{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:6OFMMQXAYXALP4HETJTVBRGTMO","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":"f2e74781f4d56563e3c59d3d0af1a8568611e7a7b3c5af48059450341627d247","cross_cats_sorted":["cs.IT","cs.LG","math.IT","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-09-07T11:33:32Z","title_canon_sha256":"8cd04b05069963b38c9fd068f5a5ef0e8fb3eac1e6dd00965a509e34ed6f9292"},"schema_version":"1.0","source":{"id":"2209.03077","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.03077","created_at":"2026-07-05T09:53:37Z"},{"alias_kind":"arxiv_version","alias_value":"2209.03077v6","created_at":"2026-07-05T09:53:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.03077","created_at":"2026-07-05T09:53:37Z"},{"alias_kind":"pith_short_12","alias_value":"6OFMMQXAYXAL","created_at":"2026-07-05T09:53:37Z"},{"alias_kind":"pith_short_16","alias_value":"6OFMMQXAYXALP4HE","created_at":"2026-07-05T09:53:37Z"},{"alias_kind":"pith_short_8","alias_value":"6OFMMQXA","created_at":"2026-07-05T09:53:37Z"}],"graph_snapshots":[{"event_id":"sha256:9cba5424b2b22ec18c479ba742c61a53e2fa642cbda10a98ef26d4d9f5fa23a8","target":"graph","created_at":"2026-07-05T09:53:37Z","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/2209.03077/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The variational lower bound (a.k.a. ELBO or free energy) is the central objective for many established as well as for many novel algorithms for unsupervised learning. Such algorithms usually increase the bound until parameters have converged to values close to a stationary point of the learning dynamics. Here we show that (for a very large class of generative models) the variational lower bound is at all stationary points of learning equal to a sum of entropies. Concretely, for standard generative models with one set of latents and one set of observed variables, the sum consists of three entro","authors_text":"Jan Warnken, J\\\"org L\\\"ucke","cross_cats":["cs.IT","cs.LG","math.IT","math.PR","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-09-07T11:33:32Z","title":"On the Convergence of the ELBO to Entropy Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.03077","kind":"arxiv","version":6},"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":"sha256:58d1a2551f65808ae9b0249b0c74732770ba77719d615388f13751479cc0d2b4","target":"record","created_at":"2026-07-05T09:53:37Z","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":"f2e74781f4d56563e3c59d3d0af1a8568611e7a7b3c5af48059450341627d247","cross_cats_sorted":["cs.IT","cs.LG","math.IT","math.PR","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-09-07T11:33:32Z","title_canon_sha256":"8cd04b05069963b38c9fd068f5a5ef0e8fb3eac1e6dd00965a509e34ed6f9292"},"schema_version":"1.0","source":{"id":"2209.03077","kind":"arxiv","version":6}},"canonical_sha256":"f38ac642e0c5c0b7f0e49a6750c4d3638034e9e6f12e57ea76d39a8ad33603e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f38ac642e0c5c0b7f0e49a6750c4d3638034e9e6f12e57ea76d39a8ad33603e0","first_computed_at":"2026-07-05T09:53:37.719981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:53:37.719981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sMgmjPS2+HdW+NFP8ybnLZq55MAQAdT4OeylrnjwcrW0Ey6fK5LMeheYu2r5msWGOY3ak0Scl1XI5h/4gwF9Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:53:37.720373Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.03077","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58d1a2551f65808ae9b0249b0c74732770ba77719d615388f13751479cc0d2b4","sha256:9cba5424b2b22ec18c479ba742c61a53e2fa642cbda10a98ef26d4d9f5fa23a8"],"state_sha256":"788d3fb9b8c39e915c5cc0e2edcd10ccb6f1a98cd946723b41fbcc41c687f415"}