{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:O76ONR6GDTDBPHDRHIS7VV4H62","short_pith_number":"pith:O76ONR6G","schema_version":"1.0","canonical_sha256":"77fce6c7c61cc6179c713a25fad787f6aeefeedb6b584df9e05339d1b8cae11f","source":{"kind":"arxiv","id":"1811.07062","version":2},"attestation_state":"computed","paper":{"title":"The Full Spectrum of Deepnet Hessians at Scale: Dynamics with SGD Training and Sample Size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Vardan Papyan","submitted_at":"2018-11-16T23:22:37Z","abstract_excerpt":"We apply state-of-the-art tools in modern high-dimensional numerical linear algebra to approximate efficiently the spectrum of the Hessian of modern deepnets, with tens of millions of parameters, trained on real data. Our results corroborate previous findings, based on small-scale networks, that the Hessian exhibits \"spiked\" behavior, with several outliers isolated from a continuous bulk. We decompose the Hessian into different components and study the dynamics with training and sample size of each term individually."},"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":"1811.07062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-11-16T23:22:37Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"75dc66b111614796b278bfa09dc7b55997ea4537b2a95c3c80fabf97fbbb0e6e","abstract_canon_sha256":"1b8770ffc46c3833f944f17d6da36f295c2646f244a4b1f516a9bb8be53ca184"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:29.906186Z","signature_b64":"kwX3QDR9grN4C7uW5YXicu7C8tju52ZfdJin6r7iUInzfE9XT7R5mDeydoUzZUVh51FhyT7fW82I7GohstygDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77fce6c7c61cc6179c713a25fad787f6aeefeedb6b584df9e05339d1b8cae11f","last_reissued_at":"2026-05-17T23:44:29.905489Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:29.905489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Full Spectrum of Deepnet Hessians at Scale: Dynamics with SGD Training and Sample Size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Vardan Papyan","submitted_at":"2018-11-16T23:22:37Z","abstract_excerpt":"We apply state-of-the-art tools in modern high-dimensional numerical linear algebra to approximate efficiently the spectrum of the Hessian of modern deepnets, with tens of millions of parameters, trained on real data. Our results corroborate previous findings, based on small-scale networks, that the Hessian exhibits \"spiked\" behavior, with several outliers isolated from a continuous bulk. We decompose the Hessian into different components and study the dynamics with training and sample size of each term individually."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07062","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":""},"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":"1811.07062","created_at":"2026-05-17T23:44:29.905598+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.07062v2","created_at":"2026-05-17T23:44:29.905598+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07062","created_at":"2026-05-17T23:44:29.905598+00:00"},{"alias_kind":"pith_short_12","alias_value":"O76ONR6GDTDB","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"O76ONR6GDTDBPHDR","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"O76ONR6G","created_at":"2026-05-18T12:32:43.782077+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":9,"internal_anchor_count":5,"sample":[{"citing_arxiv_id":"1906.09069","citing_title":"First Exit Time Analysis of Stochastic Gradient Descent Under Heavy-Tailed Gradient Noise","ref_index":38,"is_internal_anchor":true},{"citing_arxiv_id":"1907.10732","citing_title":"Hessian based analysis of SGD for Deep Nets: Dynamics and Generalization","ref_index":53,"is_internal_anchor":true},{"citing_arxiv_id":"2502.02345","citing_title":"Low Rank Based Subspace Inference for the Laplace Approximation of Bayesian Neural Networks","ref_index":16,"is_internal_anchor":true},{"citing_arxiv_id":"2605.22432","citing_title":"AMUSE: Anytime Muon with Stable Gradient Evaluation","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2102.01293","citing_title":"Scaling Laws for Transfer","ref_index":55,"is_internal_anchor":true},{"citing_arxiv_id":"2605.06081","citing_title":"Fast Gauss-Newton for Multiclass Cross-Entropy","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2112.00861","citing_title":"A General Language Assistant as a Laboratory for Alignment","ref_index":84,"is_internal_anchor":false},{"citing_arxiv_id":"2207.05221","citing_title":"Language Models (Mostly) Know What They Know","ref_index":142,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19740","citing_title":"Generalization at the Edge of Stability","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62","json":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62.json","graph_json":"https://pith.science/api/pith-number/O76ONR6GDTDBPHDRHIS7VV4H62/graph.json","events_json":"https://pith.science/api/pith-number/O76ONR6GDTDBPHDRHIS7VV4H62/events.json","paper":"https://pith.science/paper/O76ONR6G"},"agent_actions":{"view_html":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62","download_json":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62.json","view_paper":"https://pith.science/paper/O76ONR6G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.07062&json=true","fetch_graph":"https://pith.science/api/pith-number/O76ONR6GDTDBPHDRHIS7VV4H62/graph.json","fetch_events":"https://pith.science/api/pith-number/O76ONR6GDTDBPHDRHIS7VV4H62/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62/action/storage_attestation","attest_author":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62/action/author_attestation","sign_citation":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62/action/citation_signature","submit_replication":"https://pith.science/pith/O76ONR6GDTDBPHDRHIS7VV4H62/action/replication_record"}},"created_at":"2026-05-17T23:44:29.905598+00:00","updated_at":"2026-05-17T23:44:29.905598+00:00"}