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We give an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$ algorithm for multiplying two $N$-bit integers that improves the $O(N\cdot \log N\cdot \log\log N)$ algorithm by Sch\"{o}nhage-Strassen. Both these algorithms use modular arithmetic.…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
Automatic machine learning is an important problem in the forefront of machine learning. The strongest AutoML systems are based on neural networks, evolutionary algorithms, and Bayesian optimization. Recently AlphaD3M reached…
The Adapted Modular Number System (AMNS) is a sytem of representation of integers to speed up arithmetic operations modulo a prime p. Such a system can be defined by a tuple (p, n, {\gamma}, {\rho}, E) where E is in Z[X]. In [13] conditions…
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…
Current architectures are now equipped with matrix computation units designed to enhance AI and high-performance computing applications. Within these architectures, two fundamental instruction types are matrix multiplication and vector…
Word-level verification of arithmetic circuits with large operands typically relies on arbitrary-precision arithmetic, which can lead to significant computational overhead as word sizes grow. In this paper, we present a hybrid algebraic…
Complex vector light fields, classically entangled in polarization and phase, have become ubiquitous in a wide variety of research fields. This has triggered the demonstration of a wide variety of generation techniques. Of particular…
Multiple-precision floating-point branch-free algorithms can significantly accelerate multi-component arithmetic implemented by combining hardware-based binary64 and binary32, particularly for triple- and quadruple-precision computations.…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
Particle-In-Cell (PIC) codes are broadly applied to the kinetic simulation of plasmas, from laser-matter interaction to astrophysics. Their heavy simulation cost can be mitigated by using the Single Instruction Multiple Data (SIMD)…
Large neural network models are commonly trained through a combination of advanced parallelism strategies in a single program, multiple data (SPMD) paradigm. For example, training large transformer models requires combining data, model, and…
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…
Given n positive integers, the Modular Subset Sum problem asks if a subset adds up to a given target t modulo a given integer m. This is a natural generalization of the Subset Sum problem (where m=+\infty) with ties to additive…
Virtual Reality (VR) has emerged as a powerful tool for workforce training, offering immersive, interactive, and risk-free environments that enhance skill acquisition, decision-making, and confidence. Despite its advantages, developing VR…
The complexity of combustion simulations demands the latest high-performance computing tools to accelerate its time-to-solution results. A current trend on HPC systems is the utilization of CPUs with SIMD or vector extensions to exploit…
We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…
Scalable Vector Graphics (SVG) is a popular format on the web and in the design industry. However, despite the great strides made in generative modeling, SVG has remained underexplored due to the discrete and complex nature of such data. We…
Although multigrid is asymptotically optimal for solving many important partial differential equations, its efficiency relies heavily on the careful selection of the individual algorithmic components. In contrast to recent approaches that…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…