{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:HNENKDKBUEMMYB2CGWP26WYBOF","short_pith_number":"pith:HNENKDKB","canonical_record":{"source":{"id":"2310.15330","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-10-23T19:53:36Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"31652bbea648b316385f3dac0a50c29ae085de7f2ab681ee4cc219c1acc84488","abstract_canon_sha256":"c98db306e68beb17e793cb2a8bbc8f185ee77a0227547045f732795b76af8e65"},"schema_version":"1.0"},"canonical_sha256":"3b48d50d41a118cc0742359faf5b01714509a93cb7d5c4294f8caf0bf6e97ef0","source":{"kind":"arxiv","id":"2310.15330","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.15330","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"arxiv_version","alias_value":"2310.15330v3","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.15330","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"pith_short_12","alias_value":"HNENKDKBUEMM","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"pith_short_16","alias_value":"HNENKDKBUEMMYB2C","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"pith_short_8","alias_value":"HNENKDKB","created_at":"2026-07-05T10:50:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:HNENKDKBUEMMYB2CGWP26WYBOF","target":"record","payload":{"canonical_record":{"source":{"id":"2310.15330","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-10-23T19:53:36Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"31652bbea648b316385f3dac0a50c29ae085de7f2ab681ee4cc219c1acc84488","abstract_canon_sha256":"c98db306e68beb17e793cb2a8bbc8f185ee77a0227547045f732795b76af8e65"},"schema_version":"1.0"},"canonical_sha256":"3b48d50d41a118cc0742359faf5b01714509a93cb7d5c4294f8caf0bf6e97ef0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:28.502234Z","signature_b64":"ZwpZ4+kTTyl7ZA2/tRPkQSEBXOGcV0U4A4btlkKsyicWK/GBoRbm+xx+qTOoty0l3JsaSxii4+viZR6wVAFiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b48d50d41a118cc0742359faf5b01714509a93cb7d5c4294f8caf0bf6e97ef0","last_reissued_at":"2026-07-05T10:50:28.501710Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:28.501710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.15330","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:50:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3S+V74vf7Jyt04EBSCLotWldyYILAL42jKPiMoNKK4/FvF7VA8dMOmOfdENXZ4s2gnYdAPJUoxXVZFxQrgfDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T15:44:59.786737Z"},"content_sha256":"38e61cdb088ea429b984ae732a58fc66986556f204225c31f0f7510772b67d9a","schema_version":"1.0","event_id":"sha256:38e61cdb088ea429b984ae732a58fc66986556f204225c31f0f7510772b67d9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:HNENKDKBUEMMYB2CGWP26WYBOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards the Theory of Unsupervised Federated Learning: Non-asymptotic Analysis of Federated EM Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Haolei Weng, Yang Feng, Ye Tian","submitted_at":"2023-10-23T19:53:36Z","abstract_excerpt":"While supervised federated learning approaches have enjoyed significant success, the domain of unsupervised federated learning remains relatively underexplored. Several federated EM algorithms have gained popularity in practice, however, their theoretical foundations are often lacking. In this paper, we first introduce a federated gradient EM algorithm (FedGrEM) designed for the unsupervised learning of mixture models, which supplements the existing federated EM algorithms by considering task heterogeneity and potential adversarial attacks. We present a comprehensive finite-sample theory that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.15330","kind":"arxiv","version":3},"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/2310.15330/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":"2026-07-05T10:50:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jclUfYuGI+E3lNUuvK3JRHspdC9Gk7ojdqH8auXySHHdrRrPkb9W8mGGsEhlquXCHfsgi9hpGBORbRVnTg72BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T15:44:59.787236Z"},"content_sha256":"56ebe32e8028d56e94936166063741f915b68d22d01a7820c3b6c07ad8cee3d5","schema_version":"1.0","event_id":"sha256:56ebe32e8028d56e94936166063741f915b68d22d01a7820c3b6c07ad8cee3d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNENKDKBUEMMYB2CGWP26WYBOF/bundle.json","state_url":"https://pith.science/pith/HNENKDKBUEMMYB2CGWP26WYBOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNENKDKBUEMMYB2CGWP26WYBOF/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":"2026-08-07T15:44:59Z","links":{"resolver":"https://pith.science/pith/HNENKDKBUEMMYB2CGWP26WYBOF","bundle":"https://pith.science/pith/HNENKDKBUEMMYB2CGWP26WYBOF/bundle.json","state":"https://pith.science/pith/HNENKDKBUEMMYB2CGWP26WYBOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNENKDKBUEMMYB2CGWP26WYBOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HNENKDKBUEMMYB2CGWP26WYBOF","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":"c98db306e68beb17e793cb2a8bbc8f185ee77a0227547045f732795b76af8e65","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-10-23T19:53:36Z","title_canon_sha256":"31652bbea648b316385f3dac0a50c29ae085de7f2ab681ee4cc219c1acc84488"},"schema_version":"1.0","source":{"id":"2310.15330","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.15330","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"arxiv_version","alias_value":"2310.15330v3","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.15330","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"pith_short_12","alias_value":"HNENKDKBUEMM","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"pith_short_16","alias_value":"HNENKDKBUEMMYB2C","created_at":"2026-07-05T10:50:28Z"},{"alias_kind":"pith_short_8","alias_value":"HNENKDKB","created_at":"2026-07-05T10:50:28Z"}],"graph_snapshots":[{"event_id":"sha256:56ebe32e8028d56e94936166063741f915b68d22d01a7820c3b6c07ad8cee3d5","target":"graph","created_at":"2026-07-05T10:50:28Z","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/2310.15330/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"While supervised federated learning approaches have enjoyed significant success, the domain of unsupervised federated learning remains relatively underexplored. Several federated EM algorithms have gained popularity in practice, however, their theoretical foundations are often lacking. In this paper, we first introduce a federated gradient EM algorithm (FedGrEM) designed for the unsupervised learning of mixture models, which supplements the existing federated EM algorithms by considering task heterogeneity and potential adversarial attacks. We present a comprehensive finite-sample theory that ","authors_text":"Haolei Weng, Yang Feng, Ye Tian","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-10-23T19:53:36Z","title":"Towards the Theory of Unsupervised Federated Learning: Non-asymptotic Analysis of Federated EM Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.15330","kind":"arxiv","version":3},"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":"sha256:38e61cdb088ea429b984ae732a58fc66986556f204225c31f0f7510772b67d9a","target":"record","created_at":"2026-07-05T10:50:28Z","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":"c98db306e68beb17e793cb2a8bbc8f185ee77a0227547045f732795b76af8e65","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-10-23T19:53:36Z","title_canon_sha256":"31652bbea648b316385f3dac0a50c29ae085de7f2ab681ee4cc219c1acc84488"},"schema_version":"1.0","source":{"id":"2310.15330","kind":"arxiv","version":3}},"canonical_sha256":"3b48d50d41a118cc0742359faf5b01714509a93cb7d5c4294f8caf0bf6e97ef0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b48d50d41a118cc0742359faf5b01714509a93cb7d5c4294f8caf0bf6e97ef0","first_computed_at":"2026-07-05T10:50:28.501710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:50:28.501710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZwpZ4+kTTyl7ZA2/tRPkQSEBXOGcV0U4A4btlkKsyicWK/GBoRbm+xx+qTOoty0l3JsaSxii4+viZR6wVAFiBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:50:28.502234Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.15330","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38e61cdb088ea429b984ae732a58fc66986556f204225c31f0f7510772b67d9a","sha256:56ebe32e8028d56e94936166063741f915b68d22d01a7820c3b6c07ad8cee3d5"],"state_sha256":"1cf338470d376de24aea8077acf015d2e055c772eecbf44c794f189107e2c92f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nmF6LaEOEZLD/ZuUUKe11zRxKf9XdeXmGKFtPjmC5X+o2ITtjwmI8uGcWpgo9WZ7pAucGqciD5Ujta2ZvKQeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T15:44:59.798861Z","bundle_sha256":"7fb23e17e7e8cdc586cf5ae5690b3cb5c626b124562f8071d36113f2b984ab96"}}