{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:MYP2RJIEZL53XUHALFVY7W23SM","short_pith_number":"pith:MYP2RJIE","canonical_record":{"source":{"id":"2004.13135","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2020-04-27T20:02:04Z","cross_cats_sorted":["cs.LG","q-fin.MF"],"title_canon_sha256":"09a9db42f5866c4df8edd27fafa10fd9281af6647745d186fc1c581dcfe9ee6e","abstract_canon_sha256":"ecdb74711a6ad3661a0f51b589e4231db43bd670b82ba9624231542672386c90"},"schema_version":"1.0"},"canonical_sha256":"661fa8a504cafbbbd0e0596b8fdb5b932f02695a24c0390111a21ed2dc651ff3","source":{"kind":"arxiv","id":"2004.13135","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.13135","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"2004.13135v3","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.13135","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"MYP2RJIEZL53","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"pith_short_16","alias_value":"MYP2RJIEZL53XUHA","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"pith_short_8","alias_value":"MYP2RJIE","created_at":"2026-07-05T05:40:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:MYP2RJIEZL53XUHALFVY7W23SM","target":"record","payload":{"canonical_record":{"source":{"id":"2004.13135","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2020-04-27T20:02:04Z","cross_cats_sorted":["cs.LG","q-fin.MF"],"title_canon_sha256":"09a9db42f5866c4df8edd27fafa10fd9281af6647745d186fc1c581dcfe9ee6e","abstract_canon_sha256":"ecdb74711a6ad3661a0f51b589e4231db43bd670b82ba9624231542672386c90"},"schema_version":"1.0"},"canonical_sha256":"661fa8a504cafbbbd0e0596b8fdb5b932f02695a24c0390111a21ed2dc651ff3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:40:03.217524Z","signature_b64":"CvHfaO4ZqAojORNp4LIQfqUxmb6EEe7KLiQG9j9Xb9gDxlmRNI8UIZ0RZev5q+7WThrfB8IER71HhMoNYAVWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"661fa8a504cafbbbd0e0596b8fdb5b932f02695a24c0390111a21ed2dc651ff3","last_reissued_at":"2026-07-05T05:40:03.217050Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:40:03.217050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.13135","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YL/Lz+JRBlbBp+gxeWO3xwknW6HkpiLvp5tIR25golx2SzX8qHSRJZpfvwMiKeoPtSV9gP+9oNOgijhqyYO0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T07:00:30.453696Z"},"content_sha256":"da7ee3a2394d41ccd5b7c84a4b7b1d33dc3141bdadf10f320f4c473a3748d482","schema_version":"1.0","event_id":"sha256:da7ee3a2394d41ccd5b7c84a4b7b1d33dc3141bdadf10f320f4c473a3748d482"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:MYP2RJIEZL53XUHALFVY7W23SM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Lipschitz Bounds of Deep Neural Networks","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.LG","q-fin.MF"],"primary_cat":"stat.ML","authors_text":"Calypso Herrera, Florian Krach, Josef Teichmann","submitted_at":"2020-04-27T20:02:04Z","abstract_excerpt":"The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an important problem that may be useful to the broader area of non-convex optimization. The main result provides a local upper bound on the Lipschitz constants of a multi-layer feed-forward neural network and its gradient. Moreover, lower bounds are established as well, which are used to show that it is impossible to derive global upper bounds for the Lipschitz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.13135","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/2004.13135/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":"2026-07-05T05:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qhR2Grpw6Z93oEOB9JfELzBLSTQyfif3zo5z6nsVfqCKzfOWlTSeD3d6yecibEJRZqMw+bE6U1jb8L8HkBrPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T07:00:30.454206Z"},"content_sha256":"9cbbdf4a4686248837b0a247229c234dab36765556c7e55c0aaabe3827dcffd4","schema_version":"1.0","event_id":"sha256:9cbbdf4a4686248837b0a247229c234dab36765556c7e55c0aaabe3827dcffd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MYP2RJIEZL53XUHALFVY7W23SM/bundle.json","state_url":"https://pith.science/pith/MYP2RJIEZL53XUHALFVY7W23SM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MYP2RJIEZL53XUHALFVY7W23SM/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":"2026-08-06T07:00:30Z","links":{"resolver":"https://pith.science/pith/MYP2RJIEZL53XUHALFVY7W23SM","bundle":"https://pith.science/pith/MYP2RJIEZL53XUHALFVY7W23SM/bundle.json","state":"https://pith.science/pith/MYP2RJIEZL53XUHALFVY7W23SM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MYP2RJIEZL53XUHALFVY7W23SM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:MYP2RJIEZL53XUHALFVY7W23SM","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":"ecdb74711a6ad3661a0f51b589e4231db43bd670b82ba9624231542672386c90","cross_cats_sorted":["cs.LG","q-fin.MF"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2020-04-27T20:02:04Z","title_canon_sha256":"09a9db42f5866c4df8edd27fafa10fd9281af6647745d186fc1c581dcfe9ee6e"},"schema_version":"1.0","source":{"id":"2004.13135","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.13135","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"2004.13135v3","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.13135","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"MYP2RJIEZL53","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"pith_short_16","alias_value":"MYP2RJIEZL53XUHA","created_at":"2026-07-05T05:40:03Z"},{"alias_kind":"pith_short_8","alias_value":"MYP2RJIE","created_at":"2026-07-05T05:40:03Z"}],"graph_snapshots":[{"event_id":"sha256:9cbbdf4a4686248837b0a247229c234dab36765556c7e55c0aaabe3827dcffd4","target":"graph","created_at":"2026-07-05T05:40:03Z","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/2004.13135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an important problem that may be useful to the broader area of non-convex optimization. The main result provides a local upper bound on the Lipschitz constants of a multi-layer feed-forward neural network and its gradient. Moreover, lower bounds are established as well, which are used to show that it is impossible to derive global upper bounds for the Lipschitz","authors_text":"Calypso Herrera, Florian Krach, Josef Teichmann","cross_cats":["cs.LG","q-fin.MF"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2020-04-27T20:02:04Z","title":"Local Lipschitz Bounds of Deep Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.13135","kind":"arxiv","version":3},"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:da7ee3a2394d41ccd5b7c84a4b7b1d33dc3141bdadf10f320f4c473a3748d482","target":"record","created_at":"2026-07-05T05:40:03Z","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":"ecdb74711a6ad3661a0f51b589e4231db43bd670b82ba9624231542672386c90","cross_cats_sorted":["cs.LG","q-fin.MF"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2020-04-27T20:02:04Z","title_canon_sha256":"09a9db42f5866c4df8edd27fafa10fd9281af6647745d186fc1c581dcfe9ee6e"},"schema_version":"1.0","source":{"id":"2004.13135","kind":"arxiv","version":3}},"canonical_sha256":"661fa8a504cafbbbd0e0596b8fdb5b932f02695a24c0390111a21ed2dc651ff3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"661fa8a504cafbbbd0e0596b8fdb5b932f02695a24c0390111a21ed2dc651ff3","first_computed_at":"2026-07-05T05:40:03.217050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:40:03.217050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CvHfaO4ZqAojORNp4LIQfqUxmb6EEe7KLiQG9j9Xb9gDxlmRNI8UIZ0RZev5q+7WThrfB8IER71HhMoNYAVWAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:40:03.217524Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.13135","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da7ee3a2394d41ccd5b7c84a4b7b1d33dc3141bdadf10f320f4c473a3748d482","sha256:9cbbdf4a4686248837b0a247229c234dab36765556c7e55c0aaabe3827dcffd4"],"state_sha256":"4d393b84d666f353092b6e08ebc58e51ab55ee5ccdeb9c9417ff29d4f0e08939"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nQsfOjIb9THSCDKAz3x5Oqk+HXO2BTHAO9aKybW04V9hBza0MQPRmsGobwLvsgupSF3bgatNAs57NLwxd0+lAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T07:00:30.458326Z","bundle_sha256":"94c25a8218728b47967fe99da12f533467573c805f6cb66e363bddb2d9df5480"}}