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Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less…

This paper introduces Patched MOA (Mixture of Agents), an inference optimization technique that significantly enhances the performance of large language models (LLMs) across diverse software development tasks. We evaluate three inference…

软件工程 · 计算机科学 2025-05-01 Asankhaya Sharma

This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear systems. By employing…

数值分析 · 数学 2025-03-24 Jifeng Ge , Juan Zhang

Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is…

数值分析 · 计算机科学 2015-12-07 Ran Wang , Xinrui He

Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models…

While large language models (LLMs) demonstrate remarkable success in multilingual translation, their internal core translation mechanisms, even at the fundamental word level, remain insufficiently understood. To address this critical gap,…

计算与语言 · 计算机科学 2026-01-16 Hongbin Zhang , Kehai Chen , Xuefeng Bai , Xiucheng Li , Yang Xiang , Min Zhang

Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…

数值分析 · 数学 2019-12-11 Fredrik Dahlqvist , Rocco Salvia , George A Constantinides

Deep transformer models have pushed performance on NLP tasks to new limits, suggesting sophisticated treatment of complex linguistic inputs, such as phrases. However, we have limited understanding of how these models handle representation…

计算与语言 · 计算机科学 2020-10-15 Lang Yu , Allyson Ettinger

In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…

硬件体系结构 · 计算机科学 2021-01-29 Hamzah Abdel-Aziz , Ali Shafiee , Jong Hoon Shin , Ardavan Pedram , Joseph H. Hassoun

We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…

数值分析 · 计算机科学 2007-06-13 Peter Kornerup , Vincent Lefèvre , Jean-Michel Muller

While large language models (LLMs) appear to be increasingly capable of solving compositional tasks, it is an open question whether they do so using compositional mechanisms. In this work, we investigate how feedforward LLMs solve two-hop…

计算与语言 · 计算机科学 2026-05-11 Apoorv Khandelwal , Ellie Pavlick

The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…

数值分析 · 计算机科学 2012-01-31 Glauco Masotti

Transformer-based language models spread FLOPs uniformly across input sequences. In this work we demonstrate that transformers can instead learn to dynamically allocate FLOPs (or compute) to specific positions in a sequence, optimising the…

机器学习 · 计算机科学 2024-04-04 David Raposo , Sam Ritter , Blake Richards , Timothy Lillicrap , Peter Conway Humphreys , Adam Santoro

Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…

数值分析 · 数学 2026-02-05 Erin Claire Carson

The use of reduced and mixed precision computing has gained increasing attention in high-performance computing (HPC) as a means to improve computational efficiency, particularly on modern hardware architectures like GPUs. In this work, we…

计算工程、金融与科学 · 计算机科学 2025-05-28 Bálint Siklósi , Pushpender K. Sharma , David J. Lusher , István Z. Reguly , Neil D. Sandham

Answering multi-hop reasoning questions requires retrieving and synthesizing information from diverse sources. Large Language Models (LLMs) struggle to perform such reasoning consistently. Here we propose an approach to pinpoint and rectify…

计算与语言 · 计算机科学 2024-03-01 Mansi Sakarvadia , Aswathy Ajith , Arham Khan , Daniel Grzenda , Nathaniel Hudson , André Bauer , Kyle Chard , Ian Foster

Transformer based large language models have achieved tremendous success. However, the significant memory and computational costs incurred during the inference process make it challenging to deploy large models on resource-constrained…

计算与语言 · 计算机科学 2024-02-16 Wenxiao Wang , Wei Chen , Yicong Luo , Yongliu Long , Zhengkai Lin , Liye Zhang , Binbin Lin , Deng Cai , Xiaofei He

The internal structure and operation mechanism of large-scale language models are analyzed theoretically, especially how Transformer and its derivative architectures can restrict computing efficiency while capturing long-term dependencies.…

机器学习 · 计算机科学 2024-05-21 Taiyuan Mei , Yun Zi , Xiaohan Cheng , Zijun Gao , Qi Wang , Haowei Yang

Neural machine translation (NMT) models are typically trained with fixed-size input and output vocabularies, which creates an important bottleneck on their accuracy and generalization capability. As a solution, various studies proposed…

计算与语言 · 计算机科学 2018-05-08 Duygu Ataman , Marcello Federico

We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the precision. We present a systematic recurrence for a martingale…

数值分析 · 数学 2022-03-31 Eric Hallman , Ilse C. F. Ipsen