Related papers: TTML: tensor trains for general supervised machine…

Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further,…

The efficient implementation of large language models (LLMs) is crucial for deployment on resource-constrained devices. Low-rank tensor compression techniques, such as tensor-train (TT) networks, have been widely studied for…

In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches:…

Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. However, many studies rely on toy datasets or heavy feature reduction, raising concerns about their scalability.…

In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention…

Surrogate models can reduce computational costs for multivariable functions with an unknown internal structure (black boxes). In a discrete formulation, surrogate modeling is equivalent to restoring a multidimensional array (tensor) from a…

This work focuses on designing low complexity hybrid tensor networks by considering trade-offs between the model complexity and practical performance. Firstly, we exploit a low-rank tensor-train deep neural network (TT-DNN) to build an…

We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train…

Quantized tensor trains (QTTs) are a low-rank and multiscale framework that allows for efficient approximation and manipulation of multi-dimensional, high resolution data. One area of active research is their use in numerical simulation of…

In the Quantum-Train (QT) framework, mapping quantum state measurements to classical neural network weights is a critical challenge that affects the scalability and efficiency of hybrid quantum-classical models. The traditional QT framework…

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying…

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks…

We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…

A targeted learning (TL) framework is developed to estimate the difference in the restricted mean survival time (RMST) for a clinical trial with time-to-event outcomes. The approach starts by defining the target estimand as the RMST…

Multi-task learning (MTL) enables simultaneous training across related tasks, leveraging shared information to improve generalization, efficiency, and robustness, especially in data-scarce or high-dimensional scenarios. While deep learning…

We propose a multilevel tensor-train (TT) framework for solving nonlinear partial differential equations (PDEs) in a global space-time formulation. While space-time TT solvers have demonstrated significant potential for compressed…

Accurate electrical load forecasting is crucial for optimizing power system operations, planning, and management. As power systems become increasingly complex, traditional forecasting methods may fail to capture the intricate patterns and…

Incorporation of machine learning (ML) techniques into atomic-scale modeling has proven to be an extremely effective strategy to improve the accuracy and reduce the computational cost of simulations. It also entails conceptual and practical…

Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…