Related papers: Tensor-train methods for sequential state and para…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Learning multiple tasks sequentially requires neural networks to balance retaining knowledge, yet being flexible enough to adapt to new tasks. Regularizing network parameters is a common approach, but it rarely incorporates prior knowledge…

A regression-based framework for interpretable multi-way data imputation, termed Kernel Regression via Tensor Trains with Hadamard overparametrization (KReTTaH), is introduced. KReTTaH adopts a nonparametric formulation by casting…

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…

Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…

Online quantum state learning is a recently proposed problem by Aaronson et al. (2018), where the learner sequentially predicts $n$-qubit quantum states based on given measurements on states and noisy outcomes. In the previous work, the…

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…

The ability to learn compact, high-quality, and easy-to-optimize representations for visual data is paramount to many applications such as novel view synthesis and 3D reconstruction. Recent work has shown substantial success in using tensor…

We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…

We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high--dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of…

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Extracting information about dynamical systems from models learned off simulation data has become an increasingly important research topic in the natural and engineering sciences. Modeling the Koopman operator semigroup has played a central…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…

A challenge in multi-agent reinforcement learning is to be able to generalize over intractable state-action spaces. Inspired from Tesseract [Mahajan et al., 2021], this position paper investigates generalisation in state-action space over…

We present a tensor train (TT) based algorithm designed for sampling from a target distribution and employ TT approximation to capture the high-dimensional probability density evolution of overdamped Langevin dynamics. This involves…

We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Despite the predominant use of first-order methods for training deep learning models, second-order methods, and in particular, natural gradient methods, remain of interest because of their potential for accelerating training through the use…