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Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

In high-performance computing, hotspot GPU kernels are primary bottlenecks, and expert manual tuning is costly and hard to port. Large language model methods often assume kernels can be compiled and executed cheaply, which fails in large…

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

Variational Quantum Algorithms (VQAs) aim at solving classical or quantum optimization problems by optimizing parametrized trial states on a quantum device, based on the outcomes of noisy projective measurements. The associated optimization…

Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…

Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through…

The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…

We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type…

Sparse matrix-matrix multiplication (SpGEMM) is a widely used kernel in various graph, scientific computing and machine learning algorithms. In this paper, we consider SpGEMMs performed on hundreds of thousands of processors generating…

The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose…

Spectral clustering is one of the most popular graph clustering algorithms, which achieves the best performance for many scientific and engineering applications. However, existing implementations in commonly used software platforms such as…

Hardware performance monitoring (HPM) is a crucial ingredient of performance analysis tools. While there are interfaces like LIKWID, PAPI or the kernel interface perf\_event which provide HPM access with some additional features, many…

Heterogeneous computing can potentially offer significant performance and performance per watt improvements over homogeneous computing, but the question "what is the ideal mapping of algorithms to architectures?" remains an open one. In the…

The prospects of quantum computing have driven efforts to realize fully functional quantum processing units (QPUs). Recent success in developing proof-of-principle QPUs has prompted the question of how to integrate these emerging processors…

Optimizing metamaterials with complex geometries is a big challenge. Although an active learning algorithm, combining machine learning (ML), quantum computing, and optical simulation, has emerged as an efficient optimization tool, it still…

Future experiments in high-energy physics will pose stringent requirements to computing, in particular to real-time data processing. As an example, the CBM experiment at FAIR Germany intends to perform online data selection exclusively in…

Signature kernels have emerged as a powerful tool within kernel methods for sequential data. In the paper "The Signature Kernel is the solution of a Goursat PDE", the authors identify a kernel trick that demonstrates that, for continuously…

Sparse matrices, more specifically SpGEMM kernels, are commonly found in a wide range of applications, spanning graph-based path-finding to machine learning algorithms (e.g., neural networks). A particular challenge in implementing SpGEMM…

Kernel conditional mean embeddings (CMEs) offer a powerful framework for representing conditional distribution, but they often face scalability and expressiveness challenges. In this work, we propose a new method that effectively combines…

In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…