Fast Gauss Sums via Flash Attention
Abstract
Gaussian kernel sums are the computational core of maximum mean discrepancies (MMDs), kernel gradient flows, Stein variational gradient descent (SVGD), and many other kernel methods. At the same time, softmax attention has received an extraordinary amount of hardware-aware code engineering, culminating in flash attention. We show that Gauss kernel sums with arbitrary, signed weights can be evaluated via flash attention: two small input augmentations turn the normalized softmax reduction into the unnormalized Gauss sum, without writing a single line of custom GPU code. For feature dimension D>8 in fp16, this approach beats compiled PyTorch code as well as PyKeOps kernels (often significantly) in speed, memory-overhead and accuracy. Indeed, its memory scaling remains linear.
Related
BibTeX
@misc{rux2026fast,
title = {{Fast Gauss Sums via Flash Attention}},
author = {Nicolaj Rux and Sebastian Neumayer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04910},
eprint = {2609.04910},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04910},
}
RIS
TY - UNPB
TI - Fast Gauss Sums via Flash Attention
AU - Nicolaj Rux
AU - Sebastian Neumayer
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.04910
UR - https://arxiv.org/abs/2609.04910
AB - Gaussian kernel sums are the computational core of maximum mean discrepancies (MMDs), kernel gradient flows, Stein variational gradient descent (SVGD), and many other kernel methods. At the same time, softmax attention has received an extraordinary amount of hardware-aware code engineering, culminating in flash attention. We show that Gauss kernel sums with arbitrary, signed weights can be evaluated via flash attention: two small input augmentations turn the normalized softmax reduction into the unnormalized Gauss sum, without writing a single line of custom GPU code. For feature dimension D>8 in fp16, this approach beats compiled PyTorch code as well as PyKeOps kernels (often significantly) in speed, memory-overhead and accuracy. Indeed, its memory scaling remains linear.
ER -