Related papers: EinDecomp: Decomposition of Declaratively-Specifie…
In CS literature, the efforts can be divided into two groups: finding a measurement matrix that preserves the compressed information at the maximum level, and finding a reconstruction algorithm for the compressed information. In the…
The tensor network, as a facterization of tensors, aims at performing the operations that are common for normal tensors, such as addition, contraction and stacking. However, due to its non-unique network structure, only the tensor network…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
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 work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…
We propose Riemannian preconditioned algorithms for the tensor completion problem via tensor ring decomposition. A new Riemannian metric is developed on the product space of the mode-2 unfolding matrices of the core tensors in tensor ring…
ITensor is a system for programming tensor network calculations with an interface modeled on tensor diagram notation, which allows users to focus on the connectivity of a tensor network without manually bookkeeping tensor indices. The…
We study the decomposability and the subdifferential of the tensor nuclear norm. Both concepts are well understood and widely applied in matrices but remain unclear for higher-order tensors. We show that the tensor nuclear norm admits a…
Tensor algebra is widely used in many applications, such as scientific computing, machine learning, and data analytics. The tensors represented real-world data are usually large and sparse. There are tens of storage formats designed for…
A promising new algebraic approach to weighted model counting makes use of tensor networks, following a reduction from weighted model counting to tensor-network contraction. Prior work has focused on analyzing the single-core performance of…
Tensor network diagram (graphical notation) is a useful tool that graphically represents multiplications between multiple tensors using nodes and edges. Using the graphical notation, complex multiplications between tensors can be described…
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…
Tensor algebra lies at the core of computational science and machine learning. Due to its high usage, entire libraries exist dedicated to improving its performance. Conventional tensor algebra performance boosts focus on algorithmic…
Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…
We propose a new algorithm for tensor decomposition, based on Jennrich's algorithm, and apply our new algorithmic ideas to blind deconvolution and Gaussian mixture models. Our first contribution is a simple and efficient algorithm to…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…
We give a spectral algorithm for decomposing overcomplete order-4 tensors, so long as their components satisfy an algebraic non-degeneracy condition that holds for nearly all (all but an algebraic set of measure $0$) tensors over…
Deterministic execution offers many benefits for debugging, fault tolerance, and security. Running parallel programs deterministically is usually difficult and costly, however - especially if we desire system-enforced determinism, ensuring…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…