GpFlash: Maximizing Speed and Minimizing Memory for Gaussian Process Training and Prediction

Gaussian process (GP) inference in Python is dominated by libraries such as GPyTorch and GPflow, which are built on deep-learning frameworks and inherit their dispatch overhead and dependency footprint. We present LightGP, a dependency-free C++17 library for GP regression with Python bindings, supporting Apple Metal and NVIDIA CUDA backends alongside tuned CPU paths via Apple Accelerate and OpenBLAS. LightGP provides four inference paths -- exact Cholesky, matrix-free conjugate gradients, sparse variational free energy, and structured kernel interpolation with FFT -- covering problems from $N{=}100$ to $N{=}500{,}000$. On an Apple M4, LightGP CPU is 2.6--8.7$\times$ faster than GPyTorch CPU for exact GP and ${\sim}1.5\times$ faster for sparse GP at every scale tested. On an NVIDIA RTX~3060, LightGP CUDA is 2.3--6.7$\times$ faster than GPyTorch CUDA for exact GP up to $N{=}2{,}048$, with GPyTorch closing the gap at $N{=}4{,}096$. A fused matrix-free kernel-vector product on Metal achieves 32$\times$ over the explicit path at $N{=}20{,}000$ with $O(N)$ memory, and an FFT-accelerated SKI matvec via Accelerate vDSP runs in sub-millisecond time at $N{=}200{,}000$. LightGP compiles as a single static library with zero external dependencies and is installable via \texttt{pip install lightgp

Gradient observations can substantially improve Gaussian process (GP) surrogates, particularly in high-dimensional settings where function evaluations are expensive. However, exact inference with $n$ function values and $n$ full gradients in $d$ dimensions scales cubically in the joint state size, imposing an intractable $\mathcal{O}(n^3 d^3)$ computational bottleneck. We introduce TERA, a highly scalable derivative GP method based on target-specific exact gradient reduction. We prove that for stationary kernels, the gradient components orthogonal to the directions connecting the target and conditioning points are conditionally independent of the target function value; consequently, the exact conditional density is fully characterized by at most $m^2$ directional derivatives once a conditioning set of size $m$ is specified. By using these reduced, dimension-free conditionals as local factors in a Vecchia approximation, TERA effectively decouples $n$ and $d$ from the dense matrix inversion. This reduces the per-target evaluation cost to $\mathcal{O}(dm^2 + m^6)$ time and $\mathcal{O}(dm^2 + m^4)$ memory, leaving the underlying derivative GP model mathematically unchanged. Empirical evaluations demonstrate that TERA achieves state-of-the-art predictive accuracy while operating orders of magnitude faster than standard derivative GPs. Crucially, both computation time and peak GPU memory remain essentially flat with respect to $d$, enabling highly scalable inference in high-dimensional spaces.

We present a theoretically grounded Gaussian process framework that leverages neural feature maps to construct expressive kernels. We show that the learned feature map can be interpreted as an optimal low-rank approximation to a Gram matrix derived from an implied RKHS, from which we establish consistency of the GP posterior. We further analyse the spectral properties of the induced kernels and introduce product feature-map kernels to address oversmoothing. This simple yet powerful approach enables fast, scalable, and accurate exact GP inference with minimal upfront work. The flexibility of kernel design supports seamless application to both regression and classification tasks across diverse data modalities, including tabular inputs and structured domains such as images. On benchmark datasets, this approach surpasses pre-existing methods in terms of accuracy and training and prediction efficiency.