Related papers: A Dynamic Low-Rank Fast Gaussian Transform

With the growing reliance of modern supercomputers on accelerator-based architectures such a GPUs, the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority.…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…

Due to the constraints on model performance imposed by the size of the training data, data augmentation has become an essential technique in deep learning. However, most existing data augmentation methods are affected by information loss…

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the non-linear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation…

The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…

In this paper we present a novel method for efficient and effective 3D surface reconstruction in open scenes. Existing Neural Radiance Fields (NeRF) based works typically require extensive training and rendering time due to the adopted…

With advanced X-ray source and detector technologies being continuously developed, non-traditional CT geometries have been widely explored. Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an X-ray source might be…

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…

In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…

Graph neural networks (GNNs) are gaining increasing popularity as a promising approach to machine learning on graphs. Unlike traditional graph workloads where each vertex/edge is associated with a scalar, GNNs attach a feature tensor to…

Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…

This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

There are plenty of problems where the data available is scarce and expensive. We propose a generator of semi-artificial data with similar properties to the original data which enables development and testing of different data mining…

Pretrained Foundation Models (PFMs) have transformed numerous applications by enabling efficient adaptation to customized tasks. Parameter-Efficient Fine-Tuning (PEFT) has emerged as a resource-efficient alternative to full fine-tuning,…

The performance of multivariate kernel density estimation (KDE) depends strongly on the choice of bandwidth matrix. The high computational cost required for its estimation provides a big motivation to develop fast and accurate methods. One…

The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series…