{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FIGYT25QVN3TJFTLHBCALWG4D7","short_pith_number":"pith:FIGYT25Q","schema_version":"1.0","canonical_sha256":"2a0d89ebb0ab7734966b384405d8dc1fd37448e219705fa442514e4eb353e1a1","source":{"kind":"arxiv","id":"1806.00949","version":3},"attestation_state":"computed","paper":{"title":"Private PAC learning implies finite Littlestone dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CR","math.LO","stat.ML"],"primary_cat":"cs.LG","authors_text":"Maryanthe Malliaris, Noga Alon, Roi Livni, Shay Moran","submitted_at":"2018-06-04T04:35:29Z","abstract_excerpt":"We show that every approximately differentially private learning algorithm (possibly improper) for a class $H$ with Littlestone dimension~$d$ requires $\\Omega\\bigl(\\log^*(d)\\bigr)$ examples. As a corollary it follows that the class of thresholds over $\\mathbb{N}$ can not be learned in a private manner; this resolves open question due to [Bun et al., 2015, Feldman and Xiao, 2015]. We leave as an open question whether every class with a finite Littlestone dimension can be learned by an approximately differentially private algorithm."},"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":"1806.00949","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-04T04:35:29Z","cross_cats_sorted":["cs.AI","cs.CR","math.LO","stat.ML"],"title_canon_sha256":"93aec2abd55518d22241ac5d92ffecc354806b53fef1507da0adbd42f990d645","abstract_canon_sha256":"87795b57a6ca8c698d36084f71b9399b91b3509e797448f3d840b3169453c09c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:49.358627Z","signature_b64":"RAyYjuK3VZoGiJXqOx5mtEQpQ7+L1lhLIvoWqfonQs2H6qrQ4HAJ+4jD3xi3HFpCOHIeO/jaHYZYMaNbBUCNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a0d89ebb0ab7734966b384405d8dc1fd37448e219705fa442514e4eb353e1a1","last_reissued_at":"2026-05-17T23:51:49.357985Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:49.357985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Private PAC learning implies finite Littlestone dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CR","math.LO","stat.ML"],"primary_cat":"cs.LG","authors_text":"Maryanthe Malliaris, Noga Alon, Roi Livni, Shay Moran","submitted_at":"2018-06-04T04:35:29Z","abstract_excerpt":"We show that every approximately differentially private learning algorithm (possibly improper) for a class $H$ with Littlestone dimension~$d$ requires $\\Omega\\bigl(\\log^*(d)\\bigr)$ examples. As a corollary it follows that the class of thresholds over $\\mathbb{N}$ can not be learned in a private manner; this resolves open question due to [Bun et al., 2015, Feldman and Xiao, 2015]. We leave as an open question whether every class with a finite Littlestone dimension can be learned by an approximately differentially private algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00949","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":""},"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":"1806.00949","created_at":"2026-05-17T23:51:49.358074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.00949v3","created_at":"2026-05-17T23:51:49.358074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00949","created_at":"2026-05-17T23:51:49.358074+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIGYT25QVN3T","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIGYT25QVN3TJFTL","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIGYT25Q","created_at":"2026-05-18T12:32:22.470017+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/FIGYT25QVN3TJFTLHBCALWG4D7","json":"https://pith.science/pith/FIGYT25QVN3TJFTLHBCALWG4D7.json","graph_json":"https://pith.science/api/pith-number/FIGYT25QVN3TJFTLHBCALWG4D7/graph.json","events_json":"https://pith.science/api/pith-number/FIGYT25QVN3TJFTLHBCALWG4D7/events.json","paper":"https://pith.science/paper/FIGYT25Q"},"agent_actions":{"view_html":"https://pith.science/pith/FIGYT25QVN3TJFTLHBCALWG4D7","download_json":"https://pith.science/pith/FIGYT25QVN3TJFTLHBCALWG4D7.json","view_paper":"https://pith.science/paper/FIGYT25Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.00949&json=true","fetch_graph":"https://pith.science/api/pith-number/FIGYT25QVN3TJFTLHBCALWG4D7/graph.json","fetch_events":"https://pith.science/api/pith-number/FIGYT25QVN3TJFTLHBCALWG4D7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIGYT25QVN3TJFTLHBCALWG4D7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIGYT25QVN3TJFTLHBCALWG4D7/action/storage_attestation","attest_author":"https://pith.science/pith/FIGYT25QVN3TJFTLHBCALWG4D7/action/author_attestation","sign_citation":"https://pith.science/pith/FIGYT25QVN3TJFTLHBCALWG4D7/action/citation_signature","submit_replication":"https://pith.science/pith/FIGYT25QVN3TJFTLHBCALWG4D7/action/replication_record"}},"created_at":"2026-05-17T23:51:49.358074+00:00","updated_at":"2026-05-17T23:51:49.358074+00:00"}