{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:IKUNQV466PFAGA2LP3RDFKJUWT","short_pith_number":"pith:IKUNQV46","canonical_record":{"source":{"id":"2002.00107","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-01-31T23:50:03Z","cross_cats_sorted":["cs.LG","math.PR"],"title_canon_sha256":"6964346d33f0a2b6a63a490694db633836c101f896e12ae2ab6fb9b3c71dc94a","abstract_canon_sha256":"3c6f5cc99edea3d29a8785fa71fdd65ff1e5265832c840c33f048360032618bd"},"schema_version":"1.0"},"canonical_sha256":"42a8d8579ef3ca03034b7ee232a934b4f1d7f90abf4476d67d6231cb372cefad","source":{"kind":"arxiv","id":"2002.00107","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.00107","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"2002.00107v4","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.00107","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"IKUNQV466PFA","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"pith_short_16","alias_value":"IKUNQV466PFAGA2L","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"pith_short_8","alias_value":"IKUNQV46","created_at":"2026-07-05T05:04:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:IKUNQV466PFAGA2LP3RDFKJUWT","target":"record","payload":{"canonical_record":{"source":{"id":"2002.00107","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-01-31T23:50:03Z","cross_cats_sorted":["cs.LG","math.PR"],"title_canon_sha256":"6964346d33f0a2b6a63a490694db633836c101f896e12ae2ab6fb9b3c71dc94a","abstract_canon_sha256":"3c6f5cc99edea3d29a8785fa71fdd65ff1e5265832c840c33f048360032618bd"},"schema_version":"1.0"},"canonical_sha256":"42a8d8579ef3ca03034b7ee232a934b4f1d7f90abf4476d67d6231cb372cefad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:04:58.569104Z","signature_b64":"nsTUf7JmjATrEMs066gkjU0yGGQlvp/19Yk9XgLSk3CnpkXcoOxxerr/2bmdA8MeYeaiH7uP2EnnvpIEWMwSAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42a8d8579ef3ca03034b7ee232a934b4f1d7f90abf4476d67d6231cb372cefad","last_reissued_at":"2026-07-05T05:04:58.568642Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:04:58.568642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.00107","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n4fnZuaOet/SocWoOG6USrLkG6XJXvHmQouzJXFMnnUpEm2Vp58x7KUnwmWb7KxuSIuVn6OVN69d9CBaND1ICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:46:57.383549Z"},"content_sha256":"eab796c12e8ab4625ec422d69ae6de61336a9c21b147a671aed99dc0def8f142","schema_version":"1.0","event_id":"sha256:eab796c12e8ab4625ec422d69ae6de61336a9c21b147a671aed99dc0def8f142"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:IKUNQV466PFAGA2LP3RDFKJUWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generative Modeling with Denoising Auto-Encoders and Langevin Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"stat.ML","authors_text":"Adam Block, Alexander Rakhlin, Youssef Mroueh","submitted_at":"2020-01-31T23:50:03Z","abstract_excerpt":"We study convergence of a generative modeling method that first estimates the score function of the distribution using Denoising Auto-Encoders (DAE) or Denoising Score Matching (DSM) and then employs Langevin diffusion for sampling. We show that both DAE and DSM provide estimates of the score of the Gaussian smoothed population density, allowing us to apply the machinery of Empirical Processes.\n  We overcome the challenge of relying only on $L^2$ bounds on the score estimation error and provide finite-sample bounds in the Wasserstein distance between the law of the population distribution and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.00107","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.00107/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xUlKxK1n+hWm3kKXa9VOhuYWDRHiH3B2m6JqqOG/lCebu43IVrGman3iGTlfms0h61jrm6chNPRJuYH49eFJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:46:57.383926Z"},"content_sha256":"1a1e786ee33113c6ea11cec493e4f8522d2112b0707d817f80d5b89a349289be","schema_version":"1.0","event_id":"sha256:1a1e786ee33113c6ea11cec493e4f8522d2112b0707d817f80d5b89a349289be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IKUNQV466PFAGA2LP3RDFKJUWT/bundle.json","state_url":"https://pith.science/pith/IKUNQV466PFAGA2LP3RDFKJUWