Related papers: Efficiently Parallelizable Strassen-Based Multipli…
In this paper, the author present a reliable symbolic computational algorithm for inverting a general comrade matrix by using parallel computing along with recursion. The computational cost of our algorithm is O(n^2). The algorithm is…
The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log 2 (7) $\approx$ 2.8074.…
We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…
The computational cost of transfer matrix methods for the Potts model is directly related to the problem of \textit{into how many ways can two adjacent blocks of a lattice be connected}. Answering this question leads to the generation of a…
Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix…
We present Exact Causal Attention (ECA), a Strassen-style algorithm that computes exact Causal Attention using 10\% fewer operations. ECA improves a special class of matrix multiplications where either one operand or the output matrix is…
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…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
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 form of parallel computing on classical computers that is based on matrix product states. The virtual parallelization is accomplished by representing bits with matrices and by evolving these matrices from an initial product…
To fully leverage the multi-task optimization paradigm for accelerating the solution of expensive scheduling problems, this study has effectively tackled three vital concerns. The primary issue is identifying auxiliary tasks that closely…
Dataset distillation extracts a small set of synthetic training samples from a large dataset with the goal of achieving competitive performance on test data when trained on this sample. In this work, we tackle dataset distillation at its…
In this paper, we present several improvements in the parallelization of the in-place merge algorithm, which merges two contiguous sorted arrays into one with an O(T) space complexity (where T is the number of threads). The approach divides…
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…
We introduce a data distribution scheme for $\mathcal{H}$-matrices and a distributed-memory algorithm for $\mathcal{H}$-matrix-vector multiplication. Our data distribution scheme avoids an expensive $\Omega(P^2)$ scheduling procedure used…
The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…
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…
Asymmetric Tensor PCA (ATPCA) is a prototypical model for studying the trade-offs between sample complexity, computation, and memory. Existing algorithms for this problem typically require at least…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
We study matrix-matrix multiplication of two matrices, $A$ and $B$, each of size $n \times n$. This operation results in a matrix $C$ of size $n\times n$. Our goal is to produce $C$ as efficiently as possible given a cache: a 1-D limited…