{"paper":{"title":"On learning linear functions from subset and its applications in quantum computing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Anupam Prakash, G\\'abor Ivanyos, Miklos Santha","submitted_at":"2018-06-25T18:48:36Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be the finite field of size $q$ and let $\\ell: \\mathbb{F}_q^n \\to \\mathbb{F}_q$ be a linear function. We introduce the {\\em Learning From Subset} problem LFS$(q,n,d)$ of learning $\\ell$, given samples $u \\in \\mathbb{F}_q^n$ from a special distribution depending on $\\ell$: the probability of sampling $u$ is a function of $\\ell(u)$ and is non zero for at most $d$ values of $\\ell(u)$. We provide a randomized algorithm for LFS$(q,n,d)$ with sample complexity $(n+d)^{O(d)}$ and running time polynomial in $\\log q$ and $(n+d)^{O(d)}$. Our algorithm generalizes and improves upon pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09660","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"}