{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7TAV6OYXOVT3CPVXULUPR3UNNC","short_pith_number":"pith:7TAV6OYX","schema_version":"1.0","canonical_sha256":"fcc15f3b177567b13eb7a2e8f8ee8d6884ff660ca131b8e997094645c9312f9f","source":{"kind":"arxiv","id":"2309.07364","version":1},"attestation_state":"computed","paper":{"title":"Hodge-Aware Contrastive Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","eess.SP"],"primary_cat":"cs.LG","authors_text":"Alexander Immer, Alexander M\\\"ollers, Elvin Isufi, Vincent Fortuin","submitted_at":"2023-09-14T00:40:07Z","abstract_excerpt":"Simplicial complexes prove effective in modeling data with multiway dependencies, such as data defined along the edges of networks or within other higher-order structures. Their spectrum can be decomposed into three interpretable subspaces via the Hodge decomposition, resulting foundational in numerous applications. We leverage this decomposition to develop a contrastive self-supervised learning approach for processing simplicial data and generating embeddings that encapsulate specific spectral information.Specifically, we encode the pertinent data invariances through simplicial neural network"},"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":"2309.07364","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-09-14T00:40:07Z","cross_cats_sorted":["cs.AI","eess.SP"],"title_canon_sha256":"ffa7e9957931d9ddc8c9990ae8125d57f240302096e95b0fd311daed3dc7375f","abstract_canon_sha256":"0beb8e2aa3a2f576d2128a42dee6ceb64497bb3f0dbd97021b43e0dd5566cd17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:50:43.189096Z","signature_b64":"rD2G1mC1ydZyO3ksSpPggjliQBL0Bj6Iwb6nNvytQQ0IiwXCpgeO6GAzWDIJgDnkvhu5VwEXRecLVvw4+F1+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcc15f3b177567b13eb7a2e8f8ee8d6884ff660ca131b8e997094645c9312f9f","last_reissued_at":"2026-07-05T06:50:43.188703Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:50:43.188703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hodge-Aware Contrastive Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","eess.SP"],"primary_cat":"cs.LG","authors_text":"Alexander Immer, Alexander M\\\"ollers, Elvin Isufi, Vincent Fortuin","submitted_at":"2023-09-14T00:40:07Z","abstract_excerpt":"Simplicial complexes prove effective in modeling data with multiway dependencies, such as data defined along the edges of networks or within other higher-order structures. Their spectrum can be decomposed into three interpretable subspaces via the Hodge decomposition, resulting foundational in numerous applications. We leverage this decomposition to develop a contrastive self-supervised learning approach for processing simplicial data and generating embeddings that encapsulate specific spectral information.Specifically, we encode the pertinent data invariances through simplicial neural network"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.07364","kind":"arxiv","version":1},"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/2309.07364/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":"2309.07364","created_at":"2026-07-05T06:50:43.188760+00:00"},{"alias_kind":"arxiv_version","alias_value":"2309.07364v1","created_at":"2026-07-05T06:50:43.188760+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.07364","created_at":"2026-07-05T06:50:43.188760+00:00"},{"alias_kind":"pith_short_12","alias_value":"7TAV6OYXOVT3","created_at":"2026-07-05T06:50:43.188760+00:00"},{"alias_kind":"pith_short_16","alias_value":"7TAV6OYXOVT3CPVX","created_at":"2026-07-05T06:50:43.188760+00:00"},{"alias_kind":"pith_short_8","alias_value":"7TAV6OYX","created_at":"2026-07-05T06:50:43.188760+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/7TAV6OYXOVT3CPVXULUPR3UNNC","json":"https://pith.science/pith/7TAV6OYXOVT3CPVXULUPR3UNNC.json","graph_json":"https://pith.science/api/pith-number/7TAV6OYXOVT3CPVXULUPR3UNNC/graph.json","events_json":"https://pith.science/api/pith-number/7TAV6OYXOVT3CPVXULUPR3UNNC/events.json","paper":"https://pith.science/paper/7TAV6OYX"},"agent_actions":{"view_html":"https://pith.science/pith/7TAV6OYXOVT3CPVXULUPR3UNNC","download_json":"https://pith.science/pith/7TAV6OYXOVT3CPVXULUPR3UNNC.json","view_paper":"https://pith.science/paper/7TAV6OYX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2309.07364&json=true","fetch_graph":"https://pith.science/api/pith-number/7TAV6OYXOVT3CPVXULUPR3UNNC/graph.json","fetch_events":"https://pith.science/api/pith-number/7TAV6OYXOVT3CPVXULUPR3UNNC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7TAV6OYXOVT3CPVXULUPR3UNNC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7TAV6OYXOVT3CPVXULUPR3UNNC/action/storage_attestation","attest_author":"https://pith.science/pith/7TAV6OYXOVT3CPVXULUPR3UNNC/action/author_attestation","sign_citation":"https://pith.science/pith/7TAV6OYXOVT3CPVXULUPR3UNNC/action/citation_signature","submit_replication":"https://pith.science/pith/7TAV6OYXOVT3CPVXULUPR3UNNC/action/replication_record"}},"created_at":"2026-07-05T06:50:43.188760+00:00","updated_at":"2026-07-05T06:50:43.188760+00:00"}