Related papers: Fault-Tolerant Strassen-Like Matrix Multiplication

Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum…

Laderman discovered a scheme for computing the product of two 3x3 matrices using only 23 multiplications in 1976. Since then, some more such schemes were proposed, but it remains open how many there are and whether there exist schemes with…

The growth of big data in domains such as Earth Sciences, Social Networks, Physical Sciences, etc. has lead to an immense need for efficient and scalable linear algebra operations, e.g. Matrix inversion. Existing methods for efficient and…

Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf…

High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a {\em…

An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary ($\mathbb{Z}_2$), modular ternary ($\mathbb{Z}_3$) and…

Bregman parallel direction method of multipliers (BPDMM) efficiently solves distributed optimization over a network, which arises in a wide spectrum of collaborative multi-agent learning applications. In this paper, we generalize BPDMM to…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

In this paper we consider symmetric, positive semidefinite (SPSD) matrix $A$ and present two algorithms for computing the $p$-Schatten norm $\|A\|_p$. The first algorithm works for any SPSD matrix $A$. The second algorithm works for…

This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…

Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…

Conventional GPU implementations of Strassen's algorithm (Strassen) typically rely on the existing high-performance matrix multiplication (GEMM), trading space for time. As a result, such approaches can only achieve practical speedup for…

This paper proposes using a method named Double Score Matching (DSM) to do mass-imputation and presents an application to make inferences with a nonprobability sample. DSM is a $k$-Nearest Neighbors algorithm that uses two balance scores…

Inexpensive cloud services, such as serverless computing, are often vulnerable to straggling nodes that increase end-to-end latency for distributed computation. We propose and implement simple yet principled approaches for straggler…

Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…

We consider the problem of developing an efficient multi-threaded implementation of the matrix-vector multiplication algorithm for sparse matrices with structural symmetry. Matrices are stored using the compressed sparse row-column format…

With increasing usage of fingerprints as an important biometric data, the need to compress the large fingerprint databases has become essential. The most recommended compression algorithm, even by standards, is JPEG2K. But at high…

Graph neural networks (GNNs) are emerging as a powerful technique for modeling graph structures. Due to the sparsity of real-world graph data, GNN performance is limited by extensive sparse matrix multiplication (SpMM) operations involved…

Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…

We study the problem of multiplying two bit matrices with entries either over the Boolean algebra $(0,1,\vee,\wedge)$ or over the binary field $(0,1,+,\cdot)$. We engineer high-performance open-source algorithm implementations for…