{"paper":{"title":"Lower Bounds for Compressed Sensing with Generative Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"cs.DS","authors_text":"Akshay Kamath, Eric Price, Sushrut Karmalkar","submitted_at":"2019-12-06T00:51:51Z","abstract_excerpt":"The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \\approx Ax$. In traditional compressed sensing, \"structure\" is represented by sparsity in some known basis. Inspired by the success of deep learning in modeling images, recent work starting with~\\cite{BJPD17} has instead considered structure to come from a generative model $G: \\mathbb{R}^k \\to \\mathbb{R}^n$. We present two results establishing the difficulty of this latter task, showing that existing bounds are tight. First, we provide a lower bound matching the~\\cite{BJPD17"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.02938","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/1912.02938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}