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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…
The increasing demand for on-device training of deep neural networks (DNNs) aims to leverage personal data for high-performance applications while addressing privacy concerns and reducing communication latency. However, resource-constrained…
This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density…
This paper develops a first-order optimization method for coupled structured matrix factorization (CoSMF) problems that arise in the context of hyperspectral super-resolution (HSR) in remote sensing. To best leverage the problem structures…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
Polynomial multiplication is one of the fundamental operations in many applications, such as fully homomorphic encryption (FHE). However, the computational inefficiency stemming from polynomials with many large-bit coefficients poses a…
We propose an accelerated block proximal linear framework with adaptive momentum (ABPL$^+$) for nonconvex and nonsmooth optimization. We analyze the potential causes of the extrapolation step failing in some algorithms, and resolve this…
Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently…
Nonconvex sparse learning plays an essential role in many areas, such as signal processing and deep network compression. Iterative hard thresholding (IHT) methods are the state-of-the-art for nonconvex sparse learning due to their…
Currently, the size of scientific data is growing at an unprecedented rate. Data in the form of tensors exhibit high-order, high-dimensional, and highly sparse features. Although tensor-based analysis methods are very effective, the large…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…
Tensor network contraction on arbitrary graphs is a fundamental computational challenge with applications ranging from quantum simulation to error correction. While belief propagation (BP) provides a powerful approximation algorithm for…
Dealing with sparse rewards is a long-standing challenge in reinforcement learning (RL). Hindsight Experience Replay (HER) addresses this problem by reusing failed trajectories for one goal as successful trajectories for another. This…
Identifying recurring patterns in high-dimensional time series data is an important problem in many scientific domains. A popular model to achieve this is convolutive nonnegative matrix factorization (CNMF), which extends classic…
Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here,…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
Multi-goal robot manipulation tasks with sparse rewards are difficult for reinforcement learning (RL) algorithms due to the inefficiency in collecting successful experiences. Recent algorithms such as Hindsight Experience Replay (HER)…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
The importance of unsupervised clustering and topic modeling is well recognized with ever-increasing volumes of text data. In this paper, we propose a fast method for hierarchical clustering and topic modeling called HierNMF2. Our method is…