State-of-the-art methods for scalable Gaussian processes use iterative
algorithms, requiring fast matrix vector multiplies (MVMs) with the covariance
kernel. The Structured Kernel Interpolation (SKI) framework accelerates these
MVMs by performing efficient MVMs on a grid and interpolating back to the
original space. In this work, we develop a connection between SKI and the
permutohedral lattice used for high-dimensional fast bilateral filtering. Using
a sparse simplicial grid instead of a dense rectangular one, we can perform GP
inference exponentially faster in the dimension than SKI. Our approach,
Simplex-GP, enables scaling SKI to high dimensions, while maintaining strong
predictive performance. We additionally provide a CUDA implementation of
Simplex-GP, which enables significant GPU acceleration of MVM based inference.

通过将稠密的格子转化为稀疏的单纯形网格，我们提出了一种新的方法 Simplex-GP，把最新的可扩展高斯过程方法 SKI 推广到更高的维度，同时保持较强的预测性能，并提供了一个 CUDA 实现，从而获得了显著的 GPU 加速。

在单纯形上滑行：可扩展高斯过程的 Permutohedral 格子核插值

SKIing on Simplices: Kernel Interpolation on the Permutohedral Lattice  for Scalable Gaussian Processes

This paper presents a convolutional layer that is able to process sparse
input features. As an example, for image recognition problems this allows an
efficient filtering of signals that do not lie on a dense grid (like pixel
position), but of more general features (such as color values). The presented
algorithm makes use of the permutohedral lattice data structure. The
permutohedral lattice was introduced to efficiently implement a bilateral
filter, a commonly used image processing operation. Its use allows for a
generalization of the convolution type found in current (spatial) convolutional
network architectures.

本文提出了一种卷积层，能够处理稀疏的输入特征。它利用 Permiutohedral 网格数据结构实现了一个波透镜卷积算法，从而使得卷积神经网络具有更广泛的应用场景。