Related papers: Solidfmm: A highly optimised library of operations…
Large language models (LLMs) have the potential to revolutionize how we design and implement compilers and code translation tools. However, existing LLMs struggle to handle long and complex programs. We introduce LEGO-Compiler, a novel…
As distributed optimization scales to meet the demands of Large Language Model (LLM) training, hardware failures become increasingly non-negligible. Existing fault-tolerant training methods often introduce significant computational or…
Recent advances in large language models (LLMs) have significantly accelerated progress in code translation, enabling more accurate and efficient transformation across programming languages. While originally developed for natural language…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…
We introduce new reliability definitions for bit and check nodes. Maximizing global reliability, which is the sum reliability of all bit nodes, is shown to be equivalent to minimizing a decoding metric which is closely related to the…
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic…
We present Matrix Distributed Processing, a C++ library for fast development of efficient parallel algorithms. MDP is based on MPI and consists of a collection of C++ classes and functions such as lattice, site and field. Once an algorithm…
Fast Multipole Methods (FMM) are a fundamental operation for the simulation of many physical problems. The high performance design of such methods usually requires to carefully tune the algorithm for both the targeted physics and the…
We introduce Adapters, an open-source library that unifies parameter-efficient and modular transfer learning in large language models. By integrating 10 diverse adapter methods into a unified interface, Adapters offers ease of use and…
Optical Flow algorithms are of high importance for many applications. Recently, the Flow Field algorithm and its modifications have shown remarkable results, as they have been evaluated with top accuracy on different data sets. In our…
Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models…
In this paper, we present Ginkgo, a modern C++ math library for scientific high performance computing. While classical linear algebra libraries act on matrix and vector objects, Ginkgo's design principle abstracts all functionality as…
A quick review of the features of FermiQCD, a C++ library for fast development of parallel Lattice QCD applications. FermiQCD is fully Object Oriented and is based on MPI but, it required no previsius knowledge of parallel programming. It…
The largenet2 C++ library provides an infrastructure for the simulation of large dynamic and adaptive networks with discrete node and link states. The library is released as free software. It is available at…
We present an easily accessible, object oriented code (written exclusively in Matlab) for adaptive finite element simulations in 2D. It features various refinement routines for triangular meshes as well as fully vectorized FEM ansatz spaces…
A fast multipole method (FMM) for asymptotically smooth kernel functions (1/r, 1/r^4, Gauss and Stokes kernels, radial basis functions, etc.) based on a Chebyshev interpolation scheme has been introduced in [Fong et al., 2009]. The method…
The Fast Multipole Method (FMM) is an efficient numerical algorithm for computation of long-ranged forces in $N$-body problems within gravitational and electrostatic fields. This method utilizes multipole expansions of the Green's function…