{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UU2URVQEMGQKP53XBUIVSTEX22","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":"a802fdb52353a6d5907a74c1c55c859d37bd7b0563282d69777f95e79cfdbe6c","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-20T17:00:37Z","title_canon_sha256":"5b1189a4b05eefd25f56ce5117dc61e7614ecdcfb97f5c94b901b1db097e5815"},"schema_version":"1.0","source":{"id":"2605.21402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21402","created_at":"2026-05-21T02:05:33Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21402v1","created_at":"2026-05-21T02:05:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21402","created_at":"2026-05-21T02:05:33Z"},{"alias_kind":"pith_short_12","alias_value":"UU2URVQEMGQK","created_at":"2026-05-21T02:05:33Z"},{"alias_kind":"pith_short_16","alias_value":"UU2URVQEMGQKP53X","created_at":"2026-05-21T02:05:33Z"},{"alias_kind":"pith_short_8","alias_value":"UU2URVQE","created_at":"2026-05-21T02:05:33Z"}],"graph_snapshots":[{"event_id":"sha256:6464b16a203cb267bd8b46ef5bdf8a689293965d6a2b136f90cbdd257109587f","target":"graph","created_at":"2026-05-21T02:05:33Z","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/2605.21402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Generative neural networks learn how to produce highly realistic images from a large, but finite number of examples - or do they simply memorise their training set? To settle this question, Kadkhodaie, Guth, Simoncelli and Mallat (ICLR '24) trained diffusion models independently on disjoint subsets of a dataset and showed that they converge to nearly the same density when the number of training images is large enough. This result raises two basic questions: how much data do you need for convergence, and what does convergence capture about learning the data distribution? Here, we address these ","authors_text":"Antoine Maillard, Sebastian Goldt","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-20T17:00:37Z","title":"Memorisation, convergence and generalisation in generative models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21402","kind":"arxiv","version":1},"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":"sha256:871d98a9698e60c9d1c019856e022e09861a9b13f6177acba80745299d0049d4","target":"record","created_at":"2026-05-21T02:05:33Z","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":"a802fdb52353a6d5907a74c1c55c859d37bd7b0563282d69777f95e79cfdbe6c","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2026-05-20T17:00:37Z","title_canon_sha256":"5b1189a4b05eefd25f56ce5117dc61e7614ecdcfb97f5c94b901b1db097e5815"},"schema_version":"1.0","source":{"id":"2605.21402","kind":"arxiv","version":1}},"canonical_sha256":"a53548d60461a0a7f7770d11594c97d6bc7bb63a94e8fe3ba1ae5ce2cb309339","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a53548d60461a0a7f7770d11594c97d6bc7bb63a94e8fe3ba1ae5ce2cb309339","first_computed_at":"2026-05-21T02:05:33.014982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T02:05:33.014982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqvD0jPgNr26voiIAag9ZPgwaCBrNtSKDNOSN1+GqsAjIsjo6JJ4pU1B3xX+altlZqAfJ0OH9f+JtKqzboFrAg==","signature_status":"signed_v1","signed_at":"2026-05-21T02:05:33.015727Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.21402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:871d98a9698e60c9d1c019856e022e09861a9b13f6177acba80745299d0049d4","sha256:6464b16a203cb267bd8b46ef5bdf8a689293965d6a2b136f90cbdd257109587f"],"state_sha256":"9f4774885d6f7784091d110a6890bef1b006adf678d9ca64cb85c219cb429684"}