{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XNNEPINLACRQLTOFG7SS35OHZC","short_pith_number":"pith:XNNEPINL","schema_version":"1.0","canonical_sha256":"bb5a47a1ab00a305cdc537e52df5c7c8a5583b9486742f051657769539b176c7","source":{"kind":"arxiv","id":"1803.09138","version":1},"attestation_state":"computed","paper":{"title":"Posterior Concentration for Sparse Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Nicholas Polson, Veronika Rockova","submitted_at":"2018-03-24T17:51:15Z","abstract_excerpt":"Spike-and-Slab Deep Learning (SS-DL) is a fully Bayesian alternative to Dropout for improving generalizability of deep ReLU networks. This new type of regularization enables provable recovery of smooth input-output maps with unknown levels of smoothness. Indeed, we show that the posterior distribution concentrates at the near minimax rate for $\\alpha$-H\\\"older smooth maps, performing as well as if we knew the smoothness level $\\alpha$ ahead of time. Our result sheds light on architecture design for deep neural networks, namely the choice of depth, width and sparsity level. These network attrib"},"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":"1803.09138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-24T17:51:15Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0459d6b284e4fb435cee9b574e641016e6d345c92ecdcceb49dc685ae1518f91","abstract_canon_sha256":"afa8f899c0c6607b6e88196b9d8c9973bcdc6dd925b3a484c814465c3c731189"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:12.529526Z","signature_b64":"PSb0pnpuevHybWJQ3lt+S/QYcPUCxZUnXQom1V26nXOxeXOrvDXeiOa0USJK8CY5UyjvDCIFmMwIx230fRO/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb5a47a1ab00a305cdc537e52df5c7c8a5583b9486742f051657769539b176c7","last_reissued_at":"2026-05-18T00:20:12.529073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:12.529073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Posterior Concentration for Sparse Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Nicholas Polson, Veronika Rockova","submitted_at":"2018-03-24T17:51:15Z","abstract_excerpt":"Spike-and-Slab Deep Learning (SS-DL) is a fully Bayesian alternative to Dropout for improving generalizability of deep ReLU networks. This new type of regularization enables provable recovery of smooth input-output maps with unknown levels of smoothness. Indeed, we show that the posterior distribution concentrates at the near minimax rate for $\\alpha$-H\\\"older smooth maps, performing as well as if we knew the smoothness level $\\alpha$ ahead of time. Our result sheds light on architecture design for deep neural networks, namely the choice of depth, width and sparsity level. These network attrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09138","kind":"arxiv","version":1},"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":"1803.09138","created_at":"2026-05-18T00:20:12.529144+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.09138v1","created_at":"2026-05-18T00:20:12.529144+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09138","created_at":"2026-05-18T00:20:12.529144+00:00"},{"alias_kind":"pith_short_12","alias_value":"XNNEPINLACRQ","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XNNEPINLACRQLTOF","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XNNEPINL","created_at":"2026-05-18T12:33:01.666342+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/XNNEPINLACRQLTOFG7SS35OHZC","json":"https://pith.science/pith/XNNEPINLACRQLTOFG7SS35OHZC.json","graph_json":"https://pith.science/api/pith-number/XNNEPINLACRQLTOFG7SS35OHZC/graph.json","events_json":"https://pith.science/api/pith-number/XNNEPINLACRQLTOFG7SS35OHZC/events.json","paper":"https://pith.science/paper/XNNEPINL"},"agent_actions":{"view_html":"https://pith.science/pith/XNNEPINLACRQLTOFG7SS35OHZC","download_json":"https://pith.science/pith/XNNEPINLACRQLTOFG7SS35OHZC.json","view_paper":"https://pith.science/paper/XNNEPINL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.09138&json=true","fetch_graph":"https://pith.science/api/pith-number/XNNEPINLACRQLTOFG7SS35OHZC/graph.json","fetch_events":"https://pith.science/api/pith-number/XNNEPINLACRQLTOFG7SS35OHZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XNNEPINLACRQLTOFG7SS35OHZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XNNEPINLACRQLTOFG7SS35OHZC/action/storage_attestation","attest_author":"https://pith.science/pith/XNNEPINLACRQLTOFG7SS35OHZC/action/author_attestation","sign_citation":"https://pith.science/pith/XNNEPINLACRQLTOFG7SS35OHZC/action/citation_signature","submit_replication":"https://pith.science/pith/XNNEPINLACRQLTOFG7SS35OHZC/action/replication_record"}},"created_at":"2026-05-18T00:20:12.529144+00:00","updated_at":"2026-05-18T00:20:12.529144+00:00"}