{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Z27J7TO2CLD6OVJPKRYHWWA5AQ","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":"aa809b013209e5e52cf9d24bc68812b51ac764456e09f29510c7160ffdcc22b3","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-11-11T05:06:02Z","title_canon_sha256":"6ac621e320856837f59cb5f6865b31c56c1c15d3eab0d2aa45186d11deffbd06"},"schema_version":"1.0","source":{"id":"1811.04351","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04351","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04351v1","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04351","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"pith_short_12","alias_value":"Z27J7TO2CLD6","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z27J7TO2CLD6OVJP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z27J7TO2","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:d45e627f30317e21e55b09f2372885f7df5743b857734fdf87c1dbc21f517bff","target":"graph","created_at":"2026-05-18T00:01:05Z","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 vicinal risk minimization (VRM) principle, first proposed by \\citet{vapnik1999nature}, is an empirical risk minimization (ERM) variant that replaces Dirac masses with vicinal functions. Although there is strong numerical evidence showing that VRM outperforms ERM if appropriate vicinal functions are chosen, a comprehensive theoretical understanding of VRM is still lacking. In this paper, we study the generalization bounds for VRM. Our results support Vapnik's original arguments and additionally provide deeper insights into VRM. First, we prove that the complexity of function classes convolv","authors_text":"Chao Zhang, Dacheng Tao, Min-Hsiu Hsieh","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-11-11T05:06:02Z","title":"Generalization Bounds for Vicinal Risk Minimization Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04351","kind":"arxiv","version":1},"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":"sha256:79f425d2f5f6b03eda179b179a29b9cbe592938bfe1462be4b5e94e4a905f9e3","target":"record","created_at":"2026-05-18T00:01:05Z","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":"aa809b013209e5e52cf9d24bc68812b51ac764456e09f29510c7160ffdcc22b3","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-11-11T05:06:02Z","title_canon_sha256":"6ac621e320856837f59cb5f6865b31c56c1c15d3eab0d2aa45186d11deffbd06"},"schema_version":"1.0","source":{"id":"1811.04351","kind":"arxiv","version":1}},"canonical_sha256":"cebe9fcdda12c7e7552f54707b581d041e3481d6b0047591da73f97db6871939","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cebe9fcdda12c7e7552f54707b581d041e3481d6b0047591da73f97db6871939","first_computed_at":"2026-05-18T00:01:05.464679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:05.464679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+NOV9NQ19wiubmSI7upbHJS1KzkVm7QF5G0B85eFIMc9n9b4tsqmSnBXP7EBHV/Ue0JIxk36zuZyRT4RgogCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:05.465293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04351","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79f425d2f5f6b03eda179b179a29b9cbe592938bfe1462be4b5e94e4a905f9e3","sha256:d45e627f30317e21e55b09f2372885f7df5743b857734fdf87c1dbc21f517bff"],"state_sha256":"a209e109e8b061a75e15bf07e01b81c742d0e652334c63631bf50b4ffa0e95e4"}