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Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
We consider the problem of automatically decomposing operations over tensors or arrays so that they can be executed in parallel on multiple devices. We address two, closely-linked questions. First, what programming abstraction should…
A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…
The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…
This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…
The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of…
Tensor network contraction is a powerful computational tool in quantum many-body physics, quantum information and quantum chemistry. The complexity of contracting a tensor network is thought to mainly depend on its entanglement properties,…
Tensor networks serve as a powerful tool for efficiently representing and manipulating high-dimensional data in applications such as quantum physics, machine learning, and data compression. Tensor Decision Diagrams (TDDs) offer an efficient…
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…
Tensors provide a robust framework for managing high-dimensional data. Consequently, tensor analysis has emerged as an active research area in various domains, including machine learning, signal processing, computer vision, graph analysis,…
A new implementation of the canonical polyadic decomposition (CPD) is presented. It features lower computational complexity and memory usage than the available state of art implementations available. The CPD of tensors is a challenging…
The fully-connected tensor network (FCTN) decomposition has gained prominence in the field of tensor completion owing to its powerful capacity to capture the low-rank characteristics of tensors. Nevertheless, the recovery of local details…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
Constraint programming is a general and exact method based on constraint propagation and backtracking search. We provide a function decomposing a constraint network into a ternary constraint network (TCN) with a reduced number of operators.…
A cascadic tensor multigrid method and an economic cascadic tensor multigrid method is presented for solving the image restoration models. The methods use quadratic interpolation as prolongation operator to provide more accurate initial…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…
Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on…
Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over…
In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…