English
Related papers

Related papers: Binary Classification of Gaussian Mixtures: Abunda…

200 papers

Overparameterization in deep learning typically refers to settings where a trained neural network (NN) has representational capacity to fit the training data in many ways, some of which generalize well, while others do not. In the case of…

Machine Learning · Computer Science 2023-03-24 Edo Cohen-Karlik , Itamar Menuhin-Gruman , Raja Giryes , Nadav Cohen , Amir Globerson

Learned classifiers should often possess certain invariance properties meant to encourage fairness, robustness, or out-of-distribution generalization. However, multiple recent works empirically demonstrate that common invariance-inducing…

Machine Learning · Computer Science 2024-07-04 Yoav Wald , Gal Yona , Uri Shalit , Yair Carmon

Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…

Machine Learning · Computer Science 2020-01-08 E Zhenqian , Gao Weiguo

Several works have proposed Simplicity Bias (SB)---the tendency of standard training procedures such as Stochastic Gradient Descent (SGD) to find simple models---to justify why neural networks generalize well [Arpit et al. 2017, Nakkiran et…

Machine Learning · Computer Science 2020-10-29 Harshay Shah , Kaustav Tamuly , Aditi Raghunathan , Prateek Jain , Praneeth Netrapalli

Most classification algorithms used in high energy physics fall under the category of supervised machine learning. Such methods require a training set containing both signal and background events and are prone to classification errors…

Data Analysis, Statistics and Probability · Physics 2015-06-03 Mikael Kuusela , Tommi Vatanen , Eric Malmi , Tapani Raiko , Timo Aaltonen , Yoshikazu Nagai

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…

Machine Learning · Statistics 2017-10-11 Madhu S. Advani , Andrew M. Saxe

Gaussian multiplicative noise is commonly used as a stochastic regularisation technique in training of deterministic neural networks. A recent paper reinterpreted the technique as a specific algorithm for approximate inference in Bayesian…

Machine Learning · Statistics 2017-11-09 Jiri Hron , Alexander G. de G. Matthews , Zoubin Ghahramani

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and…

Machine Learning · Computer Science 2017-10-06 Shao-Bo Lin , Jinshan Zeng , Xiangyu Chang

We provide a general framework for studying recurrent neural networks (RNNs) trained by injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as discretizations of stochastic differential equations driven by…

Machine Learning · Statistics 2021-12-02 Soon Hoe Lim , N. Benjamin Erichson , Liam Hodgkinson , Michael W. Mahoney

This work is substituted by the paper in arXiv:2011.14066. Stochastic gradient descent is the de facto algorithm for training deep neural networks (DNNs). Despite its popularity, it still requires fine tuning in order to achieve its best…

Machine Learning · Statistics 2020-12-02 Vatsal Shah , Anastasios Kyrillidis , Sujay Sanghavi

Recent years have witnessed strong empirical performance of over-parameterized neural networks on various tasks and many advances in the theory, e.g. the universal approximation and provable convergence to global minimum. In this paper, we…

Machine Learning · Statistics 2021-01-26 Shiyun Xu , Zhiqi Bu

It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully-connected neural networks. This paper studies the learning…

Machine Learning · Statistics 2023-08-17 Tian-Yi Zhou , Xiaoming Huo

Motivated by surprisingly good generalization properties of learned deep neural networks in overparameterized scenarios and by the related double descent phenomenon, this paper analyzes the relation between smoothness and low generalization…

Machine Learning · Computer Science 2021-10-29 Yuege Xie , Hung-Hsu Chou , Holger Rauhut , Rachel Ward

This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a…

Information Theory · Computer Science 2020-03-31 Abla Kammoun , Mohamed-Slim Alouini

A common strategy to train deep neural networks (DNNs) is to use very large architectures and to train them until they (almost) achieve zero training error. Empirically observed good generalization performance on test data, even in the…

Machine Learning · Statistics 2021-07-26 Nicole Mücke , Ingo Steinwart

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…

Machine Learning · Computer Science 2022-03-31 Andrew Gordon Wilson , Pavel Izmailov

Using information-theoretic principles, we consider the generalization error (gen-error) of iterative semi-supervised learning (SSL) algorithms that iteratively generate pseudo-labels for a large amount of unlabelled data to progressively…

Machine Learning · Computer Science 2022-09-20 Haiyun He , Hanshu Yan , Vincent Y. F. Tan

This paper analyzes the convergence and generalization of training a one-hidden-layer neural network when the input features follow the Gaussian mixture model consisting of a finite number of Gaussian distributions. Assuming the labels are…

Machine Learning · Computer Science 2023-01-30 Hongkang Li , Shuai Zhang , Meng Wang

Deep neural networks are often trained in the over-parametrized regime (i.e. with far more parameters than training examples), and understanding why the training converges to solutions that generalize remains an open problem. Several…

Machine Learning · Statistics 2018-03-23 Hartmut Maennel , Olivier Bousquet , Sylvain Gelly

Self-distillation (SD), a technique where a model improves itself using its own predictions, has attracted attention as a simple yet powerful approach in machine learning. Despite its widespread use, the mechanisms underlying its…

Machine Learning · Statistics 2025-11-20 Kaito Takanami , Takashi Takahashi , Ayaka Sakata