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Foundation models (FMs) have shown prominent success in a wide range of tasks. Their applicability to specific domain-task pairings relies on the availability of, both, high-quality data and significant computational resources. These…

The Nonnegative Matrix Factorization (NMF) of the rating matrix has shown to be an effective method to tackle the recommendation problem. In this paper we propose new methods based on the NMF of the rating matrix and we compare them with…

The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on…

Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…

Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…

Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…

NVIDIA Tensor Cores and AMD Matrix Cores (together called Matrix Accelerators) are of growing interest in high-performance computing and machine learning owing to their high performance. Unfortunately, their numerical behaviors are not…

DFT is the numerical implementation of Fourier transform (FT), and it has many forms. Ordinary DFT (ODFT) and symmetric DFT (SDFT) are the two main forms of DFT. The most widely used DFT is ODFT, and the phase spectrum of this form is…

Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…

Positive semidefinite matrix factorization (PSDMF) expresses each entry of a nonnegative matrix as the inner product of two positive semidefinite (psd) matrices. When all these psd matrices are constrained to be diagonal, this model is…

Recently, deep matrix factorization has been established as a powerful model for unsupervised tasks, achieving promising results, especially for multi-view clustering. However, existing methods often lack effective feature selection…

The construction of the Hamiltonian matrix \textbf{H} is an essential, yet computationally expensive step in \textit{ab-initio} device simulations based on density-functional theory (DFT). In homogeneous structures, the fact that a unit…

In this paper we consider a general matrix factorization model which covers a large class of existing models with many applications in areas such as machine learning and imaging sciences. To solve this possibly nonconvex, nonsmooth and…

Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…

The Fast Tracker (FTK) is a proposed upgrade to the ATLAS trigger system that will operate at full Level-1 output rates and provide high quality tracks reconstructed over the entire detector by the start of processing in Level-2. FTK solves…

With the rapid growth of deep neural networks (DNNs), compute-in-memory (CIM) has emerged as a promising energy-efficient paradigm for accelerating multiply-and-accumulate (MAC) operations. Yet, current CIM architectures are largely limited…

The combination of deep learning and ab initio materials calculations is emerging as a trending frontier of materials science research, with deep-learning density functional theory (DFT) electronic structure being particularly promising. In…

Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in error correction coding. Hence, reducing the computational complexities of DFTs is of great significance, especially for long DFTs as increasingly longer…

This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…

As safety-critical applications increasingly rely on data-parallel floating-point computations, there is an increasing need for flexible and configurable fault tolerance in parallel floating-point accelerators such as tensor engines. While…