# Fast Summation of Radial Kernels via QMC Slicing

arXiv: https://arxiv.org/abs/2410.01316 · HTML: https://mlsanity.com/paper/2410.01316/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 83 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 22 of 22)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Orthogonal Random Features](https://mlsanity.com/paper/1610.09072/) (2016)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Quasi-Monte Carlo Feature Maps for Shift-Invariant Kernels](https://mlsanity.com/paper/1412.8293/) (2014)
- [Generative Sliced MMD Flows with Riesz Kernels](https://mlsanity.com/paper/2305.11463/) (2023)
- [Quadrature-based features for kernel approximation](https://mlsanity.com/paper/1802.03832/) (2018)
- [Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernel](https://mlsanity.com/paper/2310.03054/) (2023)
- [Generalization Bounds for Sparse Random Feature Expansions](https://mlsanity.com/paper/2103.03191/) (2021)
- [Quasi-Monte Carlo for 3D Sliced Wasserstein](https://mlsanity.com/paper/2309.11713/) (2023)
- [Deep MMD Gradient Flow without adversarial training](https://mlsanity.com/paper/2405.06780/) (2024)
- [(De)-regularized Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/2409.14980/) (2024)
- [ASKIT: Approximate Skeletonization Kernel-Independent Treecode in High Dimensions](https://mlsanity.com/paper/1410.0260/) (2014)
- [Momentum Particle Maximum Likelihood](https://mlsanity.com/paper/2312.07335/) (2023)
- [cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs](https://mlsanity.com/paper/2102.08463/) (2021)
- [The Fast Kernel Transform](https://mlsanity.com/paper/2106.04487/) (2021)
- [Fast Kernel Summation in High Dimensions via Slicing and Fourier Transforms](https://mlsanity.com/paper/2401.08260/) (2024)
- [Fast spatial Gaussian process maximum likelihood estimation via skeletonization factorizations](https://mlsanity.com/paper/1603.08057/) (2016)
- [On the design of scalable, high-precision spherical-radial Fourier features](https://mlsanity.com/paper/2408.13231/) (2024)

## Built on by (most cited first, 7 of 7)

- [A Novel Sliced Fused Gromov-Wasserstein Distance](https://mlsanity.com/paper/2508.02364/) (2025)
- [Slicing the Gaussian Mixture Wasserstein Distance](https://mlsanity.com/paper/2504.08544/) (2025)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Generative Feature Training of Thin 2-Layer Networks](https://mlsanity.com/paper/2411.06848/) (2024)
- [Smoothed Distance Kernels for MMDs and Applications in Wasserstein Gradient Flows](https://mlsanity.com/paper/2504.07820/) (2025)
- [Randomized Quasi-Monte Carlo Features for Kernel Approximation](https://mlsanity.com/paper/2503.06041/) (2025)
- [Quasi Linear Kernel Attention with Infinite Capacity](https://mlsanity.com/paper/2609.35349/) (2026)

## Abstract (arXiv)

The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random projections to one-dimensional subspaces and fast Fourier summation. We prove bounds for the slicing error and propose a quasi-Monte Carlo (QMC) approach for selecting the projections based on spherical quadrature rules. Numerical examples demonstrate that our QMC-slicing approach significantly outperforms existing methods like (QMC-)random Fourier features, orthogonal Fourier features or non-QMC slicing on standard test datasets.