{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SKJZJQ7ZIEOW6PLDT7BTC3I66P","short_pith_number":"pith:SKJZJQ7Z","canonical_record":{"source":{"id":"1706.04454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-06-14T12:50:00Z","cross_cats_sorted":[],"title_canon_sha256":"8f65047c1bd0116a91b51e7a0bc79b3bf369107262955beabe1df872d4779bb9","abstract_canon_sha256":"f5e3ad147b8b566e36896de2c8d56201c1a248da8bf4a83b781ef3a5c137099c"},"schema_version":"1.0"},"canonical_sha256":"929394c3f9411d6f3d639fc3316d1ef3fd01bd461ad2a89afc8f11284ef108f5","source":{"kind":"arxiv","id":"1706.04454","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04454","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04454v3","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04454","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"pith_short_12","alias_value":"SKJZJQ7ZIEOW","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SKJZJQ7ZIEOW6PLD","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SKJZJQ7Z","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SKJZJQ7ZIEOW6PLDT7BTC3I66P","target":"record","payload":{"canonical_record":{"source":{"id":"1706.04454","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-06-14T12:50:00Z","cross_cats_sorted":[],"title_canon_sha256":"8f65047c1bd0116a91b51e7a0bc79b3bf369107262955beabe1df872d4779bb9","abstract_canon_sha256":"f5e3ad147b8b566e36896de2c8d56201c1a248da8bf4a83b781ef3a5c137099c"},"schema_version":"1.0"},"canonical_sha256":"929394c3f9411d6f3d639fc3316d1ef3fd01bd461ad2a89afc8f11284ef108f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:45.252801Z","signature_b64":"R4+PD7EnY6FfxF7Jfi7P4WAH4d9ZAIXqc6w94Gmb0ZOoAvUQuk4kyEA0p40uXZqJXi1cEA9qteWho7T9OLHUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"929394c3f9411d6f3d639fc3316d1ef3fd01bd461ad2a89afc8f11284ef108f5","last_reissued_at":"2026-05-18T00:16:45.252198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:45.252198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.04454","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":"2026-05-18T00:16:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WeyKlBnJb0OKMmhA+5jkidDbrYj76gijUV9rqmoSDjgbNg+3kQ0M2Fyj6Xp1f/GlbvU7Z3iglBqjev7qf4AqBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:13:59.282758Z"},"content_sha256":"fa52aef614a6162f816ba8d174ff8d599675eeca7e870245b23685268805b994","schema_version":"1.0","event_id":"sha256:fa52aef614a6162f816ba8d174ff8d599675eeca7e870245b23685268805b994"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SKJZJQ7ZIEOW6PLDT7BTC3I66P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Empirical Analysis of the Hessian of Over-Parametrized Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Leon Bottou, Levent Sagun, Utku Evci, V. Ugur Guney, Yann Dauphin","submitted_at":"2017-06-14T12:50:00Z","abstract_excerpt":"We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04454","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":""},"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":"2026-05-18T00:16:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qgNZnsUnyE5GhHweeWKFcu9nMEUInIz6bJu4RL/kzNB0KsCgtEj7Ucwy6FgvNGjSECernHg55lOvd58dmg4rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:13:59.283145Z"},"content_sha256":"4546d89f622292461e32b8d876e039d5e4e4fc2d2b2dcc9c5831dd20d2f9ffb1","schema_version":"1.0","event_id":"sha256:4546d89f622292461e32b8d876e039d5e4e4fc2d2b2dcc9c5831dd20d2f9ffb1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKJZJQ7ZIEOW6PLDT7BTC3I66P/bundle.json","state_url":"https://pith.science/pith/SKJZJQ7ZIEOW6PLDT7BTC3I66P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKJZJQ7ZIEOW6PLDT7BTC3I66P/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":"2026-05-26T22:13:59Z","links":{"resolver":"https://pith.science/pith/SKJZJQ7ZIEOW6PLDT7BTC3I66P","bundle":"https://pith.science/pith/SKJZJQ7ZIEOW6PLDT7BTC3I66P/bundle.json","state":"https://pith.science/pith/SKJZJQ7ZIEOW6PLDT7BTC3I66P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKJZJQ7ZIEOW6PLDT7BTC3I66P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SKJZJQ7ZIEOW6PLDT7BTC3I66P","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":"f5e3ad147b8b566e36896de2c8d56201c1a248da8bf4a83b781ef3a5c137099c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-06-14T12:50:00Z","title_canon_sha256":"8f65047c1bd0116a91b51e7a0bc79b3bf369107262955beabe1df872d4779bb9"},"schema_version":"1.0","source":{"id":"1706.04454","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04454","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04454v3","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04454","created_at":"2026-05-18T00:16:45Z"},{"alias_kind":"pith_short_12","alias_value":"SKJZJQ7ZIEOW","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SKJZJQ7ZIEOW6PLD","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SKJZJQ7Z","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:4546d89f622292461e32b8d876e039d5e4e4fc2d2b2dcc9c5831dd20d2f9ffb1","target":"graph","created_at":"2026-05-18T00:16:45Z","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"},"paper":{"abstract_excerpt":"We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable)","authors_text":"Leon Bottou, Levent Sagun, Utku Evci, V. Ugur Guney, Yann Dauphin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-06-14T12:50:00Z","title":"Empirical Analysis of the Hessian of Over-Parametrized Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04454","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:fa52aef614a6162f816ba8d174ff8d599675eeca7e870245b23685268805b994","target":"record","created_at":"2026-05-18T00:16:45Z","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":"f5e3ad147b8b566e36896de2c8d56201c1a248da8bf4a83b781ef3a5c137099c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-06-14T12:50:00Z","title_canon_sha256":"8f65047c1bd0116a91b51e7a0bc79b3bf369107262955beabe1df872d4779bb9"},"schema_version":"1.0","source":{"id":"1706.04454","kind":"arxiv","version":3}},"canonical_sha256":"929394c3f9411d6f3d639fc3316d1ef3fd01bd461ad2a89afc8f11284ef108f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"929394c3f9411d6f3d639fc3316d1ef3fd01bd461ad2a89afc8f11284ef108f5","first_computed_at":"2026-05-18T00:16:45.252198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:45.252198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R4+PD7EnY6FfxF7Jfi7P4WAH4d9ZAIXqc6w94Gmb0ZOoAvUQuk4kyEA0p40uXZqJXi1cEA9qteWho7T9OLHUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:45.252801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04454","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa52aef614a6162f816ba8d174ff8d599675eeca7e870245b23685268805b994","sha256:4546d89f622292461e32b8d876e039d5e4e4fc2d2b2dcc9c5831dd20d2f9ffb1"],"state_sha256":"e9aa69db04f97dca86127b7892cb553c0831e45d07aa11b10e913db5194dbe2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/a85sMUz6kOMzG19Bz5OR2R+UMu4pOpM5Dj1hME5u9WPBxD+NzmO3hL+p5I3ZfxO/MuROGKqUGWnSVxuaAcDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:13:59.285499Z","bundle_sha256":"5ce185f2eb2fa13d719284fc0a68e5f135a9a6a8abef336874602afed2969e96"}}