Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2205.05339

An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods

Farah Benmouhoub·Pierre-Loïc Garoche·Matthieu Martel
View original source ↗Read source document ↗Export metadata ↓

Abstract

Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of computation, used everywhere, is the sum of a sequence of numbers. This sum is subject to many numerical errors in floating-point arithmetic. To alleviate this issue, we have introduced a new parallel algorithm for summing a sequence of floating-point numbers. This algorithm which scales up easily with the number of processors, adds numbers of the same exponents first. In this article, our main contribution is an extensive analysis of its efficiency with respect to several properties: accuracy, convergence and reproducibility. In order to show the usefulness of our algorithm, we have chosen a set of representative numerical methods which are Simpson, Jacobi, LU factorization and the Iterated power method.

Explore related subjects

cs.CLcs.FL

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Farah Benmouhoub, Pierre-Loïc Garoche, Matthieu Martel. 2022-05-11. An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods. https://doi.org/10.1007/978-3-030-95561-8_10

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

LiSeCo: Linear Semantic Control for Language Generation

The prevalence of Large Language Models (LLMs) in critical applications highlights the need for controlled language generation methods that are both computationally efficient and enjoy performance guarantees. To address this need, we use a common model of concept semantics as linearly represented in an LLM's latent space. In particular, we take the view that natural language generation traces a trajectory in this continuous semantic space, realized by the language model's hidden activations. This view permits a control-theoretic treatment of text generation in latent space, in which we propose Linear Semantic Control (LiSeCo), a lightweight, gradient-free intervention that dynamically steers trajectories away from regions corresponding to undesired meanings. In particular, we propose to directly intervene, in an online fashion, the activations of the token that is being generated in embedding space. Crucially, LiSeCo does not simply steer activations towards a desirable region. Instead, it relies on classical techniques from control theory to precisely control activations in a context-dependent way, and guarantees that they are brought into a specific pre-defined region of embedding space that corresponds to allowed semantics. The intervention is computed in closed form according to an optimal controller formulation, minimally impacting generation time. This control of the activations in embedding space allows for fine-grained steering of attributes of the generated sequence. We demonstrate that our approach is effective on different tasks -- toxicity, sentiment, and language (English/Spanish) steering -- while maintaining text quality.

cs.CL↗
arXiv2026

VMMU: A Vietnamese Multitask Multimodal Understanding and Reasoning Benchmark

We introduce VMMU, a Vietnamese Multitask Multimodal Understanding and Reasoning Benchmark designed to evaluate how vision-language models (VLMs) interpret and reason over visual and textual information beyond English. VMMU consists of 2.5k multimodal questions across 7 tasks, covering a diverse range of problem contexts, including STEM problem solving, data interpretation, rule-governed visual reasoning, and abstract visual reasoning. All questions require genuine multimodal integration, rather than reliance on text-only cues or OCR-based shortcuts. We evaluate a diverse set of state-of-the-art proprietary and open-source VLMs on VMMU. Despite strong Vietnamese OCR performance, proprietary models achieve only 66% mean accuracy. Further analysis shows that the primary source of failure is not OCR, but instead multimodal grounding and reasoning over text and visual evidence. Code and data are available at https://vmmu-bench.github.io/

cs.CL↗
arXiv2026

RapidUn: Influence-Driven Parameter Reweighting for Efficient Large Language Model Unlearning

Machine unlearning for large language models (LLMs) remains challenging because full retraining is costly, while approximate methods often struggle to remove targeted behaviors without degrading retained utility, especially under limited post-deployment supervision. We consider a practical PEFT setting for targeted behavioral contamination removal with a small forget set, a limited retain buffer, and LoRA-only updates, and propose RapidUn, an influence-guided framework that converts cross-sample influence estimates into fixed sample-specific weights for weighted LoRA unlearning. Across Llama-3-8B on Dolly-15k and Alpaca-57k, with cross-model validation on Mistral-7B + Dolly-15k, RapidUn achieves lower seen-trigger and OOD-trigger-family ASR than Fisher, GA, and LoReUn while maintaining competitive clean utility. On Llama-3-8B + Alpaca-57k, it achieves a 77x wall-clock speedup over the clean-corpus LoRA retraining reference. Complementary TOFU, semantic LLM-judge, and IFEval evaluations further support the effectiveness of influence-guided sample reweighting beyond the controlled trigger benchmark.

cs.CL↗