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Understanding the training dynamics of transformers is important to explain the impressive capabilities behind large language models. In this work, we study the dynamics of training a shallow transformer on a task of recognizing…

Machine Learning · Computer Science 2024-10-15 Hongru Yang , Bhavya Kailkhura , Zhangyang Wang , Yingbin Liang

Despite the remarkable success of transformer-based models in various real-world tasks, their underlying mechanisms remain poorly understood. Recent studies have suggested that transformers can implement gradient descent as an in-context…

Machine Learning · Computer Science 2024-08-09 Xingwu Chen , Lei Zhao , Difan Zou

We present an error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method. Our main contribution is a redesigned hybrid solver [Larios-C\'ardenas and Gibou, J. Comput. Phys. (May 2022),…

Numerical Analysis · Mathematics 2022-09-29 Luis Ángel Larios-Cárdenas , Frédéric Gibou

Does the use of auto-differentiation yield reasonable updates for deep neural networks (DNNs)? Specifically, when DNNs are designed to adhere to neural ODE architectures, can we trust the gradients provided by auto-differentiation? Through…

Machine Learning · Computer Science 2026-03-31 Yewei Xu , Shi Chen , Qin Li

Training large language models is a computationally intensive process that often requires substantial resources to achieve state-of-the-art results. Incremental layer-wise training has been proposed as a potential strategy to optimize the…

Computation and Language · Computer Science 2024-12-02 Miles Q. Li , Benjamin C. M. Fung , Shih-Chia Huang

Optical approaches have made great strides towards the goal of high-speed, energy-efficient computing necessary for modern deep learning and AI applications. Read-in and read-out of data, however, limit the overall performance of existing…

Emerging Technologies · Computer Science 2024-02-06 Alexander Song , Sai Nikhilesh Murty Kottapalli , Rahul Goyal , Bernhard Schölkopf , Peer Fischer

Solving different types of optimization models (including parameters fitting) for support vector machines on large-scale training data is often an expensive computational task. This paper proposes a multilevel algorithmic framework that…

Machine Learning · Statistics 2014-10-14 Talayeh Razzaghi , Ilya Safro

Multi-task learning (MTL) aims to improve the generalization of several related tasks by learning them jointly. As a comparison, in addition to the joint training scheme, modern meta-learning allows unseen tasks with limited labels during…

Machine Learning · Computer Science 2021-06-17 Haoxiang Wang , Han Zhao , Bo Li

We show that a constant number of self-attention layers can efficiently simulate, and be simulated by, a constant number of communication rounds of Massively Parallel Computation. As a consequence, we show that logarithmic depth is…

Machine Learning · Computer Science 2024-02-15 Clayton Sanford , Daniel Hsu , Matus Telgarsky

In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the…

Machine Learning · Computer Science 2022-02-04 Daniel Bershatsky , Aleksandr Mikhalev , Alexandr Katrutsa , Julia Gusak , Daniil Merkulov , Ivan Oseledets

Recent advancements in vision transformers (ViTs) have demonstrated that larger models often achieve superior performance. However, training these models remains computationally intensive and costly. To address this challenge, we introduce…

Computer Vision and Pattern Recognition · Computer Science 2025-10-23 Zhiwei Hao , Jianyuan Guo , Li Shen , Kai Han , Yehui Tang , Han Hu , Yunhe Wang

Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature. For many years this bottleneck has persisted, as many thought…

Machine Learning · Computer Science 2024-01-17 Yi Heng Lim , Qi Zhu , Joshua Selfridge , Muhammad Firmansyah Kasim

We present a methodology for training foundational transformer models capable of processing collider data with diverse kinematic signatures. Our universal foundation model is designed for simultaneous analysis of all processes involving…

High Energy Physics - Phenomenology · Physics 2025-11-13 E. Abasov , L. Dudko , E. Iudin , A. Markina , P. Volkov , M. Perfilov , A. Zaborenko

Reconstructive phase transitions involving breaking and reconstruction of primary chemical bonds are ubiquitous and important for many technological applications. In contrast to displacive phase transitions, the dynamics of reconstructive…

Despite their prevalence in deep-learning communities, over-parameterized models convey high demands of computational costs for proper training. This work studies the fine-grained, modular-level learning dynamics of over-parameterized…

We propose an efficient layer-specific optimization (ELO) method designed to enhance continual pretraining (CP) for specific languages in multilingual large language models (MLLMs). This approach addresses the common challenges of high…

Computation and Language · Computer Science 2026-01-21 HanGyeol Yoo , ChangSu Choi , Minjun Kim , Seohyun Song , SeungWoo Song , Inho Won , Jongyoul Park , Cheoneum Park , KyungTae Lim

The training of Deep Neural Networks usually needs tremendous computing resources. Therefore many deep models are trained in large cluster instead of single machine or GPU. Though major researchs at present try to run whole model on all…

Machine Learning · Computer Science 2018-06-12 Hao Dong , Shuai Li , Dongchang Xu , Yi Ren , Di Zhang

Stochastic Gradient Descent is used for large datasets to train models to reduce the training time. On top of that data parallelism is widely used as a method to efficiently train neural networks using multiple worker nodes in parallel.…

Machine Learning · Computer Science 2024-07-02 Aakash Sudhirbhai Vora , Dhrumil Chetankumar Joshi , Aksh Kantibhai Patel

We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror…

Machine Learning · Statistics 2017-12-13 Luca Franceschi , Michele Donini , Paolo Frasconi , Massimiliano Pontil

Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an…

Machine Learning · Statistics 2019-05-09 Arild Nøkland , Lars Hiller Eidnes