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Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition…
Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…
The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed.…
The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper,…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
A novel approach for solving linear estimation problem in multi-user massive MIMO systems is proposed. In this approach, the difficulty of matrix inversion is attributed to the incomplete definition of the dot product. The general…
The era of exascale computing opens new venues for innovations and discoveries in many scientific, engineering, and commercial fields. However, with the exaflops also come the extra-large high-dimensional data generated by high-performance…
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…
A tensor is a multidimensional array of numbers that can be used to store data, encode a computational relation and represent quantum entanglement. In this sense a tensor can be viewed as valuable resource whose transformation can lead to…
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…
We introduce a simple yet significant improvement to the time-evolving block decimation (TEBD) tensor network algorithm for simulating the time dynamics of strongly correlated one-dimensional (1D) mixed quantum states. The efficiency of 1D…
Today's HPC applications are producing extremely large amounts of data, such that data storage and analysis are becoming more challenging for scientific research. In this work, we design a new error-controlled lossy compression algorithm…
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,…
Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…
Recently Implicit Neural Representations (INRs) gained attention as a novel and effective representation for various data types. Thus far, prior work mostly focused on optimizing their reconstruction performance. This work investigates INRs…
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…