{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:G4IZ4NARMH5LGJLJM7HSB2MTIY","short_pith_number":"pith:G4IZ4NAR","canonical_record":{"source":{"id":"1806.02390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-06T19:13:53Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7d62d0ecfb4580b73224f075dd91f55c9ef62f82ff1b488cfccdaa23b9caa4be","abstract_canon_sha256":"8c4303bc5b8b8a5077262683f2b1269ff599f3cd41cb04637459e23f9fa14b5a"},"schema_version":"1.0"},"canonical_sha256":"37119e341161fab3256967cf20e9934627b12af6fff6e06b2ce092fc17ef8b99","source":{"kind":"arxiv","id":"1806.02390","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02390","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02390v2","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02390","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"G4IZ4NARMH5L","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4IZ4NARMH5LGJLJ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4IZ4NAR","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:G4IZ4NARMH5LGJLJM7HSB2MTIY","target":"record","payload":{"canonical_record":{"source":{"id":"1806.02390","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-06T19:13:53Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7d62d0ecfb4580b73224f075dd91f55c9ef62f82ff1b488cfccdaa23b9caa4be","abstract_canon_sha256":"8c4303bc5b8b8a5077262683f2b1269ff599f3cd41cb04637459e23f9fa14b5a"},"schema_version":"1.0"},"canonical_sha256":"37119e341161fab3256967cf20e9934627b12af6fff6e06b2ce092fc17ef8b99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:59.479011Z","signature_b64":"ebT8YnU2vdTzWjEvGjAG2AIm/C3fvW/FHqngSnJ4IewoR7YaxuUaCv0KgLfiZcxlHBiDghl4M/L2Ltg/jZYDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37119e341161fab3256967cf20e9934627b12af6fff6e06b2ce092fc17ef8b99","last_reissued_at":"2026-05-17T23:44:59.478380Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:59.478380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.02390","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":"2026-05-17T23:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZbpNp6BxBMDQtYd8rSi+ltn1IpQK+GjOvdDrtUKcBAUa3rLxmBaN7876OuS9D2vPFeDzX9jP4mjcko8/g8kCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:42:42.742345Z"},"content_sha256":"8aa07538eec8ca00b7d4d2cdff48b4c2ee5efc4ee805d43b5de21f6b4e42d67c","schema_version":"1.0","event_id":"sha256:8aa07538eec8ca00b7d4d2cdff48b4c2ee5efc4ee805d43b5de21f6b4e42d67c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:G4IZ4NARMH5LGJLJM7HSB2MTIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Implicit Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Chao Ma, Jos\\'e Miguel Hern\\'andez-Lobato, Yingzhen Li","submitted_at":"2018-06-06T19:13:53Z","abstract_excerpt":"We introduce the implicit processes (IPs), a stochastic process that places implicitly defined multivariate distributions over any finite collections of random variables. IPs are therefore highly flexible implicit priors over functions, with examples including data simulators, Bayesian neural networks and non-linear transformations of stochastic processes. A novel and efficient approximate inference algorithm for IPs, namely the variational implicit processes (VIPs), is derived using generalised wake-sleep updates. This method returns simple update equations and allows scalable hyper-parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02390","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":"2026-05-17T23:44:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvCXp/vaZsrEPU46O6nBADUzBYi8XjFTr/t4N3GqixSmvtz6zKzDuEIajd1NXri7zaEZ8nbkvmE3snOHgd+cDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:42:42.742700Z"},"content_sha256":"045160636634ee3f953458b2361d84d45fb7e67647e204fa99f2e5660f0d9812","schema_version":"1.0","event_id":"sha256:045160636634ee3f953458b2361d84d45fb7e67647e204fa99f2e5660f0d9812"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4IZ4NARMH5LGJLJM7HSB2MTIY/bundle.json","state_url":"https://pith.science/pith/G4IZ4NARMH5LGJLJM7HSB2MTIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4IZ4NARMH5LGJLJM7HSB2MTIY/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":"2026-06-12T01:42:42Z","links":{"resolver":"https://pith.science/pith/G4IZ4NARMH5LGJLJM7HSB2MTIY","bundle":"https://pith.science/pith/G4IZ4NARMH5LGJLJM7HSB2MTIY/bundle.json","state":"https://pith.science/pith/G4IZ4NARMH5LGJLJM7HSB2MTIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4IZ4NARMH5LGJLJM7HSB2MTIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G4IZ4NARMH5LGJLJM7HSB2MTIY","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":"8c4303bc5b8b8a5077262683f2b1269ff599f3cd41cb04637459e23f9fa14b5a","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-06T19:13:53Z","title_canon_sha256":"7d62d0ecfb4580b73224f075dd91f55c9ef62f82ff1b488cfccdaa23b9caa4be"},"schema_version":"1.0","source":{"id":"1806.02390","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02390","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02390v2","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02390","created_at":"2026-05-17T23:44:59Z"},{"alias_kind":"pith_short_12","alias_value":"G4IZ4NARMH5L","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4IZ4NARMH5LGJLJ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4IZ4NAR","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:045160636634ee3f953458b2361d84d45fb7e67647e204fa99f2e5660f0d9812","target":"graph","created_at":"2026-05-17T23:44:59Z","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 introduce the implicit processes (IPs), a stochastic process that places implicitly defined multivariate distributions over any finite collections of random variables. IPs are therefore highly flexible implicit priors over functions, with examples including data simulators, Bayesian neural networks and non-linear transformations of stochastic processes. A novel and efficient approximate inference algorithm for IPs, namely the variational implicit processes (VIPs), is derived using generalised wake-sleep updates. This method returns simple update equations and allows scalable hyper-parameter","authors_text":"Chao Ma, Jos\\'e Miguel Hern\\'andez-Lobato, Yingzhen Li","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-06T19:13:53Z","title":"Variational Implicit Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02390","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":"sha256:8aa07538eec8ca00b7d4d2cdff48b4c2ee5efc4ee805d43b5de21f6b4e42d67c","target":"record","created_at":"2026-05-17T23:44:59Z","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":"8c4303bc5b8b8a5077262683f2b1269ff599f3cd41cb04637459e23f9fa14b5a","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-06-06T19:13:53Z","title_canon_sha256":"7d62d0ecfb4580b73224f075dd91f55c9ef62f82ff1b488cfccdaa23b9caa4be"},"schema_version":"1.0","source":{"id":"1806.02390","kind":"arxiv","version":2}},"canonical_sha256":"37119e341161fab3256967cf20e9934627b12af6fff6e06b2ce092fc17ef8b99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37119e341161fab3256967cf20e9934627b12af6fff6e06b2ce092fc17ef8b99","first_computed_at":"2026-05-17T23:44:59.478380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:59.478380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ebT8YnU2vdTzWjEvGjAG2AIm/C3fvW/FHqngSnJ4IewoR7YaxuUaCv0KgLfiZcxlHBiDghl4M/L2Ltg/jZYDDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:59.479011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02390","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8aa07538eec8ca00b7d4d2cdff48b4c2ee5efc4ee805d43b5de21f6b4e42d67c","sha256:045160636634ee3f953458b2361d84d45fb7e67647e204fa99f2e5660f0d9812"],"state_sha256":"d1f64c5c89b97ce855f26c978d462146b3638f17f3d19ce11c0160fedd580499"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N46xtm3C4w4Cq3fP7I7Ey/jb2u8Dxy00RwwUfIQgNPNJibazqHP5H2eYYdBBmPoVF1CD8Hz4fg4fYz+kmUaTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:42:42.744661Z","bundle_sha256":"19ccaf492735451cf4fcfac4a230307f937997c3446a64a61b60a2309c1dbfdd"}}