{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3OKCFKBAPYUJEEIGGR3X3QP5UT","short_pith_number":"pith:3OKCFKBA","schema_version":"1.0","canonical_sha256":"db9422a8207e2892110634777dc1fda4fe077700b7bca0c8d50fa108793c91a2","source":{"kind":"arxiv","id":"1811.00139","version":1},"attestation_state":"computed","paper":{"title":"Testing Halfspaces over Rotation-Invariant Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Nathaniel Harms","submitted_at":"2018-10-31T22:25:27Z","abstract_excerpt":"We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\\tilde O(\\sqrt{n}\\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability whether $f$ is of the form $f(x) = sign(\\sum_i w_ix_i-t)$ or is $\\epsilon$-far from all such functions. This sample size is significantly smaller than the well-known requirement of $\\Omega(n)$ samples for learning halfspaces, and known lower bounds imply that our sample size is optimal (in its dependence on $n$) up to logarithmic factors. The algorithm is distri"},"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":"1811.00139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-31T22:25:27Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5590c78a9c3d270746cedc9f73c6052c737d1946f7d6ae07a94729c4b6613919","abstract_canon_sha256":"7314119986d1444e1e0d7cbe648485bb403bd307aee36e736f68aea0995d6d54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:48.116110Z","signature_b64":"ZqBfYKdpqNKvpgtqEEN7GiQSlTOYV0DKy5va360cVJf27lSuyPS7esCRrNYlswDBvOF2zhiBlHctPer8B2MICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db9422a8207e2892110634777dc1fda4fe077700b7bca0c8d50fa108793c91a2","last_reissued_at":"2026-05-18T00:01:48.115651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:48.115651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Testing Halfspaces over Rotation-Invariant Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Nathaniel Harms","submitted_at":"2018-10-31T22:25:27Z","abstract_excerpt":"We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\\tilde O(\\sqrt{n}\\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability whether $f$ is of the form $f(x) = sign(\\sum_i w_ix_i-t)$ or is $\\epsilon$-far from all such functions. This sample size is significantly smaller than the well-known requirement of $\\Omega(n)$ samples for learning halfspaces, and known lower bounds imply that our sample size is optimal (in its dependence on $n$) up to logarithmic factors. The algorithm is distri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00139","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":""},"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":"1811.00139","created_at":"2026-05-18T00:01:48.115716+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.00139v1","created_at":"2026-05-18T00:01:48.115716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00139","created_at":"2026-05-18T00:01:48.115716+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OKCFKBAPYUJ","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OKCFKBAPYUJEEIG","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OKCFKBA","created_at":"2026-05-18T12:32:02.567920+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/3OKCFKBAPYUJEEIGGR3X3QP5UT","json":"https://pith.science/pith/3OKCFKBAPYUJEEIGGR3X3QP5UT.json","graph_json":"https://pith.science/api/pith-number/3OKCFKBAPYUJEEIGGR3X3QP5UT/graph.json","events_json":"https://pith.science/api/pith-number/3OKCFKBAPYUJEEIGGR3X3QP5UT/events.json","paper":"https://pith.science/paper/3OKCFKBA"},"agent_actions":{"view_html":"https://pith.science/pith/3OKCFKBAPYUJEEIGGR3X3QP5UT","download_json":"https://pith.science/pith/3OKCFKBAPYUJEEIGGR3X3QP5UT.json","view_paper":"https://pith.science/paper/3OKCFKBA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.00139&json=true","fetch_graph":"https://pith.science/api/pith-number/3OKCFKBAPYUJEEIGGR3X3QP5UT/graph.json","fetch_events":"https://pith.science/api/pith-number/3OKCFKBAPYUJEEIGGR3X3QP5UT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OKCFKBAPYUJEEIGGR3X3QP5UT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OKCFKBAPYUJEEIGGR3X3QP5UT/action/storage_attestation","attest_author":"https://pith.science/pith/3OKCFKBAPYUJEEIGGR3X3QP5UT/action/author_attestation","sign_citation":"https://pith.science/pith/3OKCFKBAPYUJEEIGGR3X3QP5UT/action/citation_signature","submit_replication":"https://pith.science/pith/3OKCFKBAPYUJEEIGGR3X3QP5UT/action/replication_record"}},"created_at":"2026-05-18T00:01:48.115716+00:00","updated_at":"2026-05-18T00:01:48.115716+00:00"}