{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:PNLLGOCZWIDSEJJHDS42BDBIZA","short_pith_number":"pith:PNLLGOCZ","schema_version":"1.0","canonical_sha256":"7b56b33859b2072225271cb9a08c28c825b39231a40af5b121fa0efea6a2a257","source":{"kind":"arxiv","id":"2102.07835","version":4},"attestation_state":"computed","paper":{"title":"Topological Graph Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Bastian Rieck, Edward De Brouwer, Karsten Borgwardt, Max Horn, Michael Moor, Yves Moreau","submitted_at":"2021-02-15T20:27:56Z","abstract_excerpt":"Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can"},"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":"2102.07835","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-15T20:27:56Z","cross_cats_sorted":["math.AT","stat.ML"],"title_canon_sha256":"af702a9f2628c4b0b3b26f14de70d885346f6b18feb7d38af7bb6be8aa4adadc","abstract_canon_sha256":"ee6eb964d3f5138fb9ce317521b7db70a948cab7e56c78c42cd24c81218c5117"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:05:56.896053Z","signature_b64":"6z26Y9E2augx6/+FvkxJU0wf12lmbVlawh2A3npo5ob01eqQiKZw9pZacoa6ErEMuaf9sU6IfgD13UzErMC1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b56b33859b2072225271cb9a08c28c825b39231a40af5b121fa0efea6a2a257","last_reissued_at":"2026-07-05T04:05:56.895625Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:05:56.895625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Graph Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Bastian Rieck, Edward De Brouwer, Karsten Borgwardt, Max Horn, Michael Moor, Yves Moreau","submitted_at":"2021-02-15T20:27:56Z","abstract_excerpt":"Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07835","kind":"arxiv","version":4},"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/2102.07835/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":"2102.07835","created_at":"2026-07-05T04:05:56.895687+00:00"},{"alias_kind":"arxiv_version","alias_value":"2102.07835v4","created_at":"2026-07-05T04:05:56.895687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.07835","created_at":"2026-07-05T04:05:56.895687+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNLLGOCZWIDS","created_at":"2026-07-05T04:05:56.895687+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNLLGOCZWIDSEJJH","created_at":"2026-07-05T04:05:56.895687+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNLLGOCZ","created_at":"2026-07-05T04:05:56.895687+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.11911","citing_title":"From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features","ref_index":84,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13997","citing_title":"HodgeCover: Higher-Order Topological Coverage Drives Compression of Sparse Mixture-of-Experts","ref_index":27,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA","json":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA.json","graph_json":"https://pith.science/api/pith-number/PNLLGOCZWIDSEJJHDS42BDBIZA/graph.json","events_json":"https://pith.science/api/pith-number/PNLLGOCZWIDSEJJHDS42BDBIZA/events.json","paper":"https://pith.science/paper/PNLLGOCZ"},"agent_actions":{"view_html":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA","download_json":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA.json","view_paper":"https://pith.science/paper/PNLLGOCZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2102.07835&json=true","fetch_graph":"https://pith.science/api/pith-number/PNLLGOCZWIDSEJJHDS42BDBIZA/graph.json","fetch_events":"https://pith.science/api/pith-number/PNLLGOCZWIDSEJJHDS42BDBIZA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA/action/storage_attestation","attest_author":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA/action/author_attestation","sign_citation":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA/action/citation_signature","submit_replication":"https://pith.science/pith/PNLLGOCZWIDSEJJHDS42BDBIZA/action/replication_record"}},"created_at":"2026-07-05T04:05:56.895687+00:00","updated_at":"2026-07-05T04:05:56.895687+00:00"}