{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:KZNFAJJND7C54VMD7YJL7P6ECL","short_pith_number":"pith:KZNFAJJN","schema_version":"1.0","canonical_sha256":"565a50252d1fc5de5583fe12bfbfc412ccd43bb7ff13f65c2596b0288f3977a9","source":{"kind":"arxiv","id":"2203.12094","version":1},"attestation_state":"computed","paper":{"title":"Learning curves for the multi-class teacher-student perceptron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG"],"primary_cat":"stat.ML","authors_text":"Bruno Loureiro, C\\'edric Gerbelot, Elisabetta Cornacchia, Francesca Mignacco, Lenka Zdeborov\\'a, Rodrigo Veiga","submitted_at":"2022-03-22T23:16:36Z","abstract_excerpt":"One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with the single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal estimation and empirical risk minimisation (ERM) were extensively analysed for this setting. At the same time, a considerable part of modern machine learning practice concerns multi-class classification. Yet, an analogous analysis for the corresponding multi-class teacher-student perceptron was missing. In this manuscript we fill this gap by der"},"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":"2203.12094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-03-22T23:16:36Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG"],"title_canon_sha256":"89accaa793b21b007f9c98d199f681c061b9a41f284b3b01be0cc2e0001b35c1","abstract_canon_sha256":"f3fbebb868e3e421cffff09f2b998132a2439147c1389ea17b33ce10a9db5729"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:16:59.495505Z","signature_b64":"H2h1qtl7Zdy5F1apbs634xfSozdjMtaUr0nz56lQaB1QvCJwQhco2PKnetROVbMKSqWotikJmJWGL/J99cCFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"565a50252d1fc5de5583fe12bfbfc412ccd43bb7ff13f65c2596b0288f3977a9","last_reissued_at":"2026-07-05T06:16:59.495054Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:16:59.495054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning curves for the multi-class teacher-student perceptron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG"],"primary_cat":"stat.ML","authors_text":"Bruno Loureiro, C\\'edric Gerbelot, Elisabetta Cornacchia, Francesca Mignacco, Lenka Zdeborov\\'a, Rodrigo Veiga","submitted_at":"2022-03-22T23:16:36Z","abstract_excerpt":"One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with the single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal estimation and empirical risk minimisation (ERM) were extensively analysed for this setting. At the same time, a considerable part of modern machine learning practice concerns multi-class classification. Yet, an analogous analysis for the corresponding multi-class teacher-student perceptron was missing. In this manuscript we fill this gap by der"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.12094","kind":"arxiv","version":1},"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/2203.12094/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":"2203.12094","created_at":"2026-07-05T06:16:59.495113+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.12094v1","created_at":"2026-07-05T06:16:59.495113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.12094","created_at":"2026-07-05T06:16:59.495113+00:00"},{"alias_kind":"pith_short_12","alias_value":"KZNFAJJND7C5","created_at":"2026-07-05T06:16:59.495113+00:00"},{"alias_kind":"pith_short_16","alias_value":"KZNFAJJND7C54VMD","created_at":"2026-07-05T06:16:59.495113+00:00"},{"alias_kind":"pith_short_8","alias_value":"KZNFAJJN","created_at":"2026-07-05T06:16:59.495113+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/KZNFAJJND7C54VMD7YJL7P6ECL","json":"https://pith.science/pith/KZNFAJJND7C54VMD7YJL7P6ECL.json","graph_json":"https://pith.science/api/pith-number/KZNFAJJND7C54VMD7YJL7P6ECL/graph.json","events_json":"https://pith.science/api/pith-number/KZNFAJJND7C54VMD7YJL7P6ECL/events.json","paper":"https://pith.science/paper/KZNFAJJN"},"agent_actions":{"view_html":"https://pith.science/pith/KZNFAJJND7C54VMD7YJL7P6ECL","download_json":"https://pith.science/pith/KZNFAJJND7C54VMD7YJL7P6ECL.json","view_paper":"https://pith.science/paper/KZNFAJJN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.12094&json=true","fetch_graph":"https://pith.science/api/pith-number/KZNFAJJND7C54VMD7YJL7P6ECL/graph.json","fetch_events":"https://pith.science/api/pith-number/KZNFAJJND7C54VMD7YJL7P6ECL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KZNFAJJND7C54VMD7YJL7P6ECL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KZNFAJJND7C54VMD7YJL7P6ECL/action/storage_attestation","attest_author":"https://pith.science/pith/KZNFAJJND7C54VMD7YJL7P6ECL/action/author_attestation","sign_citation":"https://pith.science/pith/KZNFAJJND7C54VMD7YJL7P6ECL/action/citation_signature","submit_replication":"https://pith.science/pith/KZNFAJJND7C54VMD7YJL7P6ECL/action/replication_record"}},"created_at":"2026-07-05T06:16:59.495113+00:00","updated_at":"2026-07-05T06:16:59.495113+00:00"}