{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V3K5XM5MIVNXFFRO7SKIHRYVEP","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":"2b11d01ff4f97cf3d56efc88d414e76f7630b73a40facfb342809def6aa45001","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-07-05T07:41:40Z","title_canon_sha256":"8fbfcbc4f9b760d6ded99670fd5065af8189be2e4c96060281775e0ab5ccccc4"},"schema_version":"1.0","source":{"id":"1707.01242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01242","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01242v1","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01242","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"V3K5XM5MIVNX","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V3K5XM5MIVNXFFRO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V3K5XM5M","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:b7d04ba4e8905182d3d061557e6fabf0f5b0e801508862ccacdab5a47de866ec","target":"graph","created_at":"2026-05-18T00:40:53Z","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"},"paper":{"abstract_excerpt":"We study the efficient learnability of geometric concept classes - specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces - when a fraction of the data is adversarially corrupted. We give the first polynomial-time PAC learning algorithms for these concept classes with dimension-independent error guarantees in the presence of nasty noise under the Gaussian distribution. In the nasty noise model, an omniscient adversary can arbitrarily corrupt a small fraction of both the unlabeled data points and their labels. This model generalizes well-studied noise mod","authors_text":"Alistair Stewart, Daniel M. Kane, Ilias Diakonikolas","cross_cats":["cs.CC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-07-05T07:41:40Z","title":"Learning Geometric Concepts with Nasty Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01242","kind":"arxiv","version":1},"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":"sha256:00b6026e58c8f830e43622a9bf7db9e00164fd226ab41a2cc967d8a937ce00e0","target":"record","created_at":"2026-05-18T00:40:53Z","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":"2b11d01ff4f97cf3d56efc88d414e76f7630b73a40facfb342809def6aa45001","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-07-05T07:41:40Z","title_canon_sha256":"8fbfcbc4f9b760d6ded99670fd5065af8189be2e4c96060281775e0ab5ccccc4"},"schema_version":"1.0","source":{"id":"1707.01242","kind":"arxiv","version":1}},"canonical_sha256":"aed5dbb3ac455b72962efc9483c71523eb37cf8f0ea161a0d572a8d3919e68aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aed5dbb3ac455b72962efc9483c71523eb37cf8f0ea161a0d572a8d3919e68aa","first_computed_at":"2026-05-18T00:40:53.339352Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:53.339352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OjsH0/LTnqHu9SsijiIKMjWOk4gVDo1ChQXMVdtvavmsGmEwgS7+siDVxGft3bXjRcgfhrLPVT0ZsLHBZUKSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:53.339768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00b6026e58c8f830e43622a9bf7db9e00164fd226ab41a2cc967d8a937ce00e0","sha256:b7d04ba4e8905182d3d061557e6fabf0f5b0e801508862ccacdab5a47de866ec"],"state_sha256":"2c1e931d3531516c4eb7c32cd4f3f55ed5c62f7cd76a34b2b80ee59659853c9e"}