{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:RDMRZDCAJO2GEQ4WMNGKSY7RCA","short_pith_number":"pith:RDMRZDCA","schema_version":"1.0","canonical_sha256":"88d91c8c404bb4624396634ca963f1103786598f163c14d4fe17ac08a9b8d1bf","source":{"kind":"arxiv","id":"1905.12560","version":2},"attestation_state":"computed","paper":{"title":"On the equivalence between graph isomorphism testing and function approximation with GNNs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Joan Bruna, Lei Chen, Soledad Villar, Zhengdao Chen","submitted_at":"2019-05-29T16:14:23Z","abstract_excerpt":"Graph Neural Networks (GNNs) have achieved much success on graph-structured data. In light of this, there have been increasing interests in studying their expressive power. One line of work studies the capability of GNNs to approximate permutation-invariant functions on graphs, and another focuses on the their power as tests for graph isomorphism. Our work connects these two perspectives and proves their equivalence. We further develop a framework of the expressive power of GNNs that incorporates both of these viewpoints using the language of sigma-algebra, through which we compare the express"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.12560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-29T16:14:23Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bb48c4a6db6e2425ac698899578552d3b0f25fd5a3fdfd15f2b1b8aa5ec0764c","abstract_canon_sha256":"5991782beee69f8d080b3c3a75d344b5a3dabd0e7c97332ad3d4d023fdc17b40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:40:40.970993Z","signature_b64":"DN3k6/Fy+ACvjehDYd+Y+3yBlBXNa30EtWId9UZ2SFumXEl/7Z7f8hkv6XesqugcXlTHCYxd55Opic2QrFYGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88d91c8c404bb4624396634ca963f1103786598f163c14d4fe17ac08a9b8d1bf","last_reissued_at":"2026-07-05T05:40:40.970428Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:40:40.970428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the equivalence between graph isomorphism testing and function approximation with GNNs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Joan Bruna, Lei Chen, Soledad Villar, Zhengdao Chen","submitted_at":"2019-05-29T16:14:23Z","abstract_excerpt":"Graph Neural Networks (GNNs) have achieved much success on graph-structured data. In light of this, there have been increasing interests in studying their expressive power. One line of work studies the capability of GNNs to approximate permutation-invariant functions on graphs, and another focuses on the their power as tests for graph isomorphism. Our work connects these two perspectives and proves their equivalence. We further develop a framework of the expressive power of GNNs that incorporates both of these viewpoints using the language of sigma-algebra, through which we compare the express"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12560","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/1905.12560/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.12560","created_at":"2026-07-05T05:40:40.970497+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.12560v2","created_at":"2026-07-05T05:40:40.970497+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12560","created_at":"2026-07-05T05:40:40.970497+00:00"},{"alias_kind":"pith_short_12","alias_value":"RDMRZDCAJO2G","created_at":"2026-07-05T05:40:40.970497+00:00"},{"alias_kind":"pith_short_16","alias_value":"RDMRZDCAJO2GEQ4W","created_at":"2026-07-05T05:40:40.970497+00:00"},{"alias_kind":"pith_short_8","alias_value":"RDMRZDCA","created_at":"2026-07-05T05:40:40.970497+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA","json":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA.json","graph_json":"https://pith.science/api/pith-number/RDMRZDCAJO2GEQ4WMNGKSY7RCA/graph.json","events_json":"https://pith.science/api/pith-number/RDMRZDCAJO2GEQ4WMNGKSY7RCA/events.json","paper":"https://pith.science/paper/RDMRZDCA"},"agent_actions":{"view_html":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA","download_json":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA.json","view_paper":"https://pith.science/paper/RDMRZDCA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.12560&json=true","fetch_graph":"https://pith.science/api/pith-number/RDMRZDCAJO2GEQ4WMNGKSY7RCA/graph.json","fetch_events":"https://pith.science/api/pith-number/RDMRZDCAJO2GEQ4WMNGKSY7RCA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA/action/storage_attestation","attest_author":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA/action/author_attestation","sign_citation":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA/action/citation_signature","submit_replication":"https://pith.science/pith/RDMRZDCAJO2GEQ4WMNGKSY7RCA/action/replication_record"}},"created_at":"2026-07-05T05:40:40.970497+00:00","updated_at":"2026-07-05T05:40:40.970497+00:00"}