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Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the…

Machine Learning · Computer Science 2019-02-27 Ryan Spring , Anastasios Kyrillidis , Vijai Mohan , Anshumali Shrivastava

Effective training of today's large language models (LLMs) depends on large batches and long sequences for throughput and accuracy. To handle variable-length sequences on hardware accelerators, it is common practice to introduce padding…

Computation and Language · Computer Science 2022-10-07 Mario Michael Krell , Matej Kosec , Sergio P. Perez , Andrew Fitzgibbon

Mini-batch SGD with momentum is a fundamental algorithm for learning large predictive models. In this paper we develop a new analytic framework to analyze noise-averaged properties of mini-batch SGD for linear models at constant learning…

Machine Learning · Computer Science 2023-03-10 Maksim Velikanov , Denis Kuznedelev , Dmitry Yarotsky

Increasing the number of parameters in language models is a common strategy to enhance their performance. However, smaller language models remain valuable due to their lower operational costs. Despite their advantages, smaller models…

Computation and Language · Computer Science 2024-10-16 Richard Diehl Martinez , Pietro Lesci , Paula Buttery

Momentum methods were originally introduced for their superiority to stochastic gradient descent (SGD) in deterministic settings with convex objective functions. However, despite their widespread application to deep neural networks -- a…

Machine Learning · Computer Science 2025-09-22 Kento Imaizumi , Hideaki Iiduka

Large language models (LLMs) achieve strong reasoning performance by allocating substantial computation at inference time, often generating long and verbose reasoning traces. While recent work on efficient reasoning reduces this overhead…

Computation and Language · Computer Science 2026-04-28 Han Wang , Xiaodong Yu , Jialian Wu , Jiang Liu , Ximeng Sun , Mohit Bansal , Zicheng Liu

Large Language Models (LLMs) can perform many NLP tasks well, but fully fine-tuning them is expensive and requires a lot of memory. Parameter-Efficient Fine-Tuning (PEFT) methods such as LoRA reduce this cost by adding small low-rank…

Machine Learning · Computer Science 2025-12-19 Anshul Kumar , Gagan Raj Gupta , Manisha Chawla

Asynchronous stochastic gradient descent (ASGD) is a standard way to exploit heterogeneous compute resources in distributed learning: instead of forcing fast workers to wait for slow ones, the server updates the model whenever a gradient…

Machine Learning · Computer Science 2026-05-14 Ammar Mahran , Artavazd Maranjyan , Peter Richtárik

As models for nature language processing (NLP), computer vision (CV) and recommendation systems (RS) require surging computation, a large number of GPUs/TPUs are paralleled as a large batch (LB) to improve training throughput. However,…

Machine Learning · Computer Science 2023-09-26 Guo-qing Jiang , Jinlong Liu , Zixiang Ding , Lin Guo , Wei Lin

This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of…

Machine Learning · Computer Science 2019-12-16 Andrew Jacobsen , Matthew Schlegel , Cameron Linke , Thomas Degris , Adam White , Martha White

Full fine-tuning of Large Language Models (LLMs) is notoriously memory-intensive, primarily because conventional optimizers such as SGD or Adam assume access to exact gradients derived from cached activations. Existing solutions either…

Machine Learning · Computer Science 2025-10-28 Jing Yang , Kaitong Cai , Yijia Fan , Yufeng Yang , Keze Wang

New hardware can substantially increase the speed and efficiency of deep neural network training. To guide the development of future hardware architectures, it is pertinent to explore the hardware and machine learning properties of…

Machine Learning · Computer Science 2021-04-13 Atli Kosson , Vitaliy Chiley , Abhinav Venigalla , Joel Hestness , Urs Köster

Large language models (LLMs) have recently emerged as powerful tools for tackling many language-processing tasks. Despite their success, training and fine-tuning these models is still far too computationally and memory intensive. In this…

Computer Vision and Pattern Recognition · Computer Science 2024-10-22 Roy Miles , Pradyumna Reddy , Ismail Elezi , Jiankang Deng

Large language models (LLMs) have achieved remarkable performance across a wide range of tasks, but their increasing parameter sizes significantly slow down inference. Speculative decoding mitigates this issue by leveraging a smaller draft…

Computation and Language · Computer Science 2026-05-27 Kuan-Wei Lu , Ding-Yong Hong , Pangfeng Liu , Jan-Jan Wu

Stochastic gradient descent (SGD) optimization methods such as the plain vanilla SGD method and the popular Adam optimizer are nowadays the method of choice in the training of artificial neural networks (ANNs). Despite the remarkable…

Optimization and Control · Mathematics 2024-02-09 Arnulf Jentzen , Adrian Riekert

For many machine learning problems, data is abundant and it may be prohibitive to make multiple passes through the full training set. In this context, we investigate strategies for dynamically increasing the effective sample size, when…

Machine Learning · Computer Science 2016-10-10 Hadi Daneshmand , Aurelien Lucchi , Thomas Hofmann

We present results from Alexa speech teams on semi-supervised learning (SSL) of acoustic models (AM) with experiments spanning over 3000 hours of GPU time, making our study one of the largest of its kind. We discuss SSL for AMs in a small…

Recent findings by Cohen et al., 2021, demonstrate that when training neural networks using full-batch gradient descent with a step size of $\eta$, the largest eigenvalue $\lambda_{\max}$ of the full-batch Hessian consistently stabilizes…

Machine Learning · Computer Science 2025-12-30 Arseniy Andreyev , Pierfrancesco Beneventano

Packing and shuffling tokens is a common practice in training auto-regressive language models (LMs) to prevent overfitting and improve efficiency. Typically documents are concatenated to chunks of maximum sequence length (MSL) and then…

Computation and Language · Computer Science 2024-08-20 Yanbing Chen , Ruilin Wang , Zihao Yang , Lavender Yao Jiang , Eric Karl Oermann

While large language models (LLMs) dominate the AI landscape, Small-scale large Language Models (SLMs) are gaining attention due to cost and efficiency demands from consumers. However, there is limited research on the training behavior and…