{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7URLFG4GZZM4HNOWHXDV43XABM","short_pith_number":"pith:7URLFG4G","canonical_record":{"source":{"id":"1506.02557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-08T15:37:56Z","cross_cats_sorted":["cs.LG","stat.CO"],"title_canon_sha256":"aeb1b8e9fd51efe690311011030c2a1de90f503222e3a54ed482c463986a5469","abstract_canon_sha256":"5ad34b7255c8a8af185aad436b63d2034f657f4b3b7521e5c750d62b8bda46c9"},"schema_version":"1.0"},"canonical_sha256":"fd22b29b86ce59c3b5d63dc75e6ee00b1988d4c7d940fe73ebbeba0c98470a59","source":{"kind":"arxiv","id":"1506.02557","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02557","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02557v2","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02557","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"7URLFG4GZZM4","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7URLFG4GZZM4HNOW","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7URLFG4G","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7URLFG4GZZM4HNOWHXDV43XABM","target":"record","payload":{"canonical_record":{"source":{"id":"1506.02557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-08T15:37:56Z","cross_cats_sorted":["cs.LG","stat.CO"],"title_canon_sha256":"aeb1b8e9fd51efe690311011030c2a1de90f503222e3a54ed482c463986a5469","abstract_canon_sha256":"5ad34b7255c8a8af185aad436b63d2034f657f4b3b7521e5c750d62b8bda46c9"},"schema_version":"1.0"},"canonical_sha256":"fd22b29b86ce59c3b5d63dc75e6ee00b1988d4c7d940fe73ebbeba0c98470a59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:03.639958Z","signature_b64":"1cGcRhU+QyajVECeXA9zKzf8nmnpI8ZrGqCT/iOTFY4tx7D2Gl7f1jzcZ5N5tUDCBJpKodNYxQ3/uZzdD+1KCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd22b29b86ce59c3b5d63dc75e6ee00b1988d4c7d940fe73ebbeba0c98470a59","last_reissued_at":"2026-05-18T01:24:03.639335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:03.639335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.02557","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pocUM95aHxnzsvhW+UakdnDmkmCd4bZgfHqi8FLPKRXoC/qFgs8VhsKth6wPW5gVW0G/uP9+4g8WQcsGDWhFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:03:46.024698Z"},"content_sha256":"a1c2165901b3dcb4012c78003b358d2034d3067cb5e7a6316599ad62cee40289","schema_version":"1.0","event_id":"sha256:a1c2165901b3dcb4012c78003b358d2034d3067cb5e7a6316599ad62cee40289"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7URLFG4GZZM4HNOWHXDV43XABM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Dropout and the Local Reparameterization Trick","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.CO"],"primary_cat":"stat.ML","authors_text":"Diederik P. Kingma, Max Welling, Tim Salimans","submitted_at":"2015-06-08T15:37:56Z","abstract_excerpt":"We investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gau"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02557","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5P2ucwBjqnQMbvu1w3OBIx79H24xpLvrrC6aZV0OYOH0NnTKyMBdgjtitMTtV3iRO4vJTrvp/1yPg7UstB2lDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:03:46.025219Z"},"content_sha256":"e65363a7d2592a0ca843dac725d72fc8579f74dd1fccd8b47394b17e9e4ca913","schema_version":"1.0","event_id":"sha256:e65363a7d2592a0ca843dac725d72fc8579f74dd1fccd8b47394b17e9e4ca913"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7URLFG4GZZM4HNOWHXDV43XABM/bundle.json","state_url":"https://pith.science/pith/7URLFG4GZZM4HNOWHXDV43XABM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7URLFG4GZZM4HNOWHXDV43XABM/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":"2026-05-27T13:03:46Z","links":{"resolver":"https://pith.science/pith/7URLFG4GZZM4HNOWHXDV43XABM","bundle":"https://pith.science/pith/7URLFG4GZZM4HNOWHXDV43XABM/bundle.json","state":"https://pith.science/pith/7URLFG4GZZM4HNOWHXDV43XABM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7URLFG4GZZM4HNOWHXDV43XABM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7URLFG4GZZM4HNOWHXDV43XABM","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":"5ad34b7255c8a8af185aad436b63d2034f657f4b3b7521e5c750d62b8bda46c9","cross_cats_sorted":["cs.LG","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-08T15:37:56Z","title_canon_sha256":"aeb1b8e9fd51efe690311011030c2a1de90f503222e3a54ed482c463986a5469"},"schema_version":"1.0","source":{"id":"1506.02557","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02557","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02557v2","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02557","created_at":"2026-05-18T01:24:03Z"},{"alias_kind":"pith_short_12","alias_value":"7URLFG4GZZM4","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7URLFG4GZZM4HNOW","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7URLFG4G","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:e65363a7d2592a0ca843dac725d72fc8579f74dd1fccd8b47394b17e9e4ca913","target":"graph","created_at":"2026-05-18T01:24:03Z","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 investigate a local reparameterizaton technique for greatly reducing the variance of stochastic gradients for variational Bayesian inference (SGVB) of a posterior over model parameters, while retaining parallelizability. This local reparameterization translates uncertainty about global parameters into local noise that is independent across datapoints in the minibatch. Such parameterizations can be trivially parallelized and have variance that is inversely proportional to the minibatch size, generally leading to much faster convergence. Additionally, we explore a connection with dropout: Gau","authors_text":"Diederik P. Kingma, Max Welling, Tim Salimans","cross_cats":["cs.LG","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-08T15:37:56Z","title":"Variational Dropout and the Local Reparameterization Trick"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02557","kind":"arxiv","version":2},"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:a1c2165901b3dcb4012c78003b358d2034d3067cb5e7a6316599ad62cee40289","target":"record","created_at":"2026-05-18T01:24:03Z","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":"5ad34b7255c8a8af185aad436b63d2034f657f4b3b7521e5c750d62b8bda46c9","cross_cats_sorted":["cs.LG","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2015-06-08T15:37:56Z","title_canon_sha256":"aeb1b8e9fd51efe690311011030c2a1de90f503222e3a54ed482c463986a5469"},"schema_version":"1.0","source":{"id":"1506.02557","kind":"arxiv","version":2}},"canonical_sha256":"fd22b29b86ce59c3b5d63dc75e6ee00b1988d4c7d940fe73ebbeba0c98470a59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd22b29b86ce59c3b5d63dc75e6ee00b1988d4c7d940fe73ebbeba0c98470a59","first_computed_at":"2026-05-18T01:24:03.639335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:03.639335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1cGcRhU+QyajVECeXA9zKzf8nmnpI8ZrGqCT/iOTFY4tx7D2Gl7f1jzcZ5N5tUDCBJpKodNYxQ3/uZzdD+1KCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:03.639958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02557","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1c2165901b3dcb4012c78003b358d2034d3067cb5e7a6316599ad62cee40289","sha256:e65363a7d2592a0ca843dac725d72fc8579f74dd1fccd8b47394b17e9e4ca913"],"state_sha256":"771d1759c92dd71e9b203aee2bc788176a854c76cbe9746e6833e25a08e20e65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/sNrcEgQwPNq2pIpYpcis57AYw2NC5oM2KqdaZvifZNdDhGHQiAWF+tlE4PkbFKqb22xeUmgo/eD8k0/mEilCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:03:46.028462Z","bundle_sha256":"a7e0264af83800fd2f4c1fbf463d06e8da05dabf52a94b01c10549f8c8414945"}}