{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EMVBLB42BVKOCTXZ2NOAGVGWLN","short_pith_number":"pith:EMVBLB42","schema_version":"1.0","canonical_sha256":"232a15879a0d54e14ef9d35c0354d65b44b9479cb73107b4b3e78a2a2f691c20","source":{"kind":"arxiv","id":"1706.09814","version":2},"attestation_state":"computed","paper":{"title":"Data-dependent Generalization Bounds for Multi-class Classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ding-Xuan Zhou, Marius Kloft, Urun Dogan, Yunwen Lei","submitted_at":"2017-06-29T15:41:25Z","abstract_excerpt":"In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for empirical multi-class risk minimization algorithms using an arbitrary norm as regularizer. Key to our analysis are new structural results for multi-class Gaussian complexities and empirical $\\ell_\\infty$-norm covering numbers, which exploit the Lipschitz continuity of the loss function with respect to the $\\ell_2$- and $\\ell_\\infty$-norm, respectively. We establ"},"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":"1706.09814","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-06-29T15:41:25Z","cross_cats_sorted":[],"title_canon_sha256":"474bb61beef595aef57821ee77efa5e9ce5cdcd05221cbee9855b24f3d06ad76","abstract_canon_sha256":"54e8c9811561e350371d315992572c243a8f90adef22c4f98cfdc9874d7d7215"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:04.614232Z","signature_b64":"lUpzIVmmrzOLcpPXRvtP1GP/Icq2eypg25WU9Q1+sNG4utZ4mek2tBljBsLGflgBnCQYrxmVy5VvVdKL0cbTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"232a15879a0d54e14ef9d35c0354d65b44b9479cb73107b4b3e78a2a2f691c20","last_reissued_at":"2026-05-18T00:27:04.613627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:04.613627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Data-dependent Generalization Bounds for Multi-class Classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ding-Xuan Zhou, Marius Kloft, Urun Dogan, Yunwen Lei","submitted_at":"2017-06-29T15:41:25Z","abstract_excerpt":"In this paper, we study data-dependent generalization error bounds exhibiting a mild dependency on the number of classes, making them suitable for multi-class learning with a large number of label classes. The bounds generally hold for empirical multi-class risk minimization algorithms using an arbitrary norm as regularizer. Key to our analysis are new structural results for multi-class Gaussian complexities and empirical $\\ell_\\infty$-norm covering numbers, which exploit the Lipschitz continuity of the loss function with respect to the $\\ell_2$- and $\\ell_\\infty$-norm, respectively. We establ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09814","kind":"arxiv","version":2},"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":"1706.09814","created_at":"2026-05-18T00:27:04.613700+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09814v2","created_at":"2026-05-18T00:27:04.613700+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09814","created_at":"2026-05-18T00:27:04.613700+00:00"},{"alias_kind":"pith_short_12","alias_value":"EMVBLB42BVKO","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EMVBLB42BVKOCTXZ","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EMVBLB42","created_at":"2026-05-18T12:31:12.930513+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/EMVBLB42BVKOCTXZ2NOAGVGWLN","json":"https://pith.science/pith/EMVBLB42BVKOCTXZ2NOAGVGWLN.json","graph_json":"https://pith.science/api/pith-number/EMVBLB42BVKOCTXZ2NOAGVGWLN/graph.json","events_json":"https://pith.science/api/pith-number/EMVBLB42BVKOCTXZ2NOAGVGWLN/events.json","paper":"https://pith.science/paper/EMVBLB42"},"agent_actions":{"view_html":"https://pith.science/pith/EMVBLB42BVKOCTXZ2NOAGVGWLN","download_json":"https://pith.science/pith/EMVBLB42BVKOCTXZ2NOAGVGWLN.json","view_paper":"https://pith.science/paper/EMVBLB42","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09814&json=true","fetch_graph":"https://pith.science/api/pith-number/EMVBLB42BVKOCTXZ2NOAGVGWLN/graph.json","fetch_events":"https://pith.science/api/pith-number/EMVBLB42BVKOCTXZ2NOAGVGWLN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EMVBLB42BVKOCTXZ2NOAGVGWLN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EMVBLB42BVKOCTXZ2NOAGVGWLN/action/storage_attestation","attest_author":"https://pith.science/pith/EMVBLB42BVKOCTXZ2NOAGVGWLN/action/author_attestation","sign_citation":"https://pith.science/pith/EMVBLB42BVKOCTXZ2NOAGVGWLN/action/citation_signature","submit_replication":"https://pith.science/pith/EMVBLB42BVKOCTXZ2NOAGVGWLN/action/replication_record"}},"created_at":"2026-05-18T00:27:04.613700+00:00","updated_at":"2026-05-18T00:27:04.613700+00:00"}