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The goal of this paper is to accelerate the training of machine learning models, a critical challenge since the training of large-scale deep neural models can be computationally expensive. Stochastic gradient descent (SGD) and its variants…

Machine Learning · Computer Science 2025-09-22 Yuen Chen , Yian Wang , Hari Sundaram

Deep neural networks rely heavily on normalization methods to improve their performance and learning behavior. Although normalization methods spurred the development of increasingly deep and efficient architectures, they also increase the…

Machine Learning · Computer Science 2021-10-06 Alexander Fuchs , Christian Knoll , Franz Pernkopf

Uncertainty calibration is crucial for various machine learning applications, yet it remains challenging. Many models exhibit hallucinations - confident yet inaccurate responses - due to miscalibrated confidence. Here, we show that the…

Machine Learning · Computer Science 2025-03-28 Jeonghwan Cheon , Se-Bum Paik

This paper discovers that the neural network with lower decision boundary (DB) variability has better generalizability. Two new notions, algorithm DB variability and $(\epsilon, \eta)$-data DB variability, are proposed to measure the…

Machine Learning · Computer Science 2023-12-27 Shiye Lei , Fengxiang He , Yancheng Yuan , Dacheng Tao

We investigate the generalization and optimization properties of shallow neural-network classifiers trained by gradient descent in the interpolating regime. Specifically, in a realizable scenario where model weights can achieve arbitrarily…

Machine Learning · Statistics 2023-03-29 Hossein Taheri , Christos Thrampoulidis

As deep neural networks (DNNs) achieve tremendous success across many application domains, researchers tried to explore in many aspects on why they generalize well. In this paper, we provide a novel perspective on these issues using the…

Machine Learning · Computer Science 2020-02-25 Jinlong Liu , Guoqing Jiang , Yunzhi Bai , Ting Chen , Huayan Wang

Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has…

Machine Learning · Computer Science 2018-12-11 Sanjeev Arora , Zhiyuan Li , Kaifeng Lyu

Gradient dynamics play a central role in determining the stability and generalization of deep neural networks. In this work, we provide an empirical analysis of how variance and standard deviation of gradients evolve during training,…

Machine Learning · Computer Science 2025-09-09 Vincent-Daniel Yun

Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when…

Machine Learning · Computer Science 2020-06-11 Tao Lin , Lingjing Kong , Sebastian U. Stich , Martin Jaggi

In machine learning, disparity metrics are often defined by measuring the difference in the performance or outcome of a model, across different sub-populations (groups) of datapoints. Thus, the inputs to disparity quantification consist of…

Computer Vision and Pattern Recognition · Computer Science 2022-04-15 Shervin Ardeshir , Cristina Segalin , Nathan Kallus

The accuracy of deep neural networks is significantly influenced by the effectiveness of mini-batch construction during training. In single-label scenarios, such as binary and multi-class classification tasks, it has been demonstrated that…

Machine Learning · Computer Science 2024-12-24 Ao Zhou , Bin Liu , Jin Wang , Grigorios Tsoumakas

Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely unexplored. In this paper we study SGD with increasing…

Probability · Mathematics 2026-05-11 Bartosz Glowacki , Rafal Kulik , Philippe Soulier

Deep neural network training involves both forward propagation (from features through logits to loss) and backward propagation (from loss through gradients to parameter updates). While perturbations along the forward chain, including…

Machine Learning · Computer Science 2026-05-29 Hua Li

In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a…

Data Structures and Algorithms · Computer Science 2018-04-03 Mostafa Haghir Chehreghani , Albert Bifet , Talel Abdessalem

Deep neural networks have been shown to be very powerful methods for many supervised learning tasks. However, they can also easily overfit to training set biases, i.e., label noise and class imbalance. While both learning with noisy labels…

Computer Vision and Pattern Recognition · Computer Science 2021-10-25 Tong Wei , Jiang-Xin Shi , Yu-Feng Li , Min-Ling Zhang

Distributed implementations of mini-batch stochastic gradient descent (SGD) suffer from communication overheads, attributed to the high frequency of gradient updates inherent in small-batch training. Training with large batches can reduce…

Machine Learning · Statistics 2018-06-12 Lingjiao Chen , Hongyi Wang , Jinman Zhao , Dimitris Papailiopoulos , Paraschos Koutris

Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not…

Machine Learning · Statistics 2019-11-01 Jayaraman J. Thiagarajan , Bindya Venkatesh , Deepta Rajan

Batch normalization (batch norm) is often used in an attempt to stabilize and accelerate training in deep neural networks. In many cases it indeed decreases the number of parameter updates required to achieve low training error. However, it…

Machine Learning · Computer Science 2019-05-31 Angus Galloway , Anna Golubeva , Thomas Tanay , Medhat Moussa , Graham W. Taylor

Several recent works find empirically that the average test error of deep neural networks can be estimated via the prediction disagreement of models, which does not require labels. In particular, Jiang et al. (2022) show for the…

Machine Learning · Computer Science 2022-11-08 Andreas Kirsch , Yarin Gal

To collect large scale annotated data, it is inevitable to introduce label noise, i.e., incorrect class labels. To be robust against label noise, many successful methods rely on the noisy classifiers (i.e., models trained on the noisy…

Computer Vision and Pattern Recognition · Computer Science 2020-11-23 Songzhu Zheng , Pengxiang Wu , Aman Goswami , Mayank Goswami , Dimitris Metaxas , Chao Chen