin Erichson, Omri Azencot","submitted_at":"2020-06-22T08:44:52Z","abstract_excerpt":"Viewing recurrent neural networks (RNNs) as continuous-time dynamical systems, we propose a recurrent unit that describes the hidden state's evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity. This particular functional form facilitates stability analysis of the long-term behavior of the recurrent unit using tools from nonlinear systems theory. In turn, this enables architectural design decisions before experimentation. Sufficient conditions for global stability of the recurrent unit are obtained, motivating a novel scheme for constructing hidden-to-hidd"},"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":"2006.12070","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-22T08:44:52Z","cross_cats_sorted":["math.DS","stat.ML"],"title_canon_sha256":"831665279096c1206ac9dd4eb7fd25bafc91f6fbba74e1fbab75c8c1d6967450","abstract_canon_sha256":"008489e46252f3cee0004185c8031519e20eba1ee2e84f7cdd628639dc27add1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:34:40.337799Z","signature_b64":"V3reIoXVU8xiE8WS3ArZFXR7NaZXvqVWJklX+E0nqPciLfyL5oW+tu5lfrfAv92u0VSIlGNfs9fgti9W4AnPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74b6ae1849374d22ac96d70753e8952eb7503af82e9bbc5246269c4411fffb79","last_reissued_at":"2026-07-05T02:34:40.337386Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:34:40.337386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lipschitz Recurrent Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alejandro Queiruga, Liam Hodgkinson, Michael W. Mahoney, N.Benjamin Erichson, Omri Azencot","submitted_at":"2020-06-22T08:44:52Z","abstract_excerpt":"Viewing recurrent neural networks (RNNs) as continuous-time dynamical systems, we propose a recurrent unit that describes the hidden state's evolution with two parts: a well-understood linear component plus a Lipschitz nonlinearity. This particular functional form facilitates stability analysis of the long-term behavior of the recurrent unit using tools from nonlinear systems theory. In turn, this enables architectural design decisions before experimentation. Sufficient conditions for global stability of the recurrent unit are obtained, motivating a novel scheme for constructing hidden-to-hidd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.12070","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.12070/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2006.12070","created_at":"2026-07-05T02:34:40.337445+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.12070v3","created_at":"2026-07-05T02:34:40.337445+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.12070","created_at":"2026-07-05T02:34:40.337445+00:00"},{"alias_kind":"pith_short_12","alias_value":"OS3K4GCJG5GS","created_at":"2026-07-05T02:34:40.337445+00:00"},{"alias_kind":"pith_short_16","alias_value":"OS3K4GCJG5GSFLEW","created_at":"2026-07-05T02:34:40.337445+00:00"},{"alias_kind":"pith_short_8","alias_value":"OS3K4GCJ","created_at":"2026-07-05T02:34:40.337445+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2508.12121","citing_title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2","json":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2.json","graph_json":"https://pith.science/api/pith-number/OS3K4GCJG5GSFLEW24DVH2EVF2/graph.json","events_json":"https://pith.science/api/pith-number/OS3K4GCJG5GSFLEW24DVH2EVF2/events.json","paper":"https://pith.science/paper/OS3K4GCJ"},"agent_actions":{"view_html":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2","download_json":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2.json","view_paper":"https://pith.science/paper/OS3K4GCJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.12070&json=true","fetch_graph":"https://pith.science/api/pith-number/OS3K4GCJG5GSFLEW24DVH2EVF2/graph.json","fetch_events":"https://pith.science/api/pith-number/OS3K4GCJG5GSFLEW24DVH2EVF2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2/action/storage_attestation","attest_author":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2/action/author_attestation","sign_citation":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2/action/citation_signature","submit_replication":"https://pith.science/pith/OS3K4GCJG5GSFLEW24DVH2EVF2/action/replication_record"}},"created_at":"2026-07-05T02:34:40.337445+00:00","updated_at":"2026-07-05T02:34:40.337445+00:00"}