{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YKO25LPQ2RTVXOCXJLIA4MKMDF","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":"71f0e0bef9baa44efbb1a2f3964fe97f85ed56f839ec8143669ba15897c338ca","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-11-24T10:07:10Z","title_canon_sha256":"5a71ef71075a819255c09983a85714b26c973cf1f6a8a322c193d158ccd90aae"},"schema_version":"1.0","source":{"id":"2311.14387","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.14387","created_at":"2026-07-05T09:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"2311.14387v4","created_at":"2026-07-05T09:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.14387","created_at":"2026-07-05T09:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"YKO25LPQ2RTV","created_at":"2026-07-05T09:54:00Z"},{"alias_kind":"pith_short_16","alias_value":"YKO25LPQ2RTVXOCX","created_at":"2026-07-05T09:54:00Z"},{"alias_kind":"pith_short_8","alias_value":"YKO25LPQ","created_at":"2026-07-05T09:54:00Z"}],"graph_snapshots":[{"event_id":"sha256:cf1535a34cb3a5c3471f38079c8e2b756e43e3d1e4b3c4aecf5b3fb1295bc506","target":"graph","created_at":"2026-07-05T09:54:00Z","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/2311.14387/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we investigate the margin-maximization bias exhibited by gradient-based algorithms in classifying linearly separable data. We present an in-depth analysis of the specific properties of the velocity field associated with (normalized) gradients, focusing on their role in margin maximization. Inspired by this analysis, we propose a novel algorithm called Progressive Rescaling Gradient Descent (PRGD) and show that PRGD can maximize the margin at an {\\em exponential rate}. This stands in stark contrast to all existing algorithms, which maximize the margin at a slow {\\em polynomial rat","authors_text":"Lei Wu, Mingze Wang, Zeping Min","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-11-24T10:07:10Z","title":"Achieving Margin Maximization Exponentially Fast via Progressive Norm Rescaling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.14387","kind":"arxiv","version":4},"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:e7a1498b94953e5c20e7b1142612b178ba742e8b93d8589b496cb2b7ad410502","target":"record","created_at":"2026-07-05T09:54:00Z","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":"71f0e0bef9baa44efbb1a2f3964fe97f85ed56f839ec8143669ba15897c338ca","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-11-24T10:07:10Z","title_canon_sha256":"5a71ef71075a819255c09983a85714b26c973cf1f6a8a322c193d158ccd90aae"},"schema_version":"1.0","source":{"id":"2311.14387","kind":"arxiv","version":4}},"canonical_sha256":"c29daeadf0d4675bb8574ad00e314c196b9382eeeca6e266646048aefaa69568","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c29daeadf0d4675bb8574ad00e314c196b9382eeeca6e266646048aefaa69568","first_computed_at":"2026-07-05T09:54:00.477907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:00.477907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sxe+3WrRKTrG81OYZEGr3M9pv+Vqx685SbnGwhNf/S7sAZpbvjVwBo/nn3+7yv2P2UHK7gzVc99oG8BKelJGAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:00.478363Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.14387","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7a1498b94953e5c20e7b1142612b178ba742e8b93d8589b496cb2b7ad410502","sha256:cf1535a34cb3a5c3471f38079c8e2b756e43e3d1e4b3c4aecf5b3fb1295bc506"],"state_sha256":"f8eb8968251a9dc5bf84808379909b159b60914ca5f3b74e4eff4ae0a370745e"}