{"paper":{"title":"Adaptive and Dynamic Multi-Resolution Hashing for Pairwise Summations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Aravind Reddy, Danyang Zhuo, Lianke Qin, Zhao Song, Zhaozhuo Xu","submitted_at":"2022-12-21T23:23:24Z","abstract_excerpt":"In this paper, we propose Adam-Hash: an adaptive and dynamic multi-resolution hashing data-structure for fast pairwise summation estimation. Given a data-set $X \\subset \\mathbb{R}^d$, a binary function $f:\\mathbb{R}^d\\times \\mathbb{R}^d\\to \\mathbb{R}$, and a point $y \\in \\mathbb{R}^d$, the Pairwise Summation Estimate $\\mathrm{PSE}_X(y) := \\frac{1}{|X|} \\sum_{x \\in X} f(x,y)$. For any given data-set $X$, we need to design a data-structure such that given any query point $y \\in \\mathbb{R}^d$, the data-structure approximately estimates $\\mathrm{PSE}_X(y)$ in time that is sub-linear in $|X|$. Prio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11408","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/2212.11408/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"}