Manuel Radons
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View article: Synthetic Data Generation and Differential Privacy using Tensor Networks' Matrix Product States (MPS)
Synthetic Data Generation and Differential Privacy using Tensor Networks' Matrix Product States (MPS) Open
Synthetic data generation is a key technique in modern artificial intelligence, addressing data scarcity, privacy constraints, and the need for diverse datasets in training robust models. In this work, we propose a method for generating pr…
View article: Introducing the Kernel Descent Optimizer for Variational Quantum Algorithms
Introducing the Kernel Descent Optimizer for Variational Quantum Algorithms Open
In recent years, variational quantum algorithms have garnered significant attention as a candidate approach for near-term quantum advantage using noisy intermediate-scale quantum (NISQ) devices. In this article we introduce kernel descent,…
View article: Denoising Gradient Descent in Variational Quantum Algorithms
Denoising Gradient Descent in Variational Quantum Algorithms Open
In this article we introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. This is accomplished by computing a {\emph{regularized}} local classical approximation to the obje…
View article: Denoising Gradient Descent in Variational Quantum Algorithms
Denoising Gradient Descent in Variational Quantum Algorithms Open
In this article we introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. This is accomplished by computing a {\emph{regularized}} local classical approximation to the obje…
View article: Generalized Perron Roots and Solvability of the Absolute Value Equation
Generalized Perron Roots and Solvability of the Absolute Value Equation Open
Let $A$ be a $n\\times n$ real matrix. The piecewise linear equation system\n$z-A\\vert z\\vert =b$ is called an absolute value equation (AVE). It is\nwell-known to be equivalent to the linear complementarity problem. Unique\nsolvability o…
View article: Interpolating Parametrized Quantum Circuits using Blackbox Queries
Interpolating Parametrized Quantum Circuits using Blackbox Queries Open
This article focuses on developing classical surrogates for parametrized quantum circuits using interpolation via (trigonometric) polynomials. We develop two algorithms for the construction of such surrogates and prove performance guarante…
View article: On Neural Quantum Support Vector Machines
On Neural Quantum Support Vector Machines Open
In SR23 we introduced four algorithms for the training of neural support vector machines (NSVMs) and demonstrated their feasibility. In this note we introduce neural quantum support vector machines, that is, NSVMs with a quantum kernel, an…
View article: On Neural Quantum Support Vector Machines
On Neural Quantum Support Vector Machines Open
In \cite{simon2023algorithms} we introduced four algorithms for the training of neural support vector machines (NSVMs) and demonstrated their feasibility. In this note we introduce neural quantum support vector machines, that is, NSVMs wit…
View article: Algorithms for the Training of Neural Support Vector Machines
Algorithms for the Training of Neural Support Vector Machines Open
Neural support vector machines (NSVMs) allow for the incorporation of domain knowledge in the design of the model architecture. In this article we introduce a set of training algorithms for NSVMs that leverage the Pegasos algorithm and pro…
View article: Edge-unfolding nested prismatoids
Edge-unfolding nested prismatoids Open
A $3$-Prismatoid is the convex hull of two convex polygons $A$ and $B$ which lie in parallel planes $H_A, H_B\subset\mathbb{R}^3$. Let $A'$ be the orthogonal projection of $A$ onto $H_B$. A prismatoid is called nested if $A'$ is properly c…
View article: An Open Newton Method for Piecewise Smooth Functions
An Open Newton Method for Piecewise Smooth Functions Open
Recent research has shown that piecewise smooth (PS) functions can be approximated by piecewise linear functions with second order error in the distance to a given reference point. A semismooth Newton type algorithm based on successive app…
View article: Piecewise linear secant approximation via algorithmic piecewise differentiation
Piecewise linear secant approximation via algorithmic piecewise differentiation Open
It is shown how piecewise differentiable functions $F: \mathbb R^n \mapsto \mathbb R^m $ that are defined by evaluation programs can be approximated locally by a piecewise linear model based on a pair of sample points $\check x$ and $\hat …
View article: Sign controlled solvers for the absolute value equation with an application to support vector machines
Sign controlled solvers for the absolute value equation with an application to support vector machines Open
Let $A$ be a real $n\times n$ matrix and $z,b\in \mathbb R^n$. The piecewise linear equation system $z-A\vert z\vert = b$ is called an absolute value equation. It is equivalent to the general linear complementarity problem, and thus NP har…
View article: Piecewise linear secant approximation via Algorithmic Piecewise\n Differentiation
Piecewise linear secant approximation via Algorithmic Piecewise\n Differentiation Open
It is shown how piecewise differentiable functions $F: \\mathbb R^n \\mapsto\n\\mathbb R^m $ that are defined by evaluation programs can be approximated\nlocally by a piecewise linear model based on a pair of sample points $\\check x$\nand…
View article: Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation
Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation Open
In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). When applied to such a problem the classical trapezoidal rule suffers from a loss of accuracy if …
View article: Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic\n Differentiation
Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic\n Differentiation Open
In this article we analyze a generalized trapezoidal rule for initial value\nproblems with piecewise smooth right hand side \\(F:\\R^n\\to\\R^n\\). When applied\nto such a problem the classical trapezoidal rule suffers from a loss of\naccu…
View article: $\mathcal O(n)$ working precision inverses for symmetric tridiagonal Toeplitz matrices with $\mathcal O(1)$ floating point calculations
$\mathcal O(n)$ working precision inverses for symmetric tridiagonal Toeplitz matrices with $\mathcal O(1)$ floating point calculations Open
A well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal $a$ on the diagonal and $b$ on the extra diagonals ($a, b\in \mathbb R$). The inverses of such matrices are d…