Efficient quadratic entropy with distance sketches
Abstract
We detail scalable methods for approximating the quadratic entropy pT d p for arbitrary distributions p and common distances d of negative type. We focus on the Euclidean and spherical geodesic cases, which both use random feature embeddings and projections to dramatically improve computational complexity within a simple framework. Amortization of a single large matrix multiplication and control variates further enable computation at large scale with low memory and runtime in situations where d is held constant while p varies. We demonstrate this with a comparison against direct pair sampling and bibliometric/scientometric examples on Open Graph Benchmark datasets, revealing papers, fields, and institutions with both particularly narrow and broad interdisciplinary reach from their citations and text features alone.
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BibTeX
@misc{huntsman2026efficient,
title = {{Efficient quadratic entropy with distance sketches}},
author = {Steve Huntsman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11976},
eprint = {2610.11976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11976},
}
RIS
TY - UNPB
TI - Efficient quadratic entropy with distance sketches
AU - Steve Huntsman
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.11976
UR - https://arxiv.org/abs/2610.11976
AB - We detail scalable methods for approximating the quadratic entropy p^T d p for arbitrary distributions p and common distances d of negative type. We focus on the Euclidean and spherical geodesic cases, which both use random feature embeddings and projections to dramatically improve computational complexity within a simple framework. Amortization of a single large matrix multiplication and control variates further enable computation at large scale with low memory and runtime in situations where d is held constant while p varies. We demonstrate this with a comparison against direct pair sampling and bibliometric/scientometric examples on Open Graph Benchmark datasets, revealing papers, fields, and institutions with both particularly narrow and broad interdisciplinary reach from their citations and text features alone.
ER -