Related papers: Multiword matrix multiplication over large finite …
Word-embeddings are vital components of Natural Language Processing (NLP) models and have been extensively explored. However, they consume a lot of memory which poses a challenge for edge deployment. Embedding matrices, typically, contain…
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…
In this paper, we report the results obtained from the acceleration of multi-binary64-type multiple precision matrix multiplication with AVX2. We target double-double (DD), triple-double (TD), and quad-double (QD) precision arithmetic…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
For digital over-the-air computation, the ChannelComp framework has recently been proposed to design digital modulations to compute any arbitrary function over a multiple access channel. To reduce modulation design complexity while…
Matrix-vector multiplication forms the basis of many iterative solution algorithms and as such is an important algorithm also for hierarchical matrices which are used to represent dense data in an optimized form by applying low-rank…
In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to small matrix multiplications. Here, rank of the tensors is…
Binary quantization approaches, which replace weight matrices with binary matrices and substitute costly multiplications with cheaper additions, offer a computationally efficient approach to address the increasing computational and storage…
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…
Matrix multiplication is a fundamental kernel in large-scale artificial intelligence and scientific computing, but its performance on conventional electronic accelerators is increasingly constrained by memory bandwidth and energy…
We show how to improve the efficiency of the computation of fast Fourier transforms over F_p where p is a word-sized prime. Our main technique is optimisation of the basic arithmetic, in effect decreasing the total number of reductions…
Bit-vector formulas arising from hardware verification problems often contain word-level arithmetic operations. Empirical evidence shows that state-of-the-art SMT solvers are not very efficient at reasoning about bit-vector formulas with…
Integral linear systems $Ax=b$ with matrices $A$, $b$ and solutions $x$ are also required to be in integers, can be solved using invariant factors of $A$ (by computing the Smith Canonical Form of $A$). This paper explores a new problem…
Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem of counting the number of integer points inside $P$, assuming that $P$ is $\Delta$-modular, where the polytope $P$ is called $\Delta$-modular if all the rank…
We propose a more accurate variant of an algorithm for multiplying 4x4 matrices using 48 multiplications over any ring containing an inverse of 2. This algorithm has an error bound exponent of only log 4 $\gamma$$\infty$,2 $\approx$ 2.386.…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…
The Strassen algorithm and Winograd's variant accelerate matrix multiplication by using fewer arithmetic operations than standard matrix multiplication. Although many papers have been published to accelerate single- as well as…