{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:HJ4SNSGZPBPO732KHHJEK45H6Y","short_pith_number":"pith:HJ4SNSGZ","canonical_record":{"source":{"id":"2205.08601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-05-17T19:42:23Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math.MP"],"title_canon_sha256":"1922d68063e72e1d495fef236f96eb661b9db83cd9e4c5e6cb868d18e9da2c05","abstract_canon_sha256":"9393a47127f5171c69a2c14d2c307ac880cd81dd9f5825a82eddcbce361b696d"},"schema_version":"1.0"},"canonical_sha256":"3a7926c8d9785eefef4a39d24573a7f610a6d4540f15e0dbc9565e214fc395f7","source":{"kind":"arxiv","id":"2205.08601","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.08601","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"arxiv_version","alias_value":"2205.08601v2","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.08601","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"pith_short_12","alias_value":"HJ4SNSGZPBPO","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"pith_short_16","alias_value":"HJ4SNSGZPBPO732K","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"pith_short_8","alias_value":"HJ4SNSGZ","created_at":"2026-07-05T10:50:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:HJ4SNSGZPBPO732KHHJEK45H6Y","target":"record","payload":{"canonical_record":{"source":{"id":"2205.08601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-05-17T19:42:23Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math.MP"],"title_canon_sha256":"1922d68063e72e1d495fef236f96eb661b9db83cd9e4c5e6cb868d18e9da2c05","abstract_canon_sha256":"9393a47127f5171c69a2c14d2c307ac880cd81dd9f5825a82eddcbce361b696d"},"schema_version":"1.0"},"canonical_sha256":"3a7926c8d9785eefef4a39d24573a7f610a6d4540f15e0dbc9565e214fc395f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:27.986264Z","signature_b64":"dO6Glie5OTnW2RBTzkGX159CMzUBT4fgEWO//++aztBV+HL8kmQuTwDL7Ktuu+oFtW0j4sBVMC84edeWC3d+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a7926c8d9785eefef4a39d24573a7f610a6d4540f15e0dbc9565e214fc395f7","last_reissued_at":"2026-07-05T10:50:27.985802Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:27.985802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.08601","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":"2026-07-05T10:50:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VlSBQT/q3utaQkJ2QB6FhZb4FlYpEHT4N6om5r5UHeae31MVAC0wYj8H7pkQsfsFSXz0qq8ukDduz2EeTB4yDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:38:59.867598Z"},"content_sha256":"0c78776e531181ffbe1b074fbf0ea1fa3bd9dceffcc687089d0d4336cbff01fc","schema_version":"1.0","event_id":"sha256:0c78776e531181ffbe1b074fbf0ea1fa3bd9dceffcc687089d0d4336cbff01fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:HJ4SNSGZPBPO732KHHJEK45H6Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal characteristics of deep neural network loss surfaces from random matrix theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG","math.MP"],"primary_cat":"math-ph","authors_text":"Diego Granziol, Francesco Mezzadri, Jonathan P Keating, Joseph Najnudel, Nicholas P Baskerville","submitted_at":"2022-05-17T19:42:23Z","abstract_excerpt":"This paper considers several aspects of random matrix universality in deep neural networks. Motivated by recent experimental work, we use universal properties of random matrices related to local statistics to derive practical implications for deep neural networks based on a realistic model of their Hessians. In particular we derive universal aspects of outliers in the spectra of deep neural networks and demonstrate the important role of random matrix local laws in popular pre-conditioning gradient descent algorithms. We also present insights into deep neural network loss surfaces from quite ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.08601","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/2205.08601/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":"2026-07-05T10:50:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LxhIYtNCPAmch8eTcVM8lxdO9tJuY7xGTLC04bbz2sLzCD0XxH3hZA/X23BW8rPNAZxqNQpYCZB74dkeDAOzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T12:38:59.868002Z"},"content_sha256":"8b9063bddf069315d7affa557f4b5aba3a0386af2c74acb0adf53e697b281bf3","schema_version":"1.0","event_id":"sha256:8b9063bddf069315d7affa557f4b5aba3a0386af2c74acb0adf53e697b281bf3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJ4SNSGZPBPO732KHHJEK45H6Y/bundle