Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

A. Practical implementation: In this section, we present some practical aspects for the
implementation of our model selection strategy, that is a method for the calibration of the …

In this paper, we propose new learning algorithms for approximating high-dimensional
functions using tree tensor networks in a least-squares setting. Given a dimension tree or …

Approximation of high-dimensional functions is a problem in many scientific fields that is
only feasible if advantageous structural properties, such as sparsity in a given basis, can be …

We present a theoretical approach to overcome the curse of dimensionality using a neural
computation algorithm which can be distributed across several machines. Our modular …

In these notes we present some first ideas on the composition of tensor trains for the use in
scientific computing. We discuss the relation to deep neural networks and the potential role …

This work introduces a novel method for embedding continuous variables into quantum
circuits via piecewise polynomial features, utilizing low-rank tensor networks. Our approach …

We consider the problem of the estimation of a high-dimensional probability distribution from
iid samples of the distribution using model classes of functions in tree-based tensor formats …

Abstract Mixture-of-Experts (MoEs) can scale up beyond traditional deep learning models by
employing a routing strategy in which each input is processed by a single “expert” deep …

Variational quantum algorithms (VQAs) have been proposed for solvingpartial differential
equations on quantum computers. This thesis focuses on analyzingVQAs for the stationary …