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In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…

最优化与控制 · 数学 2023-02-21 Andries Steenkamp

Initially introduced as a machine translation model, the Transformer architecture has now become the foundation for modern deep learning architecture, with applications in a wide range of fields, from computer vision to natural language…

计算与语言 · 计算机科学 2024-06-21 Martin Courtois , Malte Ostendorff , Leonhard Hennig , Georg Rehm

Fill-ins are new nonzero elements in the summation of the upper and lower triangular factors generated during LU factorization. For large sparse matrices, they will increase the memory usage and computational time, and be reduced through…

机器学习 · 计算机科学 2025-11-13 Ziwei Li , Shuzi Niu , Tao Yuan , Huiyuan Li , Wenjia Wu

As an essential ingredient of modern deep learning, attention mechanism, especially self-attention, plays a vital role in the global correlation discovery. However, is hand-crafted attention irreplaceable when modeling the global context?…

计算机视觉与模式识别 · 计算机科学 2021-12-30 Zhengyang Geng , Meng-Hao Guo , Hongxu Chen , Xia Li , Ke Wei , Zhouchen Lin

Transformer has achieved great success in NLP. However, the quadratic complexity of the self-attention mechanism in Transformer makes it inefficient in handling long sequences. Many existing works explore to accelerate Transformers by…

计算与语言 · 计算机科学 2021-09-03 Chuhan Wu , Fangzhao Wu , Tao Qi , Binxing Jiao , Daxin Jiang , Yongfeng Huang , Xing Xie

The attention mechanism of a transformer has a quadratic complexity, leading to high inference costs and latency for long sequences. However, attention matrices are mostly sparse, which implies that many entries may be omitted from…

机器学习 · 计算机科学 2025-11-25 Jeffrey Willette , Heejun Lee , Sung Ju Hwang

The self-attention mechanism, at the heart of the Transformer model, is able to effectively model pairwise interactions between tokens. However, numerous recent works have shown that it is unable to perform basic tasks involving detecting…

机器学习 · 计算机科学 2026-02-03 Sayak Chakrabarti , Toniann Pitassi , Josh Alman

The success of Transformer language models is widely credited to their dot-product attention mechanism, which interweaves a set of key design principles: mixing information across positions (enabling multi-token interactions),…

计算与语言 · 计算机科学 2025-10-14 Huiyin Xue , Nafise Sadat Moosavi , Nikolaos Aletras

Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To…

数值分析 · 数学 2025-02-06 Jonas Kusch , Steffen Schotthöfer , Alexandra Walter

Transformer models have achieved state-of-the-art results in a wide range of NLP tasks including summarization. Training and inference using large transformer models can be computationally expensive. Previous work has focused on one…

计算与语言 · 计算机科学 2021-09-10 Potsawee Manakul , Mark J. F. Gales

Inference on large language models (LLMs) can be expensive in terms of the compute and memory costs involved, especially when long sequence lengths are used. In particular, the self-attention mechanism used in LLM inference contributes…

机器学习 · 计算机科学 2024-11-11 Prajwal Singhania , Siddharth Singh , Shwai He , Soheil Feizi , Abhinav Bhatele

The quadratic computation complexity of self-attention has been a persistent challenge when applying Transformer models to vision tasks. Linear attention, on the other hand, offers a much more efficient alternative with its linear…

计算机视觉与模式识别 · 计算机科学 2023-09-04 Dongchen Han , Xuran Pan , Yizeng Han , Shiji Song , Gao Huang

Large Language Models (LLMs) have become the central paradigm in artificial intelligence, yet the core computational primitive of attention has remained structurally unchanged. Local Linear Attention (LLA) is an attention mechanism derived…

机器学习 · 计算机科学 2026-05-29 Yifei Zuo , Dhruv Pai , Zhichen Zeng , Alec Dewulf , Shuming Hu , Zhaoran Wang

Standard sequence mixing layers used in language models struggle to balance efficiency and performance. Self-attention performs well on long context tasks but has expensive quadratic compute and linear memory costs, while linear attention…

机器学习 · 计算机科学 2026-05-18 Nick Alonso , Tomas Figliolia , Beren Millidge

Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences,…

机器学习 · 计算机科学 2020-06-16 Sinong Wang , Belinda Z. Li , Madian Khabsa , Han Fang , Hao Ma

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

机器学习 · 计算机科学 2014-10-24 Jingbo Shang , Tianqi Chen , Hang Li , Zhengdong Lu , Yong Yu

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

机器学习 · 统计学 2017-11-15 Arthur Mensch , Julien Mairal , Bertrand Thirion , Gaël Varoquaux

Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…

信息检索 · 计算机科学 2026-03-26 Yining Wu , Shengyu Duan , Gaole Sai , Chenhong Cao , Guobing Zou

Pairwise dot product-based attention allows Transformers to exchange information between tokens in an input-dependent way, and is key to their success across diverse applications in language and vision. However, a typical Transformer model…

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…

最优化与控制 · 数学 2015-07-01 Duy-Khuong Nguyen , Tu-Bao Ho