Related papers: Tensor Ring Decomposition: Optimization Landscape …
Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…
Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…
The alternating least squares (ALS/AltLS) method is a widely used algorithm for computing the CP decomposition of a tensor. However, its convergence theory is still incompletely understood. In this paper, we prove explicit quantitative…
Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…
In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…
Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
In this paper we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has size exponential in $d$ where $d$ is the number of dimensions,…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
In this paper we study bipartite quantum correlations using techniques from tracial noncommutative polynomial optimization. We construct a hierarchy of semidefinite programming lower bounds on the minimal entanglement dimension of a…
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…
Tensor Train~(TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
This paper introduces a randomized variation of the alternating least squares (ALS) algorithm for rank reduction of canonical tensor formats. The aim is to address the potential numerical ill-conditioning of least squares matrices at each…
Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and…
We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian…
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…