Related papers: Fourier Analysis and q-Gaussian Functions: Analyti…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…
Inspired by the success of recent data augmentation methods for signals which act on time-frequency representations, we introduce an operator which convolves the short-time Fourier transform of a signal with a specified kernel. Analytical…
Quantum neural networks promise to extend the power of machine learning into the quantum domain, with potential applications ranging from automatic recognition of quantum states to the control of quantum devices. However, their physical…
Most of the known Fourier transforms associated with the equations of mathematical physics have a trivial kernel, and an inversion formula as well as the Parseval equality are fulfilled. In other words, the system of the eigenfunctions…
Kernel expansions are a topic of considerable interest in machine learning, also because of their relation to the so-called feature maps introduced in machine learning. Properties of the associated basis functions and weights (corresponding…
Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…
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…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
Recent advancements in computer vision have successfully extended Open-vocabulary segmentation (OVS) to the 3D domain by leveraging 3D Gaussian Splatting (3D-GS). Despite this progress, efficiently rendering the high-dimensional features…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
The overparameterization of variational quantum circuits, as a model of Quantum Neural Networks (QNN), not only improves their trainability but also serves as a method for evaluating the property of a given ansatz by investigating their…
We define fermionic convolution and demonstrate its utility in characterizing fermionic non-Gaussian components, which are essential to the computational advantage of fermionic systems. Using fermionic convolution, we propose an efficient…
The presence of irrelevant features in the input dataset tends to reduce the interpretability and predictive quality of machine learning models. Therefore, the development of feature selection methods to recognize irrelevant features is a…
Since many physical laws -- from classical mechanics to electromagnetism -- are formulated as two-body interactions, the same perspective naturally extends to biological and social dynamics. Here we focus on rhythmic phenomena, where phase…
This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…
Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few…