{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:5BJIPFSQ3HJ6RQWXEF7K7LFBCI","short_pith_number":"pith:5BJIPFSQ","schema_version":"1.0","canonical_sha256":"e852879650d9d3e8c2d7217eafaca1122a909435a13e7f4bbf74513e39668c8b","source":{"kind":"arxiv","id":"1810.05193","version":2},"attestation_state":"computed","paper":{"title":"Understanding Priors in Bayesian Neural Networks at the Unit Level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Jakob Verbeek, Julyan Arbel, Mariia Vladimirova, Pablo Mesejo","submitted_at":"2018-10-11T18:26:50Z","abstract_excerpt":"We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L2, \"weight decay\", regularization. Our results characterize a more intricate regularization effect at the level of the unit activations. Our main result establishes that the induced prior distribution on the units before and after activation becomes increasingly heavy-tailed with the depth of the layer. We show that first layer units are Gaussian, second layer units are sub-exponential, and units in deeper l"},"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":"1810.05193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-10-11T18:26:50Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0cef1ecd9c4982bdbe404c5a8663f8abbdc98c512d92a80a2b688fe80ebc832d","abstract_canon_sha256":"2a9a2947ff632996fb9ac4c6bb54d63551665f1a2e8996cd05bdd277361dea58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:31.983821Z","signature_b64":"7+deqmqz52e3w76e+DNSas7G1N3SfFKK5an3AbXwQ06vmJeruTZKoevlmIOGc5NP2WA//JSWD3VzVJpG3eegDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e852879650d9d3e8c2d7217eafaca1122a909435a13e7f4bbf74513e39668c8b","last_reissued_at":"2026-05-17T23:46:31.983041Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:31.983041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Understanding Priors in Bayesian Neural Networks at the Unit Level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Jakob Verbeek, Julyan Arbel, Mariia Vladimirova, Pablo Mesejo","submitted_at":"2018-10-11T18:26:50Z","abstract_excerpt":"We investigate deep Bayesian neural networks with Gaussian weight priors and a class of ReLU-like nonlinearities. Bayesian neural networks with Gaussian priors are well known to induce an L2, \"weight decay\", regularization. Our results characterize a more intricate regularization effect at the level of the unit activations. Our main result establishes that the induced prior distribution on the units before and after activation becomes increasingly heavy-tailed with the depth of the layer. We show that first layer units are Gaussian, second layer units are sub-exponential, and units in deeper l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05193","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":"1810.05193","created_at":"2026-05-17T23:46:31.983175+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.05193v2","created_at":"2026-05-17T23:46:31.983175+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05193","created_at":"2026-05-17T23:46:31.983175+00:00"},{"alias_kind":"pith_short_12","alias_value":"5BJIPFSQ3HJ6","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"5BJIPFSQ3HJ6RQWX","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"5BJIPFSQ","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/5BJIPFSQ3HJ6RQWXEF7K7LFBCI","json":"https://pith.science/pith/5BJIPFSQ3HJ6RQWXEF7K7LFBCI.json","graph_json":"https://pith.science/api/pith-number/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/graph.json","events_json":"https://pith.science/api/pith-number/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/events.json","paper":"https://pith.science/paper/5BJIPFSQ"},"agent_actions":{"view_html":"https://pith.science/pith/5BJIPFSQ3HJ6RQWXEF7K7LFBCI","download_json":"https://pith.science/pith/5BJIPFSQ3HJ6RQWXEF7K7LFBCI.json","view_paper":"https://pith.science/paper/5BJIPFSQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.05193&json=true","fetch_graph":"https://pith.science/api/pith-number/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/graph.json","fetch_events":"https://pith.science/api/pith-number/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/action/storage_attestation","attest_author":"https://pith.science/pith/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/action/author_attestation","sign_citation":"https://pith.science/pith/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/action/citation_signature","submit_replication":"https://pith.science/pith/5BJIPFSQ3HJ6RQWXEF7K7LFBCI/action/replication_record"}},"created_at":"2026-05-17T23:46:31.983175+00:00","updated_at":"2026-05-17T23:46:31.983175+00:00"}