{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CQ7F6VGIL7PUGOYUDRIF43HRPE","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":"b640f4fc7e0353d9d8f8c7a863bd1d2a707b1db1c9fdb45b629ae785a1b4a208","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-11T08:30:40Z","title_canon_sha256":"c6fbf000fe03b904c86d8fd7d105ae3f44cceed35227dc14fe281c051f6ddda3"},"schema_version":"1.0","source":{"id":"2606.13045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13045","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13045v1","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13045","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"pith_short_12","alias_value":"CQ7F6VGIL7PU","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"pith_short_16","alias_value":"CQ7F6VGIL7PUGOYU","created_at":"2026-06-12T01:09:38Z"},{"alias_kind":"pith_short_8","alias_value":"CQ7F6VGI","created_at":"2026-06-12T01:09:38Z"}],"graph_snapshots":[{"event_id":"sha256:f38cf13a3d2cb3a9510168f951891250b530c9352addb8c4d9d9dc2695265c3d","target":"graph","created_at":"2026-06-12T01:09:38Z","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/2606.13045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a theoretical framework for analyzing federated learning in a generative setting through a teacher-multiple interacting students scenario, in which each student receives a distinct realization of the data, either through a different noise corruption or by accessing a different subset, possibly of varying size. Using theoretical tools in equilibrium disordered system, we analytically show that interactions among students systematically enhance learning performance: highly noisy students require fewer samples to recover the underlying pattern, while low-noise students achieve a larg","authors_text":"Aur\\'elien Decelle, Beatriz Seoane, Daniele Tantari, Gianluca Manzan, Giovanni Catania","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-11T08:30:40Z","title":"A solvable model for unsupervised federated learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13045","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":"sha256:448b42aa1e8215fe7bbae74c64044608e5a3f82983645f29dbcd75545910b1e0","target":"record","created_at":"2026-06-12T01:09:38Z","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":"b640f4fc7e0353d9d8f8c7a863bd1d2a707b1db1c9fdb45b629ae785a1b4a208","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-11T08:30:40Z","title_canon_sha256":"c6fbf000fe03b904c86d8fd7d105ae3f44cceed35227dc14fe281c051f6ddda3"},"schema_version":"1.0","source":{"id":"2606.13045","kind":"arxiv","version":1}},"canonical_sha256":"143e5f54c85fdf433b141c505e6cf1792e165258bc8256233ebdba393e1982b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"143e5f54c85fdf433b141c505e6cf1792e165258bc8256233ebdba393e1982b9","first_computed_at":"2026-06-12T01:09:38.304996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:38.304996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vHn3/Mf1PolpCL48V9Q1qP3ijvzvar6HuwEeDrTrze2m6ACLaO19B7vgb+S8k5ABER0Ob+NK9lt1gX/b2+YjAw==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:38.305428Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:448b42aa1e8215fe7bbae74c64044608e5a3f82983645f29dbcd75545910b1e0","sha256:f38cf13a3d2cb3a9510168f951891250b530c9352addb8c4d9d9dc2695265c3d"],"state_sha256":"e6eede903addbc58f9a278e7ad742094f69670cddeeda5751b1d38aaa85be19c"}