{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:P3KDJ6UVI7FY3ZE6OD6GR26NMD","short_pith_number":"pith:P3KDJ6UV","canonical_record":{"source":{"id":"2211.15641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-28T18:49:09Z","cross_cats_sorted":[],"title_canon_sha256":"8a08672c25090d7762c8c8fbfac2423e81f3aca296af541e2e5ec3347b0ac776","abstract_canon_sha256":"c34a47b3498bb7f68bfc997e3bfa360b66ffb9b5db7326240a5d7ea375f57bdf"},"schema_version":"1.0"},"canonical_sha256":"7ed434fa9547cb8de49e70fc68ebcd60efe8d17b75f7d49d3b4617b0985df3ec","source":{"kind":"arxiv","id":"2211.15641","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.15641","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"2211.15641v1","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.15641","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"P3KDJ6UVI7FY","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_16","alias_value":"P3KDJ6UVI7FY3ZE6","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_8","alias_value":"P3KDJ6UV","created_at":"2026-07-05T05:20:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:P3KDJ6UVI7FY3ZE6OD6GR26NMD","target":"record","payload":{"canonical_record":{"source":{"id":"2211.15641","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-28T18:49:09Z","cross_cats_sorted":[],"title_canon_sha256":"8a08672c25090d7762c8c8fbfac2423e81f3aca296af541e2e5ec3347b0ac776","abstract_canon_sha256":"c34a47b3498bb7f68bfc997e3bfa360b66ffb9b5db7326240a5d7ea375f57bdf"},"schema_version":"1.0"},"canonical_sha256":"7ed434fa9547cb8de49e70fc68ebcd60efe8d17b75f7d49d3b4617b0985df3ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:20:06.284214Z","signature_b64":"VmeGCwFou5GySFiDe1Ow1RER3Z+MIfwT4Z24PTxLie8yF7URwkUG17OscD3LrPzrLij4lkh4NJuarH8cmybsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ed434fa9547cb8de49e70fc68ebcd60efe8d17b75f7d49d3b4617b0985df3ec","last_reissued_at":"2026-07-05T05:20:06.283723Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:20:06.283723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.15641","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":"2026-07-05T05:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pTNwCdq8ZI4ZulDAD9L2a4+mRU2o9d6nqwNWPdZECVGYaGUhZ5bJWiTFOi0/4xMnzIplbt2CzKf9ZCTHb9sYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T06:27:16.017833Z"},"content_sha256":"123efb7daf4531f045dd68f23dabfdec69686c176ff744adbe605dc1fb8474a0","schema_version":"1.0","event_id":"sha256:123efb7daf4531f045dd68f23dabfdec69686c176ff744adbe605dc1fb8474a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:P3KDJ6UVI7FY3ZE6OD6GR26NMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Arnulf Jentzen, Davide Gallon, Felix Lindner","submitted_at":"2022-11-28T18:49:09Z","abstract_excerpt":"In this article we investigate blow up phenomena for gradient descent optimization methods in the training of artificial neural networks (ANNs). Our theoretical analysis is focused on shallow ANNs with one neuron on the input layer, one neuron on the output layer, and one hidden layer. For ANNs with ReLU activation and at least two neurons on the hidden layer we establish the existence of a target function such that there exists a lower bound for the risk values of the critical points of the associated risk function which is strictly greater than the infimum of the image of the risk function. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.15641","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.15641/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":"2026-07-05T05:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSzQs5HTQQ4YgL2XM1fuvhxaNJG5zmeoHMsJtLrGnFrgLIB8yh+fJ4IyqLITRshjoYMAio4VzbbYjlxBhX/rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T06:27:16.018699Z"},"content_sha256":"8c28f3f30182adf1a6ccbd7a91c44cab38fd9b747405148575699dc9d29c137b","schema_version":"1.0","event_id":"sha256:8c28f3f30182adf1a6ccbd7a91c44cab38fd9b747405148575699dc9d29c137b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3KDJ6UVI7FY3ZE6OD6GR26NMD/bundle.json","state_url":"https://pith.science/pith/P3KDJ6UVI7FY