Related papers: Random Sampling for Distributed Coded Matrix Multi…
Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…
Distributed algorithms are often beset by the straggler effect, where the slowest compute nodes in the system dictate the overall running time. Coding-theoretic techniques have been recently proposed to mitigate stragglers via algorithmic…
We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show how to construct polynomial schemes for the outer…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks.…
The overall execution time of distributed matrix computations is often dominated by slow worker nodes (stragglers) within the clusters. Recently, different coding techniques have been utilized to mitigate the effect of stragglers where…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their…
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…
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…
We consider sketched approximate matrix multiplication and ridge regression in the novel setting of localized sketching, where at any given point, only part of the data matrix is available. This corresponds to a block diagonal structure on…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
We consider the problem of designing a coding scheme that allows both sparsity and privacy for distributed matrix-vector multiplication. Perfect information-theoretic privacy requires encoding the input sparse matrices into matrices…
Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Artificial intelligence workloads, especially transformer models, exhibit emergent sparsity in which computations perform selective sparse access to dense data. The workloads are inefficient on hardware designed for dense computations and…
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…
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…
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…
Matrix decompositions are fundamental tools in the area of applied mathematics, statistical computing, and machine learning. In particular, low-rank matrix decompositions are vital, and widely used for data analysis, dimensionality…