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Related papers: The Heavy-Tail Phenomenon in SGD

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It has repeatedly been observed that loss minimization by stochastic gradient descent (SGD) leads to heavy-tailed distributions of neural network parameters. Here, we analyze a continuous diffusion approximation of SGD, called homogenized…

Machine Learning · Statistics 2024-02-05 Zhe Jiao , Martin Keller-Ressel

Recent theoretical studies have shown that heavy-tails can emerge in stochastic optimization due to `multiplicative noise', even under surprisingly simple settings, such as linear regression with Gaussian data. While these studies have…

Machine Learning · Statistics 2025-05-06 Mert Gurbuzbalaban , Yuanhan Hu , Umut Simsekli , Kun Yuan , Lingjiong Zhu

Recent studies have shown that heavy tails can emerge in stochastic optimization and that the heaviness of the tails have links to the generalization error. While these studies have shed light on interesting aspects of the generalization…

Machine Learning · Statistics 2023-02-14 Anant Raj , Melih Barsbey , Mert Gürbüzbalaban , Lingjiong Zhu , Umut Şimşekli

The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the \emph{classical} central limit theorem (CLT) kicks in. This assumption is often made…

Machine Learning · Statistics 2019-12-03 Umut Şimşekli , Mert Gürbüzbalaban , Thanh Huy Nguyen , Gaël Richard , Levent Sagun

Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…

Machine Learning · Computer Science 2025-10-27 Xingyu Wang , Chang-Han Rhee

The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the classical central limit theorem (CLT) kicks in. This assumption is often made for…

Machine Learning · Computer Science 2019-01-21 Umut Simsekli , Levent Sagun , Mert Gurbuzbalaban

Neural network compression techniques have become increasingly popular as they can drastically reduce the storage and computation requirements for very large networks. Recent empirical studies have illustrated that even simple pruning…

Machine Learning · Statistics 2021-06-08 Melih Barsbey , Milad Sefidgaran , Murat A. Erdogdu , Gaël Richard , Umut Şimşekli

Heavy-tail phenomena in stochastic gradient descent (SGD) have been reported in several empirical studies. Experimental evidence in previous works suggests a strong interplay between the heaviness of the tails and generalization behavior of…

Machine Learning · Statistics 2023-01-31 Anant Raj , Lingjiong Zhu , Mert Gürbüzbalaban , Umut Şimşekli

Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…

Machine Learning · Statistics 2019-06-24 Thanh Huy Nguyen , Umut Şimşekli , Mert Gürbüzbalaban , Gaël Richard

Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails potentially result in iterates with diverging…

Optimization and Control · Mathematics 2021-02-23 Hongjian Wang , Mert Gürbüzbalaban , Lingjiong Zhu , Umut Şimşekli , Murat A. Erdogdu

Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…

Machine Learning · Statistics 2020-06-12 Liam Hodgkinson , Michael W. Mahoney

The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm. While many works provide high-probability guarantees, quantifying…

Machine Learning · Computer Science 2026-02-06 Aleksandar Armacki , Dragana Bajović , Dušan Jakovetić , Soummya Kar , Ali H. Sayed

A recent line of empirical studies has demonstrated that SGD might exhibit a heavy-tailed behavior in practical settings, and the heaviness of the tails might correlate with the overall performance. In this paper, we investigate the…

Machine Learning · Computer Science 2023-10-31 Krunoslav Lehman Pavasovic , Alain Durmus , Umut Simsekli

Despite its success in a wide range of applications, characterizing the generalization properties of stochastic gradient descent (SGD) in non-convex deep learning problems is still an important challenge. While modeling the trajectories of…

Machine Learning · Statistics 2022-01-12 Umut Şimşekli , Ozan Sener , George Deligiannidis , Murat A. Erdogdu

Neural network compression has been an increasingly important subject, not only due to its practical relevance, but also due to its theoretical implications, as there is an explicit connection between compressibility and generalization…

Machine Learning · Statistics 2024-02-13 Yijun Wan , Melih Barsbey , Abdellatif Zaidi , Umut Simsekli

In the era of large-scale neural network models, optimization algorithms often struggle with generalization due to an overreliance on training loss. One key insight widely accepted in the machine learning community is the idea that wide…

Machine Learning · Computer Science 2025-09-01 Bodu Gong , Gustavo Enrique Batista , Pierre Lafaye de Micheaux

While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new…

Machine Learning · Computer Science 2019-07-26 Xinyan Li , Qilong Gu , Yingxue Zhou , Tiancong Chen , Arindam Banerjee

A particular direction of recent advance about stochastic deep-learning algorithms has been about uncovering a rather mysterious heavy-tailed nature of the stationary distribution of these algorithms, even when the data distribution is not…

Machine Learning · Computer Science 2022-04-28 Sayar Karmakar , Anirbit Mukherjee

The empirical success of deep learning is often attributed to SGD's mysterious ability to avoid sharp local minima in the loss landscape, as sharp minima are known to lead to poor generalization. Recently, empirical evidence of heavy-tailed…

Machine Learning · Computer Science 2022-05-12 Xingyu Wang , Sewoong Oh , Chang-Han Rhee

Understanding the generalization properties of optimization algorithms under heavy-tailed noise has gained growing attention. However, the existing theoretical results mainly focus on stochastic gradient descent (SGD) and the analysis of…

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