{"paper":{"title":"New Insight of Variance reduce in Zero-Order Hard-Thresholding: Mitigating Gradient Error and Expansivity Contradictions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.AI","authors_text":"2) ((1) Harbin Institute of Technology, (2) Mohamed bin Zayed University of Artificial Intelligence, 3), (3) Jilin University), Bin Gu (2, Huan Xiong (1, William de Vazelhes (2), Xinzhe Yuan (1)","submitted_at":"2026-05-18T08:24:18Z","abstract_excerpt":"Hard-thresholding is an important type of algorithm in machine learning that is used to solve $\\ell_0$ constrained optimization problems. However, the true gradient of the objective function can be difficult to access in certain scenarios, which normally can be approximated by zeroth-order (ZO) methods. The SZOHT algorithm is the only algorithm tackling $\\ell_0$ sparsity constraints with ZO gradients so far. Unfortunately, SZOHT has a notable limitation on the number of random directions % in ZO gradients due to the inherent conflict between the deviation of ZO gradients and the expansivity of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18035","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/2605.18035/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.503761Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"02a6a3c80a4017df4a86165f4ee909601f018d7ccf3c360dfce6a97a63adead0"},"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"}