Related papers: Weighted balanced truncation method for approximat…
Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…
Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference…
As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the…
For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…
Recent research has shown that pruning large-scale language models for inference is an effective approach to improving model efficiency, significantly reducing model weights with minimal impact on performance. Interestingly, pruning can…
A modified $GW$ approximation to many - body systems is developed. The approximation has the same computational complexity as the traditional $GW$ approach, but uses a different truncation scheme. This scheme neglects high order connected…
We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…
The kernel truncation method (KTM) is a commonly-used algorithm to compute the convolution-type nonlocal potential $\Phi(x)=(U\ast \rho)(x), ~x \in {\mathbb R^d}$, where the convolution kernel $U(x)$ might be singular at the origin and/or…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
We present a scalable tensor-based approach to computing input-normal/output-diagonal nonlinear balancing transformations for control-affine systems with polynomial nonlinearities. This transformation is necessary to determine the states…
We study the problem of numerical differentiation of functions from weighted Wiener classes. We construct and analyze a truncation Legendre method to recover arbitrary order derivatives. The main focus is on obtaining error estimates in…
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…
Ewald summation is widely used to calculate electrostatic interactions in computer simulations of condensed-matter systems. We present an analysis of the errors arising from truncating the infinite real- and Fourier-space lattice sums in…
In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis.…
As deep neural networks are increasingly used in applications suited for low-power devices, a fundamental dilemma becomes apparent: the trend is to grow models to absorb increasing data that gives rise to memory intensive; however low-power…
In this paper, two numerical schemes for a nonlinear integral equation of Fredholm type with weakly singular kernel are proposed. These numerical methods combine sinc-collocation and sinc-convolution approximations with Newton and steepest…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
We present a memory and computation efficient ternary weight networks (TWNs) - with weights constrained to +1, 0 and -1. The Euclidian distance between full (float or double) precision weights and the ternary weights along with a scaling…
Making large language models (LLMs) more efficient in memory, latency, and serving cost is crucial for edge deployment, interactive applications, and sustainable inference at scale. Pruning is a promising technique, but existing pruning…