{"paper":{"title":"Expressivity of expand-and-sparsify representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.NE","authors_text":"Christopher Tosh, Sanjoy Dasgupta","submitted_at":"2020-06-05T23:36:59Z","abstract_excerpt":"A simple sparse coding mechanism appears in the sensory systems of several organisms: to a coarse approximation, an input $x \\in \\R^d$ is mapped to much higher dimension $m \\gg d$ by a random linear transformation, and is then sparsified by a winner-take-all process in which only the positions of the top $k$ values are retained, yielding a $k$-sparse vector $z \\in \\{0,1\\}^m$. We study the benefits of this representation for subsequent learning.\n  We first show a universal approximation property, that arbitrary continuous functions of $x$ are well approximated by linear functions of $z$, provid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.03741","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/2006.03741/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"}