Related papers: Difference between standard and quasi-conformal BF…
Quantum kernels (QK) are widely used in quantum machine learning applications; yet, their potential to surpass classical machine learning methods on classical datasets remains uncertain. This limitation can be attributed to the exponential…
The non-strictly continuous character of the Hawking radiation spectrum generates a natural correspondence between Hawking radiation and black hole (BH) quasi-normal modes (QNM). In this work, we generalize recent results on this important…
We solve the BFKL equation in the leading logarithmic approximation numerically in the Yang-Mills theory with the Higgs mechanism for the vector boson mass generation. It can be considered as a model for the amplitude with the correct…
Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact…
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…
This paper presents a convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less…
We discuss, within the context of first order perturbation theory, the correction to the NLO BFKL wavefuncyion for scattering processes with non-zero momentum transfer, arising from the fact that in NLO the kernel is not covariant under…
Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is…
Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…
Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…
In this work, the concept of quasi-type Kernel polynomials with respect to a moment functional is introduced. Difference equation satisfied by these polynomials along with the criterion for orthogonality conditions are discussed. The…
With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum…
The kernels in the tangible matter of our everyday experience are composed of light quarks. At least, they are light classically; but they don't remain light. Dynamical effects within the Standard Model of Particle Physics change them in…
The importance of analyzing nontrivial datasets when testing quantum machine learning (QML) models is becoming increasingly prominent in literature, yet a cohesive framework for understanding dataset characteristics remains elusive. In this…
The procedure to improve the convergence in transverse momentum space of the NLL BFKL kernel using a w-shift is revisited. An accurate approximation to this shift only depending on transverse momenta is presented. This approximation is…
We test the performance of a RG-improved kernel in the determination of the amplitude of a physical process, the electroproduction of two light vector mesons,in the BFKL approach at the next-to-leading approximation (NLA). We find that a…
At a surface between electromagnetic media the Maxwell equations allow either the usual boundary conditions, or exactly one alternative: continuity of E(perpendicular), H(perpendicular), D(parallel), B(parallel). These `flipped' conditions…
Quantum computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by…
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,…
The quasi-Frobenius-Lusztig kernel ${Q}\mathbf{u}_{q}(\mathfrak{sl}_{2})$ associated with $\mathfrak{sl}_{2}$ has been constructed in \cite{Liu}. In this paper we study the representations of this small quasi-quantum group. We give a…