{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:M3A4H2JB2LWKZEXCS6XCHDJXIL","short_pith_number":"pith:M3A4H2JB","schema_version":"1.0","canonical_sha256":"66c1c3e921d2ecac92e297ae238d3742d548ce25046c938729b24db830b725ea","source":{"kind":"arxiv","id":"1911.01544","version":3},"attestation_state":"computed","paper":{"title":"The generalization error of max-margin linear classifiers: Benign overfitting and high dimensional asymptotics in the overparametrized regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrea Montanari, Feng Ruan, Jun Yan, Youngtak Sohn","submitted_at":"2019-11-05T00:15:27Z","abstract_excerpt":"Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes.\n  Motivated by these phenomena, we revisit high-dimensional maximum margin classification for linearly separable data. We consider a stylized setting in which data $(y_i,{\\boldsymbol x}_i)$, $i\\le n$ are i.i.d. with ${\\boldsymbol x}_i\\sim\\mathsf{N}({\\boldsymbol 0},{\\boldsymbol \\Sigma})$ a $p$-dimensional Gaussian feature vector, and $y_i \\in\\{+1,-1\\}$ a label whose distribu"},"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":"1911.01544","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-11-05T00:15:27Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"46a77590bb6ecf0fdf9293f27751fdf3874ad8841ccfa4f6eeb8cd4a2fc1f6d7","abstract_canon_sha256":"419fad32944e104601e013dd045d5937851f8387c7d462770ce789f1158bd58c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:53:29.620127Z","signature_b64":"yg67Dt/1YC60aROTfhG6FhJK5YdiQ5VK2WBEHuplfGI//az1Hny/4SlP8DbDMSwD+Vt9PA70i0JZIMP8xDktAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66c1c3e921d2ecac92e297ae238d3742d548ce25046c938729b24db830b725ea","last_reissued_at":"2026-07-05T05:53:29.619780Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:53:29.619780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The generalization error of max-margin linear classifiers: Benign overfitting and high dimensional asymptotics in the overparametrized regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrea Montanari, Feng Ruan, Jun Yan, Youngtak Sohn","submitted_at":"2019-11-05T00:15:27Z","abstract_excerpt":"Modern machine learning classifiers often exhibit vanishing classification error on the training set. They achieve this by learning nonlinear representations of the inputs that maps the data into linearly separable classes.\n  Motivated by these phenomena, we revisit high-dimensional maximum margin classification for linearly separable data. We consider a stylized setting in which data $(y_i,{\\boldsymbol x}_i)$, $i\\le n$ are i.i.d. with ${\\boldsymbol x}_i\\sim\\mathsf{N}({\\boldsymbol 0},{\\boldsymbol \\Sigma})$ a $p$-dimensional Gaussian feature vector, and $y_i \\in\\{+1,-1\\}$ a label whose distribu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.01544","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.01544/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1911.01544","created_at":"2026-07-05T05:53:29.619835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.01544v3","created_at":"2026-07-05T05:53:29.619835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.01544","created_at":"2026-07-05T05:53:29.619835+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3A4H2JB2LWK","created_at":"2026-07-05T05:53:29.619835+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3A4H2JB2LWKZEXC","created_at":"2026-07-05T05:53:29.619835+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3A4H2JB","created_at":"2026-07-05T05:53:29.619835+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.17767","citing_title":"Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent","ref_index":127,"is_internal_anchor":false},{"citing_arxiv_id":"2605.22481","citing_title":"When Stronger Triggers Backfire: A High-Dimensional Theory of Backdoor Attacks","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2605.21494","citing_title":"Double descent for least-squares interpolation on contaminated data: A simulation study","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2605.17767","citing_title":"Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent","ref_index":127,"is_internal_anchor":false},{"citing_arxiv_id":"2605.14200","citing_title":"How to Scale Mixture-of-Experts: From muP to the Maximally Scale-Stable Parameterization","ref_index":186,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL","json":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL.json","graph_json":"https://pith.science/api/pith-number/M3A4H2JB2LWKZEXCS6XCHDJXIL/graph.json","events_json":"https://pith.science/api/pith-number/M3A4H2JB2LWKZEXCS6XCHDJXIL/events.json","paper":"https://pith.science/paper/M3A4H2JB"},"agent_actions":{"view_html":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL","download_json":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL.json","view_paper":"https://pith.science/paper/M3A4H2JB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.01544&json=true","fetch_graph":"https://pith.science/api/pith-number/M3A4H2JB2LWKZEXCS6XCHDJXIL/graph.json","fetch_events":"https://pith.science/api/pith-number/M3A4H2JB2LWKZEXCS6XCHDJXIL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL/action/storage_attestation","attest_author":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL/action/author_attestation","sign_citation":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL/action/citation_signature","submit_replication":"https://pith.science/pith/M3A4H2JB2LWKZEXCS6XCHDJXIL/action/replication_record"}},"created_at":"2026-07-05T05:53:29.619835+00:00","updated_at":"2026-07-05T05:53:29.619835+00:00"}