# Stochastic Barnes-Hut Approximation for Fast Summation on the GPU

arXiv: https://arxiv.org/abs/2506.02219 · HTML: https://mlsanity.com/paper/2506.02219/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2025.

## Built on by (most cited first, 1 of 1)

- [Points as Tori: Fast Pointwise Signed Distance for Point Clouds](https://mlsanity.com/paper/2607.16946/) (2026)

## Abstract (arXiv)

We present a novel stochastic version of the Barnes-Hut approximation. Regarding the level-of-detail (LOD) family of approximations as control variates, we construct an unbiased estimator of the kernel sum being approximated. Through several examples in graphics applications such as winding number computation and smooth distance evaluation, we demonstrate that our method is well-suited for GPU computation, capable of outperforming a GPU-optimized implementation of the deterministic Barnes-Hut approximation by achieving equal median error in up to 9.4x less time.