{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:JIX74A2YPYVZRUI6XLVUY27TN2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3f0defa0ecdb4b50da0c88154e1827b85d9ebdde9124417992b43f2b4cbfae54","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-31T22:41:35Z","title_canon_sha256":"ab1b83300857fe008ddf8c72754eb9a4bf8ab5cdf8029a6409486a586907f560"},"schema_version":"1.0","source":{"id":"2202.00132","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.00132","created_at":"2026-07-05T05:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"2202.00132v2","created_at":"2026-07-05T05:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.00132","created_at":"2026-07-05T05:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"JIX74A2YPYVZ","created_at":"2026-07-05T05:02:57Z"},{"alias_kind":"pith_short_16","alias_value":"JIX74A2YPYVZRUI6","created_at":"2026-07-05T05:02:57Z"},{"alias_kind":"pith_short_8","alias_value":"JIX74A2Y","created_at":"2026-07-05T05:02:57Z"}],"graph_snapshots":[{"event_id":"sha256:ff773dc71f9d0021f347c2ca0d3abf7afb7aa52618f8c54dc3e261a384361b6f","target":"graph","created_at":"2026-07-05T05:02:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2202.00132/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this manuscript, we offer a gentle review of submodularity and supermodularity and their properties. We offer a plethora of submodular definitions; a full description of a number of example submodular functions and their generalizations; example discrete constraints; a discussion of basic algorithms for maximization, minimization, and other operations; a brief overview of continuous submodular extensions; and some historical applications. We then turn to how submodularity is useful in machine learning and artificial intelligence. This includes summarization, and we offer a complete account ","authors_text":"Jeff Bilmes","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-31T22:41:35Z","title":"Submodularity In Machine Learning and Artificial Intelligence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.00132","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6c70bcdab71f27c610713505af8711d9ce1c03788ef928c20c74d9fa256285d0","target":"record","created_at":"2026-07-05T05:02:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3f0defa0ecdb4b50da0c88154e1827b85d9ebdde9124417992b43f2b4cbfae54","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-01-31T22:41:35Z","title_canon_sha256":"ab1b83300857fe008ddf8c72754eb9a4bf8ab5cdf8029a6409486a586907f560"},"schema_version":"1.0","source":{"id":"2202.00132","kind":"arxiv","version":2}},"canonical_sha256":"4a2ffe03587e2b98d11ebaeb4c6bf36ebc13358f37bf1ee17a241f7dafa4f6f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a2ffe03587e2b98d11ebaeb4c6bf36ebc13358f37bf1ee17a241f7dafa4f6f1","first_computed_at":"2026-07-05T05:02:57.685120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:02:57.685120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ToKB9dwBky4NrfIPo4mSbZIHRjuNKqgNVuEwRKtForOklmSPrXg7z0P3u2UjHcW+szUinfA2+dunXFFhZEg3Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:02:57.685645Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.00132","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c70bcdab71f27c610713505af8711d9ce1c03788ef928c20c74d9fa256285d0","sha256:ff773dc71f9d0021f347c2ca0d3abf7afb7aa52618f8c54dc3e261a384361b6f"],"state_sha256":"478473a5034360573b8b6dc8b660626e43f071dc07ce24cc03779ac6e3f86271"}