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We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
The big data era is swamping areas including data analysis, machine/deep learning, signal processing, statistics, scientific computing, and cloud computing. The multidimensional feature and huge volume of big data put urgent requirements to…
Dynamic quantum simulation is a leading application for achieving quantum advantage. However, high circuit depths remain a limiting factor on near-term quantum hardware. We present a compilation algorithm based on Matrix Product Operators…
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…
Deep neural networks typically impose significant computational loads and memory consumption. Moreover, the large parameters pose constraints on deploying the model on edge devices such as embedded systems. Tensor decomposition offers a…
Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…
Unlike 2D raster images, there is no single dominant representation for 3D visual data processing. Different formats like point clouds, meshes, or implicit functions each have their strengths and weaknesses. Still, grid representations such…
Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary…
We present an algorithm to compute Green's functions on quantum computers for interacting electron systems, which is a challenging task on conventional computers. It uses a continued fraction representation based on the Lanczos method,…
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…
Convolutional neural networks excel in image recognition tasks, but this comes at the cost of high computational and memory complexity. To tackle this problem, [1] developed a tensor factorization framework to compress fully-connected…
The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements. Crucially, the proposed random measurement ensembles are both designed to be…
Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex periodic exponentials and spherical harmonics, respectively,…
In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge…
Butterflies are the smallest non-trivial subgraph in bipartite graphs, and therefore having efficient computations for analyzing them is crucial to improving the quality of certain applications on bipartite graphs. In this paper, we design…