Related papers: Tensor Ring Decomposition
Tensor network (TN), a young mathematical tool of high vitality and great potential, has been undergoing extremely rapid developments in the last two decades, gaining tremendous success in condensed matter physics, atomic physics, quantum…
Deep neural networks currently demonstrate state-of-the-art performance in several domains. At the same time, models of this class are very demanding in terms of computational resources. In particular, a large amount of memory is required…
We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…
Anisotropic Tensor Renormalization Group (ATRG) is a powerful algorithm for four-dimensional tensor network calculations. However, the larger bond dimensions are known to be difficult to achieve in practice due to the higher computational…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…
This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
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 or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…
Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…
Tensor computations--in particular tensor contraction (TC)--are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication (MM) and to the availability of optimized…
Recurrent neural networks (RNN) such as long-short-term memory (LSTM) networks are essential in a multitude of daily live tasks such as speech, language, video, and multimodal learning. The shift from cloud to edge computation intensifies…
Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…
Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in…
This work aims to help resolve the two main stumbling blocks in the application of Deep Neural Networks (DNNs), that is, the exceedingly large number of trainable parameters and their physical interpretability. This is achieved through a…
We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…
In this paper, we propose a new unified optimization algorithm for general tensor decomposition which is formulated as an inverse problem for low-rank tensors in the general linear observation models. The proposed algorithm supports three…
It is well known that tensor network regression models operate on an exponentially large feature space, but questions remain as to how effectively they are able to utilize this space. Using a polynomial featurization, we propose the…