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The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many…

While convolutional neural networks (CNNs) have become the de facto standard for most image processing and computer vision applications, their deployment on edge devices remains challenging. Tensor decomposition methods provide a means of…

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…

We apply a number of atomic decomposition schemes across the standard QM7 dataset -- a small model set of organic molecules at equilibrium geometry -- to inspect the possible emergence of trends among contributions to atomization energies…

Low-rank tensor approximation approaches have become an important tool in the scientific computing community. The aim is to enable the simulation and analysis of high-dimensional problems which cannot be solved using conventional methods…

Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…

A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…

Modern computational chemistry has reached a stage at which massive exploration into chemical reaction space with unprecedented resolution with respect to the number of potentially relevant molecular structures has become possible. Various…

Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex…

Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…

We present the first deterministic, finite-step algorithm for exact tensor ring (TR) decomposition, addressing an open question about the existence of such procedures. Our method leverages blockwise simultaneous diagonalization to recover…

Over recent years it has become well accepted that user interest is not static or immutable. There are a variety of contextual factors, such as time of day, the weather or the user's mood, that influence the current interests of the user.…

High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional…

Predicting and enhancing inherent properties based on molecular structures is paramount to design tasks in medicine, materials science, and environmental management. Most of the current machine learning and deep learning approaches have…

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…

Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…

This article provides next step towards solving speed bottleneck of any system that intensively uses convolutions operations (e.g. CNN). Method described in the article is applied on deformable part models (DPM) algorithm. Method described…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…

The groundbreaking performance of deep neural networks (NNs) promoted a surge of interest in providing a mathematical basis to deep learning theory. Low-rank tensor decompositions are specially befitting for this task due to their close…