{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6IEOAEYQVMDH2ETN7AUZ2QUECE","short_pith_number":"pith:6IEOAEYQ","schema_version":"1.0","canonical_sha256":"f208e01310ab067d126df8299d4284113cab6a9e418ad99b73b98be559f52da5","source":{"kind":"arxiv","id":"1806.09597","version":4},"attestation_state":"computed","paper":{"title":"Stochastic natural gradient descent draws posterior samples in function space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Daniel Duckworth, Jascha Sohl-Dickstein, Quoc V. Le, Samuel L. Smith, Semon Rezchikov","submitted_at":"2018-06-25T17:47:42Z","abstract_excerpt":"Recent work has argued that stochastic gradient descent can approximate the Bayesian uncertainty in model parameters near local minima. In this work we develop a similar correspondence for minibatch natural gradient descent (NGD). We prove that for sufficiently small learning rates, if the model predictions on the training set approach the true conditional distribution of labels given inputs, the stationary distribution of minibatch NGD approaches a Bayesian posterior near local minima. The temperature $T = \\epsilon N / (2B)$ is controlled by the learning rate $\\epsilon$, training set size $N$"},"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":"1806.09597","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-25T17:47:42Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"ddb21d941acac31e0c5dae5b4b94b386ca6c2f5b028053612f6785ae0b5f0065","abstract_canon_sha256":"d29c3a63efa0e4385ebecfcaf6aff5f5f25cfd6fce03d1a57afdb8daba372a73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:43.561166Z","signature_b64":"tTqKBBQu8EcIEWBSbCBAUYVtfdaO5tx6UVSBlgkdx/CpW1pbpM2Eg2MatMondoRzwB0F7gkTl15/LUUExxMODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f208e01310ab067d126df8299d4284113cab6a9e418ad99b73b98be559f52da5","last_reissued_at":"2026-05-17T23:59:43.560548Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:43.560548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic natural gradient descent draws posterior samples in function space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Daniel Duckworth, Jascha Sohl-Dickstein, Quoc V. Le, Samuel L. Smith, Semon Rezchikov","submitted_at":"2018-06-25T17:47:42Z","abstract_excerpt":"Recent work has argued that stochastic gradient descent can approximate the Bayesian uncertainty in model parameters near local minima. In this work we develop a similar correspondence for minibatch natural gradient descent (NGD). We prove that for sufficiently small learning rates, if the model predictions on the training set approach the true conditional distribution of labels given inputs, the stationary distribution of minibatch NGD approaches a Bayesian posterior near local minima. The temperature $T = \\epsilon N / (2B)$ is controlled by the learning rate $\\epsilon$, training set size $N$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09597","kind":"arxiv","version":4},"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":"1806.09597","created_at":"2026-05-17T23:59:43.560629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.09597v4","created_at":"2026-05-17T23:59:43.560629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09597","created_at":"2026-05-17T23:59:43.560629+00:00"},{"alias_kind":"pith_short_12","alias_value":"6IEOAEYQVMDH","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6IEOAEYQVMDH2ETN","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6IEOAEYQ","created_at":"2026-05-18T12:32:08.215937+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE","json":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE.json","graph_json":"https://pith.science/api/pith-number/6IEOAEYQVMDH2ETN7AUZ2QUECE/graph.json","events_json":"https://pith.science/api/pith-number/6IEOAEYQVMDH2ETN7AUZ2QUECE/events.json","paper":"https://pith.science/paper/6IEOAEYQ"},"agent_actions":{"view_html":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE","download_json":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE.json","view_paper":"https://pith.science/paper/6IEOAEYQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.09597&json=true","fetch_graph":"https://pith.science/api/pith-number/6IEOAEYQVMDH2ETN7AUZ2QUECE/graph.json","fetch_events":"https://pith.science/api/pith-number/6IEOAEYQVMDH2ETN7AUZ2QUECE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE/action/storage_attestation","attest_author":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE/action/author_attestation","sign_citation":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE/action/citation_signature","submit_replication":"https://pith.science/pith/6IEOAEYQVMDH2ETN7AUZ2QUECE/action/replication_record"}},"created_at":"2026-05-17T23:59:43.560629+00:00","updated_at":"2026-05-17T23:59:43.560629+00:00"}