{"paper":{"title":"Preserving Randomness for Adaptive Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Adam R. Klivans, William M. Hoza","submitted_at":"2016-11-02T20:06:31Z","abstract_excerpt":"Suppose $\\mathsf{Est}$ is a randomized estimation algorithm that uses $n$ random bits and outputs values in $\\mathbb{R}^d$. We show how to execute $\\mathsf{Est}$ on $k$ adaptively chosen inputs using only $n + O(k \\log(d + 1))$ random bits instead of the trivial $nk$ (at the cost of mild increases in the error and failure probability). Our algorithm combines a variant of the INW pseudorandom generator (STOC '94) with a new scheme for shifting and rounding the outputs of $\\mathsf{Est}$. We prove that modifying the outputs of $\\mathsf{Est}$ is necessary in this setting, and furthermore, our algo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00783","kind":"arxiv","version":5},"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"}