Related papers: Tensor methods for the computation of MTTA in larg…

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

We present MetaTT, a Tensor Train (TT) adapter framework for fine-tuning of pre-trained transformers. MetaTT enables flexible and parameter-efficient model adaptation by using a single shared TT to factorize transformer sub-modules. This…

We describe a numerical many-body technique that is based on both tensor networks and quantum Monte Carlo. The variational ansatz is a tensor network that can harvest volume-law entanglement. It is constructed from a tensor train to which…

Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions,…

In terms of signal samples, we propose and justify a new rank reduced multi-term transform, abbreviated as MTT, which, under certain conditions, may provide better-associated accuracy than that of known optimal rank reduced transforms. The…

For three-dimensional (3D) magnetic objects with linear size $L$ exceeding a few exchange lengths, the micromagnetic state exhibits pronounced informational sparsity: low-dimensional, high-gradient regions (e.g., domain walls) coexist with…

Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…

Test-time adaptation (TTA) refers to adapting a trained model to a new domain during testing. Existing TTA techniques rely on having multiple test images from the same domain, yet this may be impractical in real-world applications such as…

This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…

Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Although there has…

Modern transportation network modeling increasingly involves the integration of diverse methodologies including sensor-based forecasting, reinforcement learning, classical flow optimization, and demand modeling that have traditionally been…

General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate…

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…

Solving the Boltzmann-BGK equation with traditional numerical methods suffers from high computational and memory costs due to the curse of dimensionality. In this paper, we propose a novel accuracy-preserved tensor-train (APTT) method to…

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…

Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…