# Efficient quadratic entropy with distance sketches

arXiv: https://arxiv.org/abs/2610.11976 · HTML: https://mlsanity.com/paper/2610.11976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 45 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 3 of 3)

- [OpenAlex: A fully-open index of scholarly works, authors, venues, institutions, and concepts](https://mlsanity.com/paper/2205.01833/) (2022)
- [Fast Large Deformation Matching with the Energy Distance Kernel](https://mlsanity.com/paper/2505.03342/) (2025)
- [Generalized Sliced Distances for Probability Distributions](https://mlsanity.com/paper/2002.12537/) (2020)

## Abstract (arXiv)

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.