{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:PVUT4JYNPEAIONBLT674IPBUEZ","short_pith_number":"pith:PVUT4JYN","schema_version":"1.0","canonical_sha256":"7d693e270d790087342b9fbfc43c342648ff36dbed2a3f582e277d9a897a9815","source":{"kind":"arxiv","id":"1811.01900","version":3},"attestation_state":"computed","paper":{"title":"Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Balasubramaniam Srinivasan, Bruno Ribeiro, Ryan L. Murphy, Vinayak Rao","submitted_at":"2018-11-05T18:26:41Z","abstract_excerpt":"We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider th"},"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":"1811.01900","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-11-05T18:26:41Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"57b993f11e72ba1c08b1a4940bf8744cb1f5b42f9d1f722507a30356acc6f81b","abstract_canon_sha256":"bad11a740845e525fdae778c6e0ca3b046a12333b171b74564d1efcbcedcbe8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:45.373636Z","signature_b64":"slGmKNFg3poH4pI9cjm/NNiXGQLydnRmfaeMH8zSxrJWEezaaAmHjcFIgkl03efhzqYqL5bvaT9+ibdlTMqdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d693e270d790087342b9fbfc43c342648ff36dbed2a3f582e277d9a897a9815","last_reissued_at":"2026-05-17T23:52:45.373051Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:45.373051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Balasubramaniam Srinivasan, Bruno Ribeiro, Ryan L. Murphy, Vinayak Rao","submitted_at":"2018-11-05T18:26:41Z","abstract_excerpt":"We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01900","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":""},"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":"1811.01900","created_at":"2026-05-17T23:52:45.373129+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01900v3","created_at":"2026-05-17T23:52:45.373129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01900","created_at":"2026-05-17T23:52:45.373129+00:00"},{"alias_kind":"pith_short_12","alias_value":"PVUT4JYNPEAI","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"PVUT4JYNPEAIONBL","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"PVUT4JYN","created_at":"2026-05-18T12:32:46.962924+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2003.03485","citing_title":"Neural Operator: Graph Kernel Network for Partial Differential Equations","ref_index":136,"is_internal_anchor":true},{"citing_arxiv_id":"2104.13478","citing_title":"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges","ref_index":62,"is_internal_anchor":false},{"citing_arxiv_id":"1810.00826","citing_title":"How Powerful are Graph Neural Networks?","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ","json":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ.json","graph_json":"https://pith.science/api/pith-number/PVUT4JYNPEAIONBLT674IPBUEZ/graph.json","events_json":"https://pith.science/api/pith-number/PVUT4JYNPEAIONBLT674IPBUEZ/events.json","paper":"https://pith.science/paper/PVUT4JYN"},"agent_actions":{"view_html":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ","download_json":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ.json","view_paper":"https://pith.science/paper/PVUT4JYN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01900&json=true","fetch_graph":"https://pith.science/api/pith-number/PVUT4JYNPEAIONBLT674IPBUEZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PVUT4JYNPEAIONBLT674IPBUEZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ/action/storage_attestation","attest_author":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ/action/author_attestation","sign_citation":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ/action/citation_signature","submit_replication":"https://pith.science/pith/PVUT4JYNPEAIONBLT674IPBUEZ/action/replication_record"}},"created_at":"2026-05-17T23:52:45.373129+00:00","updated_at":"2026-05-17T23:52:45.373129+00:00"}