{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QOQGU7K6ZWRXKKJNNAPE5D2E3Y","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":"4a05961b40252827973e58967b1921995f0426359d3e282720e83a28524c4290","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-04-18T17:57:53Z","title_canon_sha256":"fe01b71404a6b20b030612dc302308256444f3015f22c2f552e46e792f9f1bf1"},"schema_version":"1.0","source":{"id":"2404.12376","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.12376","created_at":"2026-07-05T09:45:09Z"},{"alias_kind":"arxiv_version","alias_value":"2404.12376v2","created_at":"2026-07-05T09:45:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.12376","created_at":"2026-07-05T09:45:09Z"},{"alias_kind":"pith_short_12","alias_value":"QOQGU7K6ZWRX","created_at":"2026-07-05T09:45:09Z"},{"alias_kind":"pith_short_16","alias_value":"QOQGU7K6ZWRXKKJN","created_at":"2026-07-05T09:45:09Z"},{"alias_kind":"pith_short_8","alias_value":"QOQGU7K6","created_at":"2026-07-05T09:45:09Z"}],"graph_snapshots":[{"event_id":"sha256:bea8d84b71d65abd7e9f64e12423f7e2f55e10c2a148d3e6eee9291b8f3e61a8","target":"graph","created_at":"2026-07-05T09:45:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.12376/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $k$-sparse parity problem is a classical problem in computational complexity and algorithmic theory, serving as a key benchmark for understanding computational classes. In this paper, we solve the $k$-sparse parity problem with sign stochastic gradient descent, a variant of stochastic gradient descent (SGD) on two-layer fully-connected neural networks. We demonstrate that this approach can efficiently solve the $k$-sparse parity problem on a $d$-dimensional hypercube ($k\\leq O(\\sqrt{d})$) with a sample complexity of $\\tilde{O}(d^{k-1})$ using $2^{\\Theta(k)}$ neurons, matching the establish","authors_text":"Quanquan Gu, Sham M. Kakade, Yiwen Kou, Zixiang Chen","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-04-18T17:57:53Z","title":"Matching the Statistical Query Lower Bound for $k$-Sparse Parity Problems with Sign Stochastic Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.12376","kind":"arxiv","version":2},"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:ccf207530d4c78ed26061ef8228197beedfa0a3f6fac1b0b0f1ae2ecec82f4e4","target":"record","created_at":"2026-07-05T09:45:09Z","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":"4a05961b40252827973e58967b1921995f0426359d3e282720e83a28524c4290","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-04-18T17:57:53Z","title_canon_sha256":"fe01b71404a6b20b030612dc302308256444f3015f22c2f552e46e792f9f1bf1"},"schema_version":"1.0","source":{"id":"2404.12376","kind":"arxiv","version":2}},"canonical_sha256":"83a06a7d5ecda375292d681e4e8f44de1a01ef2c5be174a5949cc6a85c2fb76a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83a06a7d5ecda375292d681e4e8f44de1a01ef2c5be174a5949cc6a85c2fb76a","first_computed_at":"2026-07-05T09:45:09.621353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:45:09.621353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IxsOJMMIAR7Y1QQ/C4VVC5CJphskZ2REegx8a7AbPuVXUxAgWOZ2IaX5IFWyn62P4QIOrNOS5uN4aza1EgC5Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:45:09.621864Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.12376","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccf207530d4c78ed26061ef8228197beedfa0a3f6fac1b0b0f1ae2ecec82f4e4","sha256:bea8d84b71d65abd7e9f64e12423f7e2f55e10c2a148d3e6eee9291b8f3e61a8"],"state_sha256":"408b02f0a340f1aa67425ecfa1dc231f8ce1bf13e451d446f1bee8c492e4707d"}