3ZE6OD6GR26NMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3KDJ6UVI7FY3ZE6OD6GR26NMD/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":"2026-08-22T06:27:16Z","links":{"resolver":"https://pith.science/pith/P3KDJ6UVI7FY3ZE6OD6GR26NMD","bundle":"https://pith.science/pith/P3KDJ6UVI7FY3ZE6OD6GR26NMD/bundle.json","state":"https://pith.science/pith/P3KDJ6UVI7FY3ZE6OD6GR26NMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3KDJ6UVI7FY3ZE6OD6GR26NMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:P3KDJ6UVI7FY3ZE6OD6GR26NMD","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":"c34a47b3498bb7f68bfc997e3bfa360b66ffb9b5db7326240a5d7ea375f57bdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-28T18:49:09Z","title_canon_sha256":"8a08672c25090d7762c8c8fbfac2423e81f3aca296af541e2e5ec3347b0ac776"},"schema_version":"1.0","source":{"id":"2211.15641","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.15641","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"2211.15641v1","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.15641","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"P3KDJ6UVI7FY","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_16","alias_value":"P3KDJ6UVI7FY3ZE6","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_8","alias_value":"P3KDJ6UV","created_at":"2026-07-05T05:20:06Z"}],"graph_snapshots":[{"event_id":"sha256:8c28f3f30182adf1a6ccbd7a91c44cab38fd9b747405148575699dc9d29c137b","target":"graph","created_at":"2026-07-05T05:20:06Z","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/2211.15641/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we investigate blow up phenomena for gradient descent optimization methods in the training of artificial neural networks (ANNs). Our theoretical analysis is focused on shallow ANNs with one neuron on the input layer, one neuron on the output layer, and one hidden layer. For ANNs with ReLU activation and at least two neurons on the hidden layer we establish the existence of a target function such that there exists a lower bound for the risk values of the critical points of the associated risk function which is strictly greater than the infimum of the image of the risk function. ","authors_text":"Arnulf Jentzen, Davide Gallon, Felix Lindner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-28T18:49:09Z","title":"Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.15641","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":"sha256:123efb7daf4531f045dd68f23dabfdec69686c176ff744adbe605dc1fb8474a0","target":"record","created_at":"2026-07-05T05:20:06Z","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":"c34a47b3498bb7f68bfc997e3bfa360b66ffb9b5db7326240a5d7ea375f57bdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-11-28T18:49:09Z","title_canon_sha256":"8a08672c25090d7762c8c8fbfac2423e81f3aca296af541e2e5ec3347b0ac776"},"schema_version":"1.0","source":{"id":"2211.15641","kind":"arxiv","version":1}},"canonical_sha256":"7ed434fa9547cb8de49e70fc68ebcd60efe8d17b75f7d49d3b4617b0985df3ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ed434fa9547cb8de49e70fc68ebcd60efe8d17b75f7d49d3b4617b0985df3ec","first_computed_at":"2026-07-05T05:20:06.283723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:20:06.283723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VmeGCwFou5GySFiDe1Ow1RER3Z+MIfwT4Z24PTxLie8yF7URwkUG17OscD3LrPzrLij4lkh4NJuarH8cmybsBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:20:06.284214Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.15641","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:123efb7daf4531f045dd68f23dabfdec69686c176ff744adbe605dc1fb8474a0","sha256:8c28f3f30182adf1a6ccbd7a91c44cab38fd9b747405148575699dc9d29c137b"],"state_sha256":"d3592d5042f8ee2b3fe6e5adf350894116049ca914a4e62d0ed41b91046afc90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2vSnN6tGiQW6GK60WsBPmMGiMQN6im2+bC2l+T+cgdAWv/DNtLJGVck4rbDgk7L6uZrK/cx+Q506bE5S9Je+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T06:27:16.022069Z","bundle_sha256":"352840a59efbb88b8a49894a36e123dfb24ef681ca4c94f68114bc92df81344d"}}