.json","state_url":"https://pith.science/pith/HJ4SNSGZPBPO732KHHJEK45H6Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJ4SNSGZPBPO732KHHJEK45H6Y/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":"2026-08-13T12:38:59Z","links":{"resolver":"https://pith.science/pith/HJ4SNSGZPBPO732KHHJEK45H6Y","bundle":"https://pith.science/pith/HJ4SNSGZPBPO732KHHJEK45H6Y/bundle.json","state":"https://pith.science/pith/HJ4SNSGZPBPO732KHHJEK45H6Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJ4SNSGZPBPO732KHHJEK45H6Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:HJ4SNSGZPBPO732KHHJEK45H6Y","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":"9393a47127f5171c69a2c14d2c307ac880cd81dd9f5825a82eddcbce361b696d","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-05-17T19:42:23Z","title_canon_sha256":"1922d68063e72e1d495fef236f96eb661b9db83cd9e4c5e6cb868d18e9da2c05"},"schema_version":"1.0","source":{"id":"2205.08601","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.08601","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"arxiv_version","alias_value":"2205.08601v2","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.08601","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"pith_short_12","alias_value":"HJ4SNSGZPBPO","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"pith_short_16","alias_value":"HJ4SNSGZPBPO732K","created_at":"2026-07-05T10:50:27Z"},{"alias_kind":"pith_short_8","alias_value":"HJ4SNSGZ","created_at":"2026-07-05T10:50:27Z"}],"graph_snapshots":[{"event_id":"sha256:8b9063bddf069315d7affa557f4b5aba3a0386af2c74acb0adf53e697b281bf3","target":"graph","created_at":"2026-07-05T10:50:27Z","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/2205.08601/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper considers several aspects of random matrix universality in deep neural networks. Motivated by recent experimental work, we use universal properties of random matrices related to local statistics to derive practical implications for deep neural networks based on a realistic model of their Hessians. In particular we derive universal aspects of outliers in the spectra of deep neural networks and demonstrate the important role of random matrix local laws in popular pre-conditioning gradient descent algorithms. We also present insights into deep neural network loss surfaces from quite ge","authors_text":"Diego Granziol, Francesco Mezzadri, Jonathan P Keating, Joseph Najnudel, Nicholas P Baskerville","cross_cats":["cond-mat.dis-nn","cs.LG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-05-17T19:42:23Z","title":"Universal characteristics of deep neural network loss surfaces from random matrix theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.08601","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":"sha256:0c78776e531181ffbe1b074fbf0ea1fa3bd9dceffcc687089d0d4336cbff01fc","target":"record","created_at":"2026-07-05T10:50:27Z","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":"9393a47127f5171c69a2c14d2c307ac880cd81dd9f5825a82eddcbce361b696d","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2022-05-17T19:42:23Z","title_canon_sha256":"1922d68063e72e1d495fef236f96eb661b9db83cd9e4c5e6cb868d18e9da2c05"},"schema_version":"1.0","source":{"id":"2205.08601","kind":"arxiv","version":2}},"canonical_sha256":"3a7926c8d9785eefef4a39d24573a7f610a6d4540f15e0dbc9565e214fc395f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a7926c8d9785eefef4a39d24573a7f610a6d4540f15e0dbc9565e214fc395f7","first_computed_at":"2026-07-05T10:50:27.985802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:50:27.985802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dO6Glie5OTnW2RBTzkGX159CMzUBT4fgEWO//++aztBV+HL8kmQuTwDL7Ktuu+oFtW0j4sBVMC84edeWC3d+BA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:50:27.986264Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.08601","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c78776e531181ffbe1b074fbf0ea1fa3bd9dceffcc687089d0d4336cbff01fc","sha256:8b9063bddf069315d7affa557f4b5aba3a0386af2c74acb0adf53e697b281bf3"],"state_sha256":"aa051e4f67b34dacba33d4fb0fe23c680fbdc486aae7a218afb6141a17c3580b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9PJ6l6DvKr5XOFaZ4CZHVeCQNC2et6Qd3oU/kU/hlgyPSsSZkVcjfJSBz6xFq6Pq439NEeG8cjBp7UC1ZAGAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T12:38:59.871053Z","bundle_sha256":"d9f5bc98965f126f80ef6f28d28fd8813513931548b1507acc1136fa066bf341"}}