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Tensor networks are a class of algorithms aimed at reducing the computational complexity of high-dimensional problems. They are used in an increasing number of applications, from quantum simulations to machine learning. Exploiting data…

Numerical Analysis · Mathematics 2024-10-25 Melven Röhrig-Zöllner , Manuel Joey Becklas , Jonas Thies , Achim Basermann

Large Language Model training with 8-bit floating point (FP8) formats promises significant efficiency improvements, but reduced numerical precision makes training challenging. It is currently possible to train in FP8 only if one is willing…

Machine Learning · Computer Science 2025-06-06 Saaketh Narayan , Abhay Gupta , Mansheej Paul , Davis Blalock

Matrix multiplication is the bedrock in Deep Learning inference application. When it comes to hardware acceleration on edge computing devices, matrix multiplication often takes up a great majority of the time. To achieve better performance…

Machine Learning · Computer Science 2021-10-12 Yuyang Zhang , Dik Hin Leung , Min Guo , Yijia Xiao , Haoyue Liu , Yunfei Li , Jiyuan Zhang , Guan Wang , Zhen Chen

The GEneral Matrix Multiplication (GEMM) is one of the essential algorithms in scientific computing. Single-thread GEMM implementations are well-optimised with techniques like blocking and autotuning. However, due to the complexity of…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-15 Yufan Xia , Marco De La Pierre , Amanda S. Barnard , Giuseppe Maria Junior Barca

Preconditioned adaptive methods have gained significant attention for training deep neural networks, as they capture rich curvature information of the loss landscape. The central challenge in this field lies in balancing preconditioning…

Machine Learning · Computer Science 2026-05-14 Shenyang Deng , Zhuoli Ouyang , Tianyu Pang , Zihang Liu , Ruochen Jin , Shuhua Yu , Yaoqing Yang

With the fast growth of parameter size, it becomes increasingly challenging to deploy large generative models as they typically require large GPU memory consumption and massive computation. Unstructured model pruning has been a common…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-09-20 Haojun Xia , Zhen Zheng , Yuchao Li , Donglin Zhuang , Zhongzhu Zhou , Xiafei Qiu , Yong Li , Wei Lin , Shuaiwen Leon Song

In this paper, we propose a simple yet effective method to stabilize extremely deep Transformers. Specifically, we introduce a new normalization function (DeepNorm) to modify the residual connection in Transformer, accompanying with…

Computation and Language · Computer Science 2022-03-02 Hongyu Wang , Shuming Ma , Li Dong , Shaohan Huang , Dongdong Zhang , Furu Wei

Kernel matrix-vector multiplication (KMVM) is a foundational operation in machine learning and scientific computing. However, as KMVM tends to scale quadratically in both memory and time, applications are often limited by these…

Numerical Analysis · Mathematics 2025-02-25 Robert Hu , Siu Lun Chau , Dino Sejdinovic , Joan Alexis Glaunès

Batch normalization (BN) has been very effective for deep learning and is widely used. However, when training with small minibatches, models using BN exhibit a significant degradation in performance. In this paper we study this peculiar…

Computer Vision and Pattern Recognition · Computer Science 2019-08-15 Saurabh Singh , Abhinav Shrivastava

Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…

Mathematical Software · Computer Science 2017-10-06 Tomonori Kouya

Current quantization methods for LLMs predominantly rely on block-wise structures to maintain efficiency, often at the cost of representational flexibility. In this work, we demonstrate that element-wise quantization can be made as…

Machine Learning · Computer Science 2026-02-02 Pingzhi Tang , Ruijie Zhou , Fanxu Meng , Wenjie Pei , Muhan Zhang

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse…

Machine Learning · Computer Science 2019-08-27 Tim Dettmers , Luke Zettlemoyer

The dedicated memory of hardware accelerators can be insufficient to store all weights and/or intermediate states of large deep learning models. Although model parallelism is a viable approach to reduce the memory pressure issue,…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-08-27 Mohamed Wahib , Haoyu Zhang , Truong Thao Nguyen , Aleksandr Drozd , Jens Domke , Lingqi Zhang , Ryousei Takano , Satoshi Matsuoka

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

Numerical Analysis · Computer Science 2016-05-02 Quanming Yao , James T. Kwok , Wenliang Zhong

Normalization layer constitutes an essential component in neural networks. In transformers, the predominantly used RMSNorm constrains vectors to a unit hypersphere, followed by dimension-wise rescaling through a learnable scaling…

Machine Learning · Computer Science 2026-02-12 Wenrui Cai , Defa Zhu , Qingjie Liu , Qiyang Min

Multimodal Large Language Models (MLLMs) are undergoing rapid progress and represent the frontier of AI development. However, their training and inference efficiency have emerged as a core bottleneck in making MLLMs more accessible and…

Modern meta-learning approaches for image classification rely on increasingly deep networks to achieve state-of-the-art performance, making batch normalization an essential component of meta-learning pipelines. However, the hierarchical…

Machine Learning · Statistics 2020-07-14 John Bronskill , Jonathan Gordon , James Requeima , Sebastian Nowozin , Richard E. Turner

Memristors enable the computation of matrix-vector multiplications (MVM) in memory and, therefore, show great potential in highly increasing the energy efficiency of deep neural network (DNN) inference accelerators. However, computations in…

Per-example gradient norms are a vital ingredient for estimating gradient noise scale (GNS) with minimal variance. Observing the tensor contractions required to compute them, we propose a method with minimal FLOPs in 3D or greater tensor…

Machine Learning · Computer Science 2024-11-05 Gavia Gray , Aman Tiwari , Shane Bergsma , Joel Hestness

State-of-the-art results in large language models (LLMs) often rely on scale, which becomes computationally expensive. This has sparked a research agenda to reduce these models' parameter counts and computational costs without significantly…

Computation and Language · Computer Science 2024-11-07 Xiuying Wei , Skander Moalla , Razvan Pascanu , Caglar Gulcehre