{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CJUJ27CANZSGCBR6ITGHPPEOII","short_pith_number":"pith:CJUJ27CA","canonical_record":{"source":{"id":"2106.15535","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-29T16:13:41Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"9ab4cfd43b57eeb3e87ffda0a80c469c095b8c5ef7831987bfe03abd72649916","abstract_canon_sha256":"3ede664a6be7b438c9cf6e4801910a3bddf22d3f6aa8eef778200840ad3718aa"},"schema_version":"1.0"},"canonical_sha256":"12689d7c406e6461063e44cc77bc8e42383d16f57c4c85fd0ce3f38387b6c572","source":{"kind":"arxiv","id":"2106.15535","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.15535","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"2106.15535v2","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.15535","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"CJUJ27CANZSG","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"pith_short_16","alias_value":"CJUJ27CANZSGCBR6","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"pith_short_8","alias_value":"CJUJ27CA","created_at":"2026-07-05T03:36:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CJUJ27CANZSGCBR6ITGHPPEOII","target":"record","payload":{"canonical_record":{"source":{"id":"2106.15535","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-29T16:13:41Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"9ab4cfd43b57eeb3e87ffda0a80c469c095b8c5ef7831987bfe03abd72649916","abstract_canon_sha256":"3ede664a6be7b438c9cf6e4801910a3bddf22d3f6aa8eef778200840ad3718aa"},"schema_version":"1.0"},"canonical_sha256":"12689d7c406e6461063e44cc77bc8e42383d16f57c4c85fd0ce3f38387b6c572","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:36:07.676597Z","signature_b64":"2SjDkxj7v8gtr15YpghL9W5kD8g+hF48aGc+jXt34rrKdcoU/9QXg0AwrhAnApg+ew1ML865ikENjUnylEhXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12689d7c406e6461063e44cc77bc8e42383d16f57c4c85fd0ce3f38387b6c572","last_reissued_at":"2026-07-05T03:36:07.676111Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:36:07.676111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.15535","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:36:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KiCYTas2o8TQDydhRc0EQYN8WElJ+gTrNw4OlFF+m8AHI0LAgmXbZwaTfqP+Rwn4m/rSwpWBFUB/berfq84oDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T16:29:35.049473Z"},"content_sha256":"7e05f05568c9411731bb8443daf35971ac21b46b34f537b494082d696d034c39","schema_version":"1.0","event_id":"sha256:7e05f05568c9411731bb8443daf35971ac21b46b34f537b494082d696d034c39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CJUJ27CANZSGCBR6ITGHPPEOII","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subgroup Generalization and Fairness of Graph Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Jiaqi Ma, Junwei Deng, Qiaozhu Mei","submitted_at":"2021-06-29T16:13:41Z","abstract_excerpt":"Despite enormous successful applications of graph neural networks (GNNs), theoretical understanding of their generalization ability, especially for node-level tasks where data are not independent and identically-distributed (IID), has been sparse. The theoretical investigation of the generalization performance is beneficial for understanding fundamental issues (such as fairness) of GNN models and designing better learning methods. In this paper, we present a novel PAC-Bayesian analysis for GNNs under a non-IID semi-supervised learning setup. Moreover, we analyze the generalization performances"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.15535","kind":"arxiv","version":2},"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/2106.15535/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":"2026-07-05T03:36:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tS1D7U2oOqDn5jdWPmqpRVfS2cHibYs7RzwgkuWunnChYdIsqSK3VKmmpBx5MXFa0H1WNOwTKOyqr2dMtzaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T16:29:35.049998Z"},"content_sha256":"f22700886e592b69b76d0999461d162bd8c2ada8bedca649e3bb47c17b1b7985","schema_version":"1.0","event_id":"sha256:f22700886e592b69b76d0999461d162bd8c2ada8bedca649e3bb47c17b1b7985"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJUJ27CANZSGCBR6ITGHPPEOII/bundle.json","state_url":"https://pith.science/pith/CJUJ27CANZSGCBR6ITGHPPEOII/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJUJ27CANZSGCBR6ITGHPPEOII/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":"2026-08-07T16:29:35Z","links":{"resolver":"https://pith.science/pith/CJUJ27CANZSGCBR6ITGHPPEOII","bundle":"https://pith.science/pith/CJUJ27CANZSGCBR6ITGHPPEOII/bundle.json","state":"https://pith.science/pith/CJUJ27CANZSGCBR6ITGHPPEOII/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJUJ27CANZSGCBR6ITGHPPEOII/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CJUJ27CANZSGCBR6ITGHPPEOII","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":"3ede664a6be7b438c9cf6e4801910a3bddf22d3f6aa8eef778200840ad3718aa","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-29T16:13:41Z","title_canon_sha256":"9ab4cfd43b57eeb3e87ffda0a80c469c095b8c5ef7831987bfe03abd72649916"},"schema_version":"1.0","source":{"id":"2106.15535","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.15535","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"arxiv_version","alias_value":"2106.15535v2","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.15535","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"pith_short_12","alias_value":"CJUJ27CANZSG","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"pith_short_16","alias_value":"CJUJ27CANZSGCBR6","created_at":"2026-07-05T03:36:07Z"},{"alias_kind":"pith_short_8","alias_value":"CJUJ27CA","created_at":"2026-07-05T03:36:07Z"}],"graph_snapshots":[{"event_id":"sha256:f22700886e592b69b76d0999461d162bd8c2ada8bedca649e3bb47c17b1b7985","target":"graph","created_at":"2026-07-05T03:36:07Z","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/2106.15535/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite enormous successful applications of graph neural networks (GNNs), theoretical understanding of their generalization ability, especially for node-level tasks where data are not independent and identically-distributed (IID), has been sparse. The theoretical investigation of the generalization performance is beneficial for understanding fundamental issues (such as fairness) of GNN models and designing better learning methods. In this paper, we present a novel PAC-Bayesian analysis for GNNs under a non-IID semi-supervised learning setup. Moreover, we analyze the generalization performances","authors_text":"Jiaqi Ma, Junwei Deng, Qiaozhu Mei","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-29T16:13:41Z","title":"Subgroup Generalization and Fairness of Graph Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.15535","kind":"arxiv","version":2},"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":"sha256:7e05f05568c9411731bb8443daf35971ac21b46b34f537b494082d696d034c39","target":"record","created_at":"2026-07-05T03:36:07Z","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":"3ede664a6be7b438c9cf6e4801910a3bddf22d3f6aa8eef778200840ad3718aa","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-29T16:13:41Z","title_canon_sha256":"9ab4cfd43b57eeb3e87ffda0a80c469c095b8c5ef7831987bfe03abd72649916"},"schema_version":"1.0","source":{"id":"2106.15535","kind":"arxiv","version":2}},"canonical_sha256":"12689d7c406e6461063e44cc77bc8e42383d16f57c4c85fd0ce3f38387b6c572","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12689d7c406e6461063e44cc77bc8e42383d16f57c4c85fd0ce3f38387b6c572","first_computed_at":"2026-07-05T03:36:07.676111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:36:07.676111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2SjDkxj7v8gtr15YpghL9W5kD8g+hF48aGc+jXt34rrKdcoU/9QXg0AwrhAnApg+ew1ML865ikENjUnylEhXBA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:36:07.676597Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.15535","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e05f05568c9411731bb8443daf35971ac21b46b34f537b494082d696d034c39","sha256:f22700886e592b69b76d0999461d162bd8c2ada8bedca649e3bb47c17b1b7985"],"state_sha256":"d0a0ee4eb096dfbc67ca469f4256c8ebca53e184ea4273369edad41ba9713d3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3J9QPwZZgG9oiXf1x6UsCWGv9aSMoAQ18RU9h4AGhyPu482yAyuQVbkmNd5gak4jHsP9hjxY0vrbL6tNUK3XDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T16:29:35.054670Z","bundle_sha256":"a6d1168b1f29c56f75d126900033e127f9f30d7e366dd0270e20208b6c24c415"}}