Related papers: Cardinality Sparsity: Applications in Matrix-Matri…

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space, while approximately preserving their pairwise distances. It has emerged as a powerful tool in various data processing tasks and has…

Tensor accelerators have gained popularity because they provide a cheap and efficient solution for speeding up computational-expensive tasks in Deep Learning and, more recently, in other Scientific Computing applications. However, since…

Diffusion models are one of the key architectures of generative AI. Their main drawback, however, is the computational costs. This study indicates that the concept of sparsity, well known especially in statistics, can provide a pathway to…

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…

Dimension reduction and data quantization are two important methods for reducing data complexity. In the paper, we study the methodology of first reducing data dimension by random projection and then quantizing the projections to ternary or…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

Many classification approaches first represent a test sample using the training samples of all the classes. This collaborative representation is then used to label the test sample. It was a common belief that sparseness of the…

Minimizing a sum of simple submodular functions of limited support is a special case of general submodular function minimization that has seen numerous applications in machine learning. We develop fast techniques for instances where…

In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…

Spectral functions of large matrices contains important structural information about the underlying data, and is thus becoming increasingly important. Many times, large matrices representing real-world data are \emph{sparse} or \emph{doubly…

Sparse data structures are commonly used in neural networks to reduce the memory footprint. These data structures are compact but cause irregularities such as random memory accesses, which prevent efficient use of the memory hierarchy. GPUs…

We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…

Scientific workloads have traditionally exploited high levels of sparsity to accelerate computation and reduce memory requirements. While deep neural networks can be made sparse, achieving practical speedups on GPUs is difficult because…

Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…

Existing approaches to distributed matrix computations involve allocating coded combinations of submatrices to worker nodes, to build resilience to stragglers and/or enhance privacy. In this study, we consider the challenge of preserving…

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…

Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…

In Artificial Intelligence, interpreting the results of a Machine Learning technique often termed as a black box is a difficult task. A counterfactual explanation of a particular "black box" attempts to find the smallest change to the input…