Related papers: Effective identifiability criteria for tensors and…
Persistent tensors, introduced in [Quantum 8 (2024), 1238], and inspired by quantum information theory, form a recursively defined class of tensors that remain stable under the substitution method and thereby yield nontrivial lower bounds…
While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention…
We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to…
Within the field of numerical multilinear algebra, block tensors are increasingly important. Accordingly, it is appropriate to develop an infrastructure that supports reasoning about block tensor computation. In this paper we establish…
Predicting tensorial properties with machine learning models typically requires carefully designed tensorial descriptors. In this work, we introduce an alternative strategy for learning tensorial quantities based on scalar descriptors. We…
Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has a symmetric nonnegative factorization, is called a…
Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
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…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
We establish a necessary density criterion for the identifiability of time-frequency structured classes of Hilbert-Schmidt operators. The density condition is based on the density criterion for Gabor frames and Riesz bases in the space of…
We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this…
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…
A Killing tensor field on a Riemannian space corresponds to an integral of the geodesic flow polynomial in momenta. A Killing tensor field is called decomposable if it is a polynomial in Killing vector fields. In this paper, we first prove…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
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…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
For any irreducible non-degenerate variety $X\subset \mathbb{P}^r$, we give a criterion for the $(k,s)$-identifiability of $X$. If $k\leq s-1 <r$, then the $(k,s)$-identifiability holds for $X$ if and only if the $s$-identifiability holds…
Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of…
The necessary and sufficient conditions for a spacetime with an invariant frame to admit a group of isometries of dimension $r$ are given in terms of the connection tensor $H$ associated with this frame. In Petrov-Bel types I, II and III,…