# Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids

arXiv: https://arxiv.org/abs/2605.08036 · HTML: https://mlsanity.com/paper/2605.08036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 79 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Stability of the Lanczos Method for Matrix Function Approximation](https://mlsanity.com/paper/1708.07788/) (2017)
- [The Lanczos algorithm for matrix functions: a handbook for scientists](https://mlsanity.com/paper/2410.11090/) (2024)
- [Hierarchical additive interaction modelling with Gaussian process prior and its efficient implementation for multidimensional grid data](https://mlsanity.com/paper/2305.07073/) (2023)

## Abstract (arXiv)

We introduce CUTS-GPR, a new method for performing numerically exact GPR in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear or even linear scaling with the amount of training data, N, and low-order polynomial scaling with dimensionality, D. This is obtained by combining an additive kernel with an incomplete grid and exploiting the resulting structure of the kernel matrix. The scalability of the matrix-vector product is verified by benchmarks with billions of data points and thousands of dimensions. We demonstrate the end-to-end scalability of CUTS-GPR by running full GPR calculations, including hyperparameter optimization, on synthetic datasets with up to N = 4,494,001 and D = 500. As a realistic and challenging test, we finally apply CUTS-GPR to a set of ten potential energy surfaces (PESs) with N = 447,265 and D = 24. The calculations are completed in a matter of hours, showing that CUTS-GPR enables Bayesian modelling of high-dimensional PESs - a longstanding challenge in computational chemistry.