{"paper":{"title":"Improving TensorSketch Using Complex Random Variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.DS","authors_text":"Amit Sharma, Keegan Kang, Mohammad Azhar Khan, Rameshwar Pratap","submitted_at":"2026-08-11T05:59:25Z","abstract_excerpt":"\\texttt{TensorSketch} by~\\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\\vec{x}^{\\otimes p} \\in \\R^{d^p}$. \\cite{kar2012random} uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, where $D$ denotes the sketch dimension, whereas~\\cite{pham2013fast} extends the sparse \\texttt{CountSketch}~\\citep{count_sketch} algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\\big(p(\\nnz{\\vec{x}} + D \\log D)\\big)$. However, the variance of both estimators grows expon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10523","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/2608.10523/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"}