{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:BCJG43N7QNH3MUB6NQVZI7C36U","short_pith_number":"pith:BCJG43N7","schema_version":"1.0","canonical_sha256":"08926e6dbf834fb6503e6c2b947c5bf53120bc76d298c7aacc80f1e8e7e8de31","source":{"kind":"arxiv","id":"2311.01356","version":4},"attestation_state":"computed","paper":{"title":"Upper and lower bounds for the Lipschitz constant of random neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"stat.ML","authors_text":"Dominik St\\\"oger, Felix Voigtlaender, Paul Geuchen, Thomas Telaar","submitted_at":"2023-11-02T16:03:26Z","abstract_excerpt":"Empirical studies have widely demonstrated that neural networks are highly sensitive to small, adversarial perturbations of the input. The worst-case robustness against these so-called adversarial examples can be quantified by the Lipschitz constant of the neural network. In this paper, we study upper and lower bounds for the Lipschitz constant of random ReLU neural networks. Specifically, we assume that the weights and biases follow a generalization of the He initialization, where general symmetric distributions for the biases are permitted. For deep networks of fixed depth and sufficiently l"},"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":"2311.01356","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-02T16:03:26Z","cross_cats_sorted":["cs.LG","math.PR"],"title_canon_sha256":"12eda4fe88c5476a0599e47a29b2f1be7c238b5a938946661dfa7b268389315f","abstract_canon_sha256":"9019f584ab5c724ca4980493291cc3bbcb7ccbf1f9a8a8ecea4b26a43ba6bdf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:30:35.018309Z","signature_b64":"rJ0uOCksCOPMZ5pGo/3OSAlgyuTsAVfnZh4jiUFWEfdJBNL7/iGahjilBgSNk4UeXFjjUn0UgBh+SuZi8FPOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08926e6dbf834fb6503e6c2b947c5bf53120bc76d298c7aacc80f1e8e7e8de31","last_reissued_at":"2026-07-05T11:30:35.017838Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:30:35.017838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper and lower bounds for the Lipschitz constant of random neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"stat.ML","authors_text":"Dominik St\\\"oger, Felix Voigtlaender, Paul Geuchen, Thomas Telaar","submitted_at":"2023-11-02T16:03:26Z","abstract_excerpt":"Empirical studies have widely demonstrated that neural networks are highly sensitive to small, adversarial perturbations of the input. The worst-case robustness against these so-called adversarial examples can be quantified by the Lipschitz constant of the neural network. In this paper, we study upper and lower bounds for the Lipschitz constant of random ReLU neural networks. Specifically, we assume that the weights and biases follow a generalization of the He initialization, where general symmetric distributions for the biases are permitted. For deep networks of fixed depth and sufficiently l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.01356","kind":"arxiv","version":4},"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/2311.01356/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":"2311.01356","created_at":"2026-07-05T11:30:35.017898+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.01356v4","created_at":"2026-07-05T11:30:35.017898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.01356","created_at":"2026-07-05T11:30:35.017898+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCJG43N7QNH3","created_at":"2026-07-05T11:30:35.017898+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCJG43N7QNH3MUB6","created_at":"2026-07-05T11:30:35.017898+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCJG43N7","created_at":"2026-07-05T11:30:35.017898+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.19282","citing_title":"A Batch-Insensitive Dynamic GNN Approach to Address Temporal Discontinuity in Graph Streams","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U","json":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U.json","graph_json":"https://pith.science/api/pith-number/BCJG43N7QNH3MUB6NQVZI7C36U/graph.json","events_json":"https://pith.science/api/pith-number/BCJG43N7QNH3MUB6NQVZI7C36U/events.json","paper":"https://pith.science/paper/BCJG43N7"},"agent_actions":{"view_html":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U","download_json":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U.json","view_paper":"https://pith.science/paper/BCJG43N7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.01356&json=true","fetch_graph":"https://pith.science/api/pith-number/BCJG43N7QNH3MUB6NQVZI7C36U/graph.json","fetch_events":"https://pith.science/api/pith-number/BCJG43N7QNH3MUB6NQVZI7C36U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U/action/storage_attestation","attest_author":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U/action/author_attestation","sign_citation":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U/action/citation_signature","submit_replication":"https://pith.science/pith/BCJG43N7QNH3MUB6NQVZI7C36U/action/replication_record"}},"created_at":"2026-07-05T11:30:35.017898+00:00","updated_at":"2026-07-05T11:30:35.017898+00:00"}