{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:2G4BGGX7RSVAZLNEGYWE7V5BC3","short_pith_number":"pith:2G4BGGX7","schema_version":"1.0","canonical_sha256":"d1b8131aff8caa0cada4362c4fd7a116f34b574148fb8d06f77ef234df1a9850","source":{"kind":"arxiv","id":"2006.08777","version":1},"attestation_state":"computed","paper":{"title":"Ordering Dimensions with Nested Dropout Normalizing Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Artur Bekasov, Iain Murray","submitted_at":"2020-06-15T21:23:24Z","abstract_excerpt":"The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided compact representations by fitting flows constrained to manifolds, but hasn't defined a density off that manifold. In this work we consider flows with full support in data space, but with ordered latent variables. Like in PCA, the leading latent dimensions define a sequence of manifolds that lie close to the data. We note a trade-off between the flow likelihood an"},"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":"2006.08777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-06-15T21:23:24Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"870863d909e5a583e7683ce1323757049720b3411f426e47a099616991b2d445","abstract_canon_sha256":"9fc33946abf0cfdb20fde1393cd1dca91142b92cd8394e352f9f17cc9ecc52bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:10:42.955147Z","signature_b64":"+EPYDIf/CTrC16ZpyppYLk7PV+Dt4Frq4lYJfHdLkFvPFU0itnNnE2OLsCcFYObzgTvZ7PomL5wvGft77CU4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1b8131aff8caa0cada4362c4fd7a116f34b574148fb8d06f77ef234df1a9850","last_reissued_at":"2026-07-05T01:10:42.954799Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:10:42.954799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ordering Dimensions with Nested Dropout Normalizing Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Artur Bekasov, Iain Murray","submitted_at":"2020-06-15T21:23:24Z","abstract_excerpt":"The latent space of normalizing flows must be of the same dimensionality as their output space. This constraint presents a problem if we want to learn low-dimensional, semantically meaningful representations. Recent work has provided compact representations by fitting flows constrained to manifolds, but hasn't defined a density off that manifold. In this work we consider flows with full support in data space, but with ordered latent variables. Like in PCA, the leading latent dimensions define a sequence of manifolds that lie close to the data. We note a trade-off between the flow likelihood an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08777","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.08777/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2006.08777","created_at":"2026-07-05T01:10:42.954860+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.08777v1","created_at":"2026-07-05T01:10:42.954860+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08777","created_at":"2026-07-05T01:10:42.954860+00:00"},{"alias_kind":"pith_short_12","alias_value":"2G4BGGX7RSVA","created_at":"2026-07-05T01:10:42.954860+00:00"},{"alias_kind":"pith_short_16","alias_value":"2G4BGGX7RSVAZLNE","created_at":"2026-07-05T01:10:42.954860+00:00"},{"alias_kind":"pith_short_8","alias_value":"2G4BGGX7","created_at":"2026-07-05T01:10:42.954860+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.12187","citing_title":"Characterizing Neural Manifolds' Properties and Curvatures using Normalizing Flows","ref_index":77,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3","json":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3.json","graph_json":"https://pith.science/api/pith-number/2G4BGGX7RSVAZLNEGYWE7V5BC3/graph.json","events_json":"https://pith.science/api/pith-number/2G4BGGX7RSVAZLNEGYWE7V5BC3/events.json","paper":"https://pith.science/paper/2G4BGGX7"},"agent_actions":{"view_html":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3","download_json":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3.json","view_paper":"https://pith.science/paper/2G4BGGX7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.08777&json=true","fetch_graph":"https://pith.science/api/pith-number/2G4BGGX7RSVAZLNEGYWE7V5BC3/graph.json","fetch_events":"https://pith.science/api/pith-number/2G4BGGX7RSVAZLNEGYWE7V5BC3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3/action/storage_attestation","attest_author":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3/action/author_attestation","sign_citation":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3/action/citation_signature","submit_replication":"https://pith.science/pith/2G4BGGX7RSVAZLNEGYWE7V5BC3/action/replication_record"}},"created_at":"2026-07-05T01:10:42.954860+00:00","updated_at":"2026-07-05T01:10:42.954860+00:00"}