{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:Y6WTXGMKCUDQOPJMIUVAK4B3I7","short_pith_number":"pith:Y6WTXGMK","schema_version":"1.0","canonical_sha256":"c7ad3b998a1507073d2c452a05703b47d2f6eb8a98b59db980bc45d369883848","source":{"kind":"arxiv","id":"2012.03174","version":2},"attestation_state":"computed","paper":{"title":"Counting Substructures with Higher-Order Graph Neural Networks: Possibility and Impossibility Results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Behrooz Tahmasebi, Derek Lim, Stefanie Jegelka","submitted_at":"2020-12-06T03:42:54Z","abstract_excerpt":"While message passing Graph Neural Networks (GNNs) have become increasingly popular architectures for learning with graphs, recent works have revealed important shortcomings in their expressive power. In response, several higher-order GNNs have been proposed that substantially increase the expressive power, albeit at a large computational cost. Motivated by this gap, we explore alternative strategies and lower bounds. In particular, we analyze a new recursive pooling technique of local neighborhoods that allows different tradeoffs of computational cost and expressive power. First, we prove tha"},"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":"2012.03174","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2020-12-06T03:42:54Z","cross_cats_sorted":[],"title_canon_sha256":"93cd18a06cebaa12226399f43b1e2cfe6626d2aa59a49b26c72430e777dd063c","abstract_canon_sha256":"d1e1e83e838313ae573c9a6b1f1a56e7b15666c57c55e5109f448a980a4209ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:32.694802Z","signature_b64":"a4zqlMJ5az1JpnrqfFs+DvQ7MI1aS7BGH1JDoeto0zbjn0Y3rLZljs8UawwqQeTZAjTgeCJGvTIFvxEkFsEYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7ad3b998a1507073d2c452a05703b47d2f6eb8a98b59db980bc45d369883848","last_reissued_at":"2026-07-05T10:20:32.694329Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:32.694329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting Substructures with Higher-Order Graph Neural Networks: Possibility and Impossibility Results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Behrooz Tahmasebi, Derek Lim, Stefanie Jegelka","submitted_at":"2020-12-06T03:42:54Z","abstract_excerpt":"While message passing Graph Neural Networks (GNNs) have become increasingly popular architectures for learning with graphs, recent works have revealed important shortcomings in their expressive power. In response, several higher-order GNNs have been proposed that substantially increase the expressive power, albeit at a large computational cost. Motivated by this gap, we explore alternative strategies and lower bounds. In particular, we analyze a new recursive pooling technique of local neighborhoods that allows different tradeoffs of computational cost and expressive power. First, we prove tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.03174","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/2012.03174/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":"2012.03174","created_at":"2026-07-05T10:20:32.694392+00:00"},{"alias_kind":"arxiv_version","alias_value":"2012.03174v2","created_at":"2026-07-05T10:20:32.694392+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.03174","created_at":"2026-07-05T10:20:32.694392+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y6WTXGMKCUDQ","created_at":"2026-07-05T10:20:32.694392+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y6WTXGMKCUDQOPJM","created_at":"2026-07-05T10:20:32.694392+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y6WTXGMK","created_at":"2026-07-05T10:20:32.694392+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.01122","citing_title":"Learning Efficient Positional Encodings with Graph Neural Networks","ref_index":53,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7","json":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7.json","graph_json":"https://pith.science/api/pith-number/Y6WTXGMKCUDQOPJMIUVAK4B3I7/graph.json","events_json":"https://pith.science/api/pith-number/Y6WTXGMKCUDQOPJMIUVAK4B3I7/events.json","paper":"https://pith.science/paper/Y6WTXGMK"},"agent_actions":{"view_html":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7","download_json":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7.json","view_paper":"https://pith.science/paper/Y6WTXGMK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2012.03174&json=true","fetch_graph":"https://pith.science/api/pith-number/Y6WTXGMKCUDQOPJMIUVAK4B3I7/graph.json","fetch_events":"https://pith.science/api/pith-number/Y6WTXGMKCUDQOPJMIUVAK4B3I7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7/action/storage_attestation","attest_author":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7/action/author_attestation","sign_citation":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7/action/citation_signature","submit_replication":"https://pith.science/pith/Y6WTXGMKCUDQOPJMIUVAK4B3I7/action/replication_record"}},"created_at":"2026-07-05T10:20:32.694392+00:00","updated_at":"2026-07-05T10:20:32.694392+00:00"}