{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RWIXMMIXIRAPRUGB5FZE2ECOQW","short_pith_number":"pith:RWIXMMIX","canonical_record":{"source":{"id":"1704.07520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-04-25T03:01:41Z","cross_cats_sorted":[],"title_canon_sha256":"87fa80dbaf534e28bfacf043558cc1736fbb4f7c52617ea42a48eeece4a98b32","abstract_canon_sha256":"3180801b5c4cdd01d0095bf697eefe15920ce682b83c66834aa51f0dadd6fd4f"},"schema_version":"1.0"},"canonical_sha256":"8d917631174440f8d0c1e9724d104e85b876ea9f71130c9024b4f8516d153b81","source":{"kind":"arxiv","id":"1704.07520","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07520","created_at":"2026-05-18T00:30:45Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07520v2","created_at":"2026-05-18T00:30:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07520","created_at":"2026-05-18T00:30:45Z"},{"alias_kind":"pith_short_12","alias_value":"RWIXMMIXIRAP","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RWIXMMIXIRAPRUGB","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RWIXMMIX","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RWIXMMIXIRAPRUGB5FZE2ECOQW","target":"record","payload":{"canonical_record":{"source":{"id":"1704.07520","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-04-25T03:01:41Z","cross_cats_sorted":[],"title_canon_sha256":"87fa80dbaf534e28bfacf043558cc1736fbb4f7c52617ea42a48eeece4a98b32","abstract_canon_sha256":"3180801b5c4cdd01d0095bf697eefe15920ce682b83c66834aa51f0dadd6fd4f"},"schema_version":"1.0"},"canonical_sha256":"8d917631174440f8d0c1e9724d104e85b876ea9f71130c9024b4f8516d153b81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:45.087464Z","signature_b64":"bLFq5vw0QniIAfeYPTiz1VHX37Ut13Cp6Y1mFg7bugtDVgYvA6P3aIraz0WLmKaoi/Z0No68RaI6Op+OAlAUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d917631174440f8d0c1e9724d104e85b876ea9f71130c9024b4f8516d153b81","last_reissued_at":"2026-05-18T00:30:45.086893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:45.086893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.07520","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":"2026-05-18T00:30:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fhskohSAI4cGj8lOoRmL29gkiTngVOuvAHuwQ3P9PGz5+lriAG85dQZ9zdtX9uwqiXbmskaHXTRG3pXfhUYADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:31:52.890076Z"},"content_sha256":"0b8b85eef4697b033cb56fa9e5a440cb389193b992bcf8f58dbdc0da96993183","schema_version":"1.0","event_id":"sha256:0b8b85eef4697b033cb56fa9e5a440cb389193b992bcf8f58dbdc0da96993183"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RWIXMMIXIRAPRUGB5FZE2ECOQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stein Variational Gradient Descent as Gradient Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Qiang Liu","submitted_at":"2017-04-25T03:01:41Z","abstract_excerpt":"Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first theoretical analysis on SVGD, discussing its weak convergence properties and showing that its asymptotic behavior is captured by a gradient flow of the KL divergence functional under a new metric structure induced by Stein operator. We also provide a number of results on Stein oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07520","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":"2026-05-18T00:30:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DzNOdwr0LVbPbgY+RAYN2KN/mhDiUTGDnWKUoU0E9r2U5NfjpCiP/xQWXN34D2YvHhOv36Zt5YxP0DFODqfcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:31:52.890864Z"},"content_sha256":"12772eafcefa8ecdfbb947d38f8b31db56d3b15fc173a4bc727250233a5423b4","schema_version":"1.0","event_id":"sha256:12772eafcefa8ecdfbb947d38f8b31db56d3b15fc173a4bc727250233a5423b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWIXMMIXIRAPRUGB5FZE2ECOQW/bundle.json","state_url":"https://pith.science/pith/RWIXMMIXIRAPRUGB5FZE2ECOQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWIXMMIXIRAPRUGB5FZE2ECOQW/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":"2026-06-01T01:31:52Z","links":{"resolver":"https://pith.science/pith/RWIXMMIXIRAPRUGB5FZE2ECOQW","bundle":"https://pith.science/pith/RWIXMMIXIRAPRUGB5FZE2ECOQW/bundle.json","state":"https://pith.science/pith/RWIXMMIXIRAPRUGB5FZE2ECOQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWIXMMIXIRAPRUGB5FZE2ECOQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RWIXMMIXIRAPRUGB5FZE2ECOQW","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":"3180801b5c4cdd01d0095bf697eefe15920ce682b83c66834aa51f0dadd6fd4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-04-25T03:01:41Z","title_canon_sha256":"87fa80dbaf534e28bfacf043558cc1736fbb4f7c52617ea42a48eeece4a98b32"},"schema_version":"1.0","source":{"id":"1704.07520","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07520","created_at":"2026-05-18T00:30:45Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07520v2","created_at":"2026-05-18T00:30:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07520","created_at":"2026-05-18T00:30:45Z"},{"alias_kind":"pith_short_12","alias_value":"RWIXMMIXIRAP","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RWIXMMIXIRAPRUGB","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RWIXMMIX","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:12772eafcefa8ecdfbb947d38f8b31db56d3b15fc173a4bc727250233a5423b4","target":"graph","created_at":"2026-05-18T00:30:45Z","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":"Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first theoretical analysis on SVGD, discussing its weak convergence properties and showing that its asymptotic behavior is captured by a gradient flow of the KL divergence functional under a new metric structure induced by Stein operator. We also provide a number of results on Stein oper","authors_text":"Qiang Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-04-25T03:01:41Z","title":"Stein Variational Gradient Descent as Gradient Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07520","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":"sha256:0b8b85eef4697b033cb56fa9e5a440cb389193b992bcf8f58dbdc0da96993183","target":"record","created_at":"2026-05-18T00:30:45Z","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":"3180801b5c4cdd01d0095bf697eefe15920ce682b83c66834aa51f0dadd6fd4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-04-25T03:01:41Z","title_canon_sha256":"87fa80dbaf534e28bfacf043558cc1736fbb4f7c52617ea42a48eeece4a98b32"},"schema_version":"1.0","source":{"id":"1704.07520","kind":"arxiv","version":2}},"canonical_sha256":"8d917631174440f8d0c1e9724d104e85b876ea9f71130c9024b4f8516d153b81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d917631174440f8d0c1e9724d104e85b876ea9f71130c9024b4f8516d153b81","first_computed_at":"2026-05-18T00:30:45.086893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:45.086893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bLFq5vw0QniIAfeYPTiz1VHX37Ut13Cp6Y1mFg7bugtDVgYvA6P3aIraz0WLmKaoi/Z0No68RaI6Op+OAlAUDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:45.087464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07520","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b8b85eef4697b033cb56fa9e5a440cb389193b992bcf8f58dbdc0da96993183","sha256:12772eafcefa8ecdfbb947d38f8b31db56d3b15fc173a4bc727250233a5423b4"],"state_sha256":"a5cb62a8c2dad71e6017536aef3a32c4a76f080a7b1493d2357ef36d41de6c53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Di5ZPxm8ARXQ21wf4w5hryfg4EIHH1k43vkpyx9pNWD4hUJIInSDGc1Oh7dC0l8or8DqlaMom7QlIZs2uhbPBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:31:52.895162Z","bundle_sha256":"57667a1124e040fda57a1aa73db64e58a578cdb74c64ffd048f99146a01d9b57"}}