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IKUNQV466PFAGA2LP3RDFKJUWT/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":"2026-07-06T20:46:57Z","links":{"resolver":"https://pith.science/pith/IKUNQV466PFAGA2LP3RDFKJUWT","bundle":"https://pith.science/pith/IKUNQV466PFAGA2LP3RDFKJUWT/bundle.json","state":"https://pith.science/pith/IKUNQV466PFAGA2LP3RDFKJUWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IKUNQV466PFAGA2LP3RDFKJUWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:IKUNQV466PFAGA2LP3RDFKJUWT","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":"3c6f5cc99edea3d29a8785fa71fdd65ff1e5265832c840c33f048360032618bd","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-01-31T23:50:03Z","title_canon_sha256":"6964346d33f0a2b6a63a490694db633836c101f896e12ae2ab6fb9b3c71dc94a"},"schema_version":"1.0","source":{"id":"2002.00107","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.00107","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"2002.00107v4","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.00107","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"IKUNQV466PFA","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"pith_short_16","alias_value":"IKUNQV466PFAGA2L","created_at":"2026-07-05T05:04:58Z"},{"alias_kind":"pith_short_8","alias_value":"IKUNQV46","created_at":"2026-07-05T05:04:58Z"}],"graph_snapshots":[{"event_id":"sha256:1a1e786ee33113c6ea11cec493e4f8522d2112b0707d817f80d5b89a349289be","target":"graph","created_at":"2026-07-05T05:04:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.00107/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study convergence of a generative modeling method that first estimates the score function of the distribution using Denoising Auto-Encoders (DAE) or Denoising Score Matching (DSM) and then employs Langevin diffusion for sampling. We show that both DAE and DSM provide estimates of the score of the Gaussian smoothed population density, allowing us to apply the machinery of Empirical Processes.\n  We overcome the challenge of relying only on $L^2$ bounds on the score estimation error and provide finite-sample bounds in the Wasserstein distance between the law of the population distribution and ","authors_text":"Adam Block, Alexander Rakhlin, Youssef Mroueh","cross_cats":["cs.LG","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-01-31T23:50:03Z","title":"Generative Modeling with Denoising Auto-Encoders and Langevin Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.00107","kind":"arxiv","version":4},"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:eab796c12e8ab4625ec422d69ae6de61336a9c21b147a671aed99dc0def8f142","target":"record","created_at":"2026-07-05T05:04:58Z","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":"3c6f5cc99edea3d29a8785fa71fdd65ff1e5265832c840c33f048360032618bd","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-01-31T23:50:03Z","title_canon_sha256":"6964346d33f0a2b6a63a490694db633836c101f896e12ae2ab6fb9b3c71dc94a"},"schema_version":"1.0","source":{"id":"2002.00107","kind":"arxiv","version":4}},"canonical_sha256":"42a8d8579ef3ca03034b7ee232a934b4f1d7f90abf4476d67d6231cb372cefad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42a8d8579ef3ca03034b7ee232a934b4f1d7f90abf4476d67d6231cb372cefad","first_computed_at":"2026-07-05T05:04:58.568642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:04:58.568642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nsTUf7JmjATrEMs066gkjU0yGGQlvp/19Yk9XgLSk3CnpkXcoOxxerr/2bmdA8MeYeaiH7uP2EnnvpIEWMwSAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:04:58.569104Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.00107","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eab796c12e8ab4625ec422d69ae6de61336a9c21b147a671aed99dc0def8f142","sha256:1a1e786ee33113c6ea11cec493e4f8522d2112b0707d817f80d5b89a349289be"],"state_sha256":"68fbf20da5a31b05d0eb078d8f53a398ddc1995ff15d77564c588406057e8737"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LUgIP+hF3Ge8M1uUr3d/C4fLWzmeLg/GFFQLVhwuhPLguRa93uZ6+vpwmrJhSbyIoWEXNkPHoL2dJeZi/zRADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:46:57.386671Z","bundle_sha256":"281d362004258e0b9d06c99d1964b6e8fcf7fe62fabecb793dd82e8bec63c3d4"}}