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Multistage stochastic programming provides a modeling framework for sequential decision-making problems that involve uncertainty. One typically overlooked aspect of this methodology is how uncertainty is incorporated into modeling.…

Optimization and Control · Mathematics 2021-09-24 Juyoung Wang , Mucahit Cevik , Merve Bodur

We present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two sub-networks, namely the branch and trunk networks. Typically, the two…

Numerical Analysis · Mathematics 2023-09-06 Sanghyun Lee , Yeonjong Shin

Very deep convolutional networks with hundreds of layers have led to significant reductions in error on competitive benchmarks. Although the unmatched expressiveness of the many layers can be highly desirable at test time, training very…

Machine Learning · Computer Science 2016-08-01 Gao Huang , Yu Sun , Zhuang Liu , Daniel Sedra , Kilian Weinberger

Modern deep networks are trained with stochastic gradient descent (SGD) whose key hyperparameters are the number of data considered at each step or batch size $B$, and the step size or learning rate $\eta$. For small $B$ and large $\eta$,…

Machine Learning · Computer Science 2024-02-29 Antonio Sclocchi , Matthieu Wyart

A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…

Machine Learning · Statistics 2016-06-14 Jonathan Rosenblatt , Boaz Nadler

We introduce a technique for tuning the learning rate scale factor of any base optimization algorithm and schedule automatically, which we call \textsc{mechanic}. Our method provides a practical realization of recent theoretical reductions…

Machine Learning · Computer Science 2023-06-05 Ashok Cutkosky , Aaron Defazio , Harsh Mehta

To train neural machine translation models simultaneously on multiple tasks (languages), it is common to sample each task uniformly or in proportion to dataset sizes. As these methods offer little control over performance trade-offs, we…

Machine Learning · Computer Science 2019-09-17 Sébastien Jean , Orhan Firat , Melvin Johnson

Inspired by human learning, researchers have proposed ordering examples during training based on their difficulty. Both curriculum learning, exposing a network to easier examples early in training, and anti-curriculum learning, showing the…

Machine Learning · Computer Science 2021-02-10 Xiaoxia Wu , Ethan Dyer , Behnam Neyshabur

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been…

Machine Learning · Statistics 2018-01-03 Elad Hoffer , Itay Hubara , Daniel Soudry

Deep learning (DL) has transformed applications in a variety of domains, including computer vision, natural language processing, and tabular data analysis. The search for improved DL model accuracy has led practitioners to explore…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-01-10 Kabir Nagrecha

Diffusion models suffer from the huge consumption of time and resources to train. For example, diffusion models need hundreds of GPUs to train for several weeks for a high-resolution generative task to meet the requirements of an extremely…

Machine Learning · Computer Science 2025-02-05 Bin Xie , Gady Agam

In this work, we introduce a novel approach for optimizing LLM training by adjusting learning rates across weights of different components in Transformer models. Traditional methods often apply a uniform learning rate across all network…

Learning curves are a measure for how the performance of machine learning models improves given a certain volume of training data. Over a wide variety of applications and models it was observed that learning curves follow -- to a large…

Machine Learning · Computer Science 2023-10-13 Laura Didyk , Brayden Yarish , Michael A. Beck , Christopher P. Bidinosti , Christopher J. Henry

Regularization plays a vital role in the context of deep learning by preventing deep neural networks from the danger of overfitting. This paper proposes a novel deep learning regularization method named as DL-Reg, which carefully reduces…

Machine Learning · Computer Science 2020-11-05 Maryam Dialameh , Ali Hamzeh , Hossein Rahmani

Stochastic gradient descent samples uniformly the training set to build an unbiased gradient estimate with a limited number of samples. However, at a given step of the training process, some data are more helpful than others to continue…

Machine Learning · Computer Science 2023-03-30 Thibault Lahire

Study Objectives: Sleep stage scoring is performed manually by sleep experts and is prone to subjective interpretation of scoring rules with low intra- and interscorer reliability. Many automatic systems rely on few small-scale databases…

Computer Vision and Pattern Recognition · Computer Science 2020-08-24 Alexander Neergaard Olesen , Poul Jennum , Emmanuel Mignot , Helge B D Sorensen

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

Machine Learning · Computer Science 2023-04-10 Roman Worschech , Bernd Rosenow

Feature learning is thought to be one of the fundamental reasons for the success of deep neural networks. It is rigorously known that in two-layer fully-connected neural networks under certain conditions, one step of gradient descent on the…

Machine Learning · Statistics 2025-04-11 Behrad Moniri , Donghwan Lee , Hamed Hassani , Edgar Dobriban

Understanding the dynamics of neural networks in different width regimes is crucial for improving their training and performance. We present an exact solution for the learning dynamics of a one-hidden-layer linear network, with…

Machine Learning · Computer Science 2025-02-24 Yizhou Xu , Liu Ziyin

Due to the scarcity of high-quality data, large language models (LLMs) are often trained on mixtures of data with varying quality levels, even after sophisticated data curation. A natural approach to better leverage high-quality data is…

Machine Learning · Computer Science 2026-05-15 Kairong Luo , Zhenbo Sun , Haodong Wen , Xinyu Shi , Jiarui Cui , Chenyi Dang , Kaifeng Lyu , Wenguang Chen