Related papers: Fast Matrix Multiplication via Ternary Meta Flip G…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
Fast matrix multiplication algorithms may be useful, provided that their running time is good in practice. Particularly, the leading coefficient of their arithmetic complexity needs to be small. Many sub-cubic algorithms have large leading…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance…
Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…
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…
Fast matrix-by-matrix multiplication (hereafter MM) is a highly recognized research subject. The record upper bound 3 of 1968 on the exponent of the complexity MM decreased below 2.38 by 1987, applies to celebrated problems in many areas of…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras. In subsequent work with Kleinberg and Szegedy, they connected this to the search for…
Scaling up the sparse matrix-vector multiplication kernel on modern Graphics Processing Units (GPU) has been at the heart of numerous studies in both academia and industry. In this article we present a novel non-parametric, self-tunable,…
As the ratio between the rate of computation and rate with which data can be retrieved from various layers of memory continues to deteriorate, a question arises: Will the current best algorithms for computing matrix-matrix multiplication on…
We show how to construct highly symmetric algorithms for matrix multiplication. In particular, we consider algorithms which decompose the matrix multiplication tensor into a sum of rank-1 tensors, where the decomposition itself consists of…
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…
Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously…
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…