{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PLKYJ5FASEBBKIAW6SPWDSSH7G","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":"41398fddeac88e1737c57a1eea99e3fc2565a19db3adb38b34c700ed7de8542b","cross_cats_sorted":["cs.LG","math.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-10T03:37:29Z","title_canon_sha256":"535c10be27c1aa74ddb3cf9b4519b84ee2056b376ee6d4548f8b4c51b155262f"},"schema_version":"1.0","source":{"id":"1810.04351","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04351","created_at":"2026-05-17T23:49:41Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04351v2","created_at":"2026-05-17T23:49:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04351","created_at":"2026-05-17T23:49:41Z"},{"alias_kind":"pith_short_12","alias_value":"PLKYJ5FASEBB","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PLKYJ5FASEBBKIAW","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PLKYJ5FA","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:65794f2932f4b6a0996826d45a13f7e380ad9ea5e402c08244c47d9abd7738e9","target":"graph","created_at":"2026-05-17T23:49:41Z","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"},"paper":{"abstract_excerpt":"The performance of traditional graph Laplacian methods for semi-supervised learning degrades substantially as the ratio of labeled to unlabeled data decreases, due to a degeneracy in the graph Laplacian. Several approaches have been proposed recently to address this, however we show that some of them remain ill-posed in the large-data limit.\n  In this paper, we show a way to correctly set the weights in Laplacian regularization so that the estimator remains well posed and stable in the large-sample limit. We prove that our semi-supervised learning algorithm converges, in the infinite sample si","authors_text":"Dejan Slepcev, Jeff Calder","cross_cats":["cs.LG","math.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-10T03:37:29Z","title":"Properly-weighted graph Laplacian for semi-supervised learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04351","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":"sha256:8c693d4e9a1ceb7e64b77ba938305725ec34132d4ea58232cf8afa1682593ca7","target":"record","created_at":"2026-05-17T23:49:41Z","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":"41398fddeac88e1737c57a1eea99e3fc2565a19db3adb38b34c700ed7de8542b","cross_cats_sorted":["cs.LG","math.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-10T03:37:29Z","title_canon_sha256":"535c10be27c1aa74ddb3cf9b4519b84ee2056b376ee6d4548f8b4c51b155262f"},"schema_version":"1.0","source":{"id":"1810.04351","kind":"arxiv","version":2}},"canonical_sha256":"7ad584f4a09102152016f49f61ca47f9ac64b544312e7777a3861d0d408d7f7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ad584f4a09102152016f49f61ca47f9ac64b544312e7777a3861d0d408d7f7e","first_computed_at":"2026-05-17T23:49:41.015656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:41.015656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KFibCbcGNHh+rdvC/zrt09dltuktqFeWLmFeootNWJkgzkz8vsqtfOm6N6VjrB0j5Tvghrdj+YpZMNIRyT7OCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:41.016277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04351","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c693d4e9a1ceb7e64b77ba938305725ec34132d4ea58232cf8afa1682593ca7","sha256:65794f2932f4b6a0996826d45a13f7e380ad9ea5e402c08244c47d9abd7738e9"],"state_sha256":"90b99e40a334b3a2c318a41d6cb6b7d4339830f748aaaa0b9a6db305210a7b46"}