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The Density Matrix Renormalization Group (DMRG) algorithm is a powerful tool for solving eigenvalue problems to model quantum systems. DMRG relies on tensor contractions and dense linear algebra to compute properties of condensed matter…

Learned sparse text embeddings have gained popularity due to their effectiveness in top-k retrieval and inherent interpretability. Their distributional idiosyncrasies, however, have long hindered their use in real-world retrieval systems.…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

Network pruning can reduce the high computation cost of deep neural network (DNN) models. However, to maintain their accuracies, sparse models often carry randomly-distributed weights, leading to irregular computations. Consequently, sparse…

This paper introduces a new method based on Deep Galerkin Methods (DGMs) for solving high-dimensional stochastic Mean Field Games (MFGs). We achieve this by using two neural networks to approximate the unknown solutions of the MFG system…

The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear…

Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…

With lowrank approximation the storage requirements for dense data are reduced down to linear complexity and with the addition of hierarchy this also works for data without global lowrank properties. However, the lowrank factors itself are…

An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia…

Dense vector retrieval is the practical backbone of Retrieval- Augmented Generation (RAG), but similarity search can suffer from precision limitations. Conversely, utility-based approaches leveraging LLM re-ranking often achieve superior…

We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…

Modern research in code generators for dense linear algebra computations has shown the ability to produce optimized code with a performance which compares and often exceeds the one of state-of-the-art implementations by domain experts.…

Normal basis is used in many applications because of the efficiency of the implementation. However, most space complexity reduction techniques for binary field multiplier are applicable for only optimal normal basis or Gaussian normal basis…

The level of abstraction at which application experts reason about linear algebra computations and the level of abstraction used by developers of high-performance numerical linear algebra libraries do not match. The former is conveniently…

Dense linear algebra kernels are critical for wireless applications, and the oncoming proliferation of 5G only amplifies their importance. Many such matrix algorithms are inductive, and exhibit ample amounts of fine-grain ordered…

Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…

Network pruning can reduce the computation cost of deep neural network (DNN) models. However, sparse models often produce randomly-distributed weights to maintain accuracy, leading to irregular computations. Consequently, unstructured…

Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…

Matrix multiplication computation acceleration has been a research hotspot across various domains. Due to the characteristics of some applications, approximate matrix multiplication can achieve significant performance improvements without…

Matrix factorization (MF) can extract the low-rank features and integrate the information of the data manifold distribution from high-dimensional data, which can consider the nonlinear neighbourhood information. Thus, MF has drawn wide…