This is the implementation to the paper "Fast Kernel Summation in High Dimensions via Slicing and Fourier Transforms" available at https://arxiv.org/abs/2401.08260
The code contains one implementation in PyTorch and one in Julia. In PyTorch, we use the package torch-NFFT available at https://github.com/dominikbuenger/torch_nfft for the NFFT. Note that this package is GPU-only. For a CPU implementation we go back to the NDFT which might be significantly slower. For Julia, we use the NFFT package [3].
The Python-scripts test_fastsum_xxx.py implement the numerical examples from the paper and the files test_xxx_vs_keops.py implment the comparison to PyKeOps [4]. The Julia-files fastsum_vs_RFF_xxx.jl implement the comparison to random Fourier features [2].
If you have any questions, feel free to contact me via the email address j.hertrich@ucl.ac.uk
[1] J. Hertrich (2024).
Fast Kernel Summation in High Dimensions via Slicing and Fourier Transforms.
Preprint available under https://arxiv.org/abs/2401.08260
[2] A. Rahimi and B. Recht (2007).
Random features for large-scale kernel machines.
Advances in Neural Information Processing Systems
[3] J. Keiner, S. Kunis, and D. Potts (2009).
Using NFFT3 - a software library for various nonequispaced fast Fourier transforms.
ACM Transactions on Mathematical Software, 36, no. 19
[4] B. Charlier, J. Feydy, J. A. Glaunes, F.-D. Collin, and G. Durif (2021).
Kernel operations on the GPU with autodiff, without memory overflows.
Journal of Machine Learning Research