Related papers: PALMA: A Lightweight Tropical Algebra Library for …

Large language models (LLMs) have transformed the way we think about language understanding and generation, enthralling both researchers and developers. However, deploying LLMs for inference has been a significant challenge due to their…

In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide…

Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting.…

TURTLE is a C library providing utilities allowing to navigate through a topography described by a Digital Elevation Model (DEM). The library has been primarily designed for the Monte Carlo transport of particles scattering over medium to…

In parallel with the continuously increasing parameter space dimensionality, search and optimization algorithms should support distributed parameter evaluations to reduce cumulative runtime. Intel's neuromorphic optimization library,…

Sparse matrix multiplication operators (i.e., SpMM and SDDMM) are widely used in deep learning and scientific computing. Modern accelerators are commonly equipped with Tensor Core Units (TCUs) and CUDA cores to accelerate sparse operators.…

This work introduces TapirXLA, a replacement for TensorFlow's XLA compiler that embeds recursive fork-join parallelism into XLA's low-level representation of code. Machine-learning applications rely on efficient parallel processing to…

Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…

Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in…

We propose NAMA (Newton-type Alternating Minimization Algorithm) for solving structured nonsmooth convex optimization problems where the sum of two functions is to be minimized, one being strongly convex and the other composed with a linear…

This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software…

We consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input--output pairs of an unknown…

On-device inference offers privacy, offline use, and instant response, but consumer hardware restricts large language models (LLMs) to low throughput and capability. To overcome this challenge, we present prima.cpp, a distributed on-device…

The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for…

Fast algorithms for the computation of $N$-body problems can be broadly classified into mesh-based interpolation methods, and hierarchical or multiresolution methods. To this last class belongs the well-known fast multipole method (FMM),…

The growth of tropical geometry has generated significant interest in the tropical semiring in the past decade. However, there are other semirings in tropical algebra that provide more information, such as the symmetrized (max, +),…

Memristor crossbars are circuits capable of performing analog matrix-vector multiplications, overcoming the fundamental energy efficiency limitations of digital logic. They have been shown to be effective in special-purpose accelerators for…

A new approach to solving a class of rankconstrained semi-definite programming (SDP) problems, which appear in many signal processing applications such as transmit beamspace design in multiple-input multiple-output (MIMO) radar, downlink…

Stencil computation is one of the fundamental computing patterns in many application domains such as scientific computing and image processing. While there are promising studies that accelerate stencils on FPGAs, there lacks an automated…

Large language models (LLMs) have achieved remarkable success across various NLP tasks with a focus on English due to English-centric pre-training and limited multilingual data. In this work, we focus on the problem of translation, and…