Related papers: Approximate Weighted $CR$ Coded Matrix Multiplicat…
Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…
The most popular method for computing the matrix logarithm is a combination of the inverse scaling and squaring method in conjunction with a Pad\'e approximation, sometimes accompanied by the Schur decomposition. The main computational…
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…
Parameter Recombination (PR) methods aim to efficiently compose the weights of a neural network for applications like Parameter-Efficient FineTuning (PEFT) and Model Compression (MC), among others. Most methods typically focus on one…
The problem of distributed matrix multiplication with straggler tolerance over finite fields is considered, focusing on field sizes for which previous solutions were not applicable (for instance, the field of two elements). We employ…
The modular composite representation (MCR) is a computing model that represents information with high-dimensional integer vectors using modular arithmetic. Originally proposed as a generalization of the binary spatter code model, it aims to…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
Supporting multiple partial computations efficiently at each of the workers is a keystone in distributed coded computing in order to speed up computations and to fully exploit the resources of heterogeneous workers in terms of…
Herein we explore a dual tree algorithm for matrix multiplication of $A\in \mathbb{R}^{M\times D}$ and $B\in\mathbb{R}^{D\times N}$, very narrowly effective if the normalized rows of $A$ and columns of $B$, treated as vectors in…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded…
In cloud computing systems slow processing nodes, often referred to as "stragglers", can significantly extend the computation time. Recent results have shown that error correction coding can be used to reduce the effect of stragglers. In…
The current BigData era routinely requires the processing of large scale data on massive distributed computing clusters. Such large scale clusters often suffer from the problem of "stragglers", which are defined as slow or failed nodes. The…
Many useful tasks in data science and machine learning applications can be written as simple variations of matrix multiplication. However, users have difficulty performing such tasks as existing matrix/vector libraries support only a…
Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected…
Distributed matrix computations over large clusters can suffer from the problem of slow or failed worker nodes (called stragglers) which can dominate the overall job execution time. Coded computation utilizes concepts from erasure coding to…
Modern computationally-heavy applications are often time-sensitive, demanding distributed strategies to accelerate them. On the other hand, distributed computing suffers from the bottleneck of slow workers in practice. Distributed coded…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Coded caching is a promising technique to smooth out network traffic by storing part of the library content at the users' local caches. The seminal work on coded caching for single file retrieval by Maddah-Ali and Niesen (MAN) showed the…
Tensor operations, such as matrix multiplication, are central to large-scale machine learning applications. For user-driven tasks these operations can be carried out on a distributed computing platform with a master server at the user side…