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Flat regions of the neural network loss landscape have long been hypothesized to correlate with better generalization properties. A closely related but distinct problem is training models that are robust to internal perturbations to their…

Machine Learning · Computer Science 2026-02-10 Philip Jacobson , Ben Feinberg , Suhas Kumar , Sapan Agarwal , T. Patrick Xiao , Christopher Bennett

Recently, flat minima are proven to be effective for improving generalization and sharpness-aware minimization (SAM) achieves state-of-the-art performance. Yet the current definition of flatness discussed in SAM and its follow-ups are…

Machine Learning · Computer Science 2023-07-07 Xingxuan Zhang , Renzhe Xu , Han Yu , Hao Zou , Peng Cui

Recent studies highlight the effectiveness of flat minima in enhancing generalization, with sharpness-aware minimization (SAM) achieving state-of-the-art performance. Additionally, insights into the intrinsic geometry of the loss landscape…

Machine Learning · Computer Science 2025-06-10 Tuan Truong , Hoang-Phi Nguyen , Haocheng Luo , Tung Pham , Mehrtash Harandi , Dinh Phung , Trung Le

The generalization performance of deep neural networks (DNNs) is a critical factor in achieving robust model behavior on unseen data. Recent studies have highlighted the importance of sharpness-based measures in promoting generalization by…

Machine Learning · Computer Science 2025-01-28 Mohamed Hassan , Aleksandar Vakanski , Boyu Zhang , Min Xian

Sharpness-Aware Minimization (SAM) is a recent optimization framework aiming to improve the deep neural network generalization, through obtaining flatter (i.e. less sharp) solutions. As SAM has been numerically successful, recent papers…

Machine Learning · Statistics 2023-05-22 Kayhan Behdin , Rahul Mazumder

Sharpness-aware minimization (SAM) has well documented merits in enhancing generalization of deep neural networks, even without sizable data augmentation. Embracing the geometry of the loss function, where neighborhoods of 'flat minima'…

Machine Learning · Computer Science 2023-12-25 Bingcong Li , Georgios B. Giannakis

We consider Sharpness-Aware Minimization (SAM), a gradient-based optimization method for deep networks that has exhibited performance improvements on image and language prediction problems. We show that when SAM is applied with a convex…

Machine Learning · Computer Science 2023-04-12 Peter L. Bartlett , Philip M. Long , Olivier Bousquet

Sharpness-aware minimization (SAM) has emerged as a highly effective technique to improve model generalization, but its underlying principles are not fully understood. We investigate m-sharpness, where SAM performance improves monotonically…

Machine Learning · Computer Science 2026-04-03 Haocheng Luo , Mehrtash Harandi , Dinh Phung , Trung Le

It is arguably believed that flatter minima can generalize better. However, it has been pointed out that the usual definitions of sharpness, which consider either the maxima or the integral of loss over a $\delta$ ball of parameters around…

Machine Learning · Computer Science 2021-01-11 Mingyang Yi , Huishuai Zhang , Wei Chen , Zhi-Ming Ma , Tie-Yan Liu

Flatness measures based on the spectrum or the trace of the Hessian of the loss are widely used as proxies for the generalization ability of deep networks. However, most existing definitions are either tailored to fully connected…

Machine Learning · Computer Science 2026-03-11 Rahman Taleghani , Maryam Mohammadi , Francesco Marchetti

Despite extensive study, the significance of sharpness -- the trace of the loss Hessian at local minima -- remains unclear. We investigate an alternative perspective: how sharpness relates to the geometric structure of neural…

Machine Learning · Computer Science 2026-02-24 Shirui Chen , Stefano Recanatesi , Eric Shea-Brown

Sharpness-aware minimization (SAM) aims to improve the generalisation of gradient-based learning by seeking out flat minima. In this work, we establish connections between SAM and Mean-Field Variational Inference (MFVI) of neural network…

Machine Learning · Statistics 2022-10-20 Szilvia Ujváry , Zsigmond Telek , Anna Kerekes , Anna Mészáros , Ferenc Huszár

A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…

Machine Learning · Computer Science 2025-12-19 Maria Matveev , Vit Fojtik , Hung-Hsu Chou , Gitta Kutyniok , Johannes Maly

The mechanisms by which certain training interventions, such as increasing learning rates and applying batch normalization, improve the generalization of deep networks remains a mystery. Prior works have speculated that "flatter" solutions…

Machine Learning · Computer Science 2023-05-25 Simran Kaur , Jeremy Cohen , Zachary C. Lipton

Recent studies on deep neural networks show that flat minima of the loss landscape correlate with improved generalization. Sharpness-aware minimization (SAM) efficiently finds flat regions by updating the parameters according to the…

Machine Learning · Computer Science 2025-02-13 Albert Kjøller Jacobsen , Georgios Arvanitidis

Regression is fundamental in computer vision and is widely used in various tasks including age estimation, depth estimation, target localization, \etc However, real-world data often exhibits imbalanced distribution, making regression models…

Computer Vision and Pattern Recognition · Computer Science 2025-08-26 Yahao Liu , Qin Wang , Lixin Duan , Wen Li

The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…

Machine Learning · Computer Science 2022-12-01 Yuxin Dong , Tieliang Gong , Shujian Yu , Hong Chen , Chen Li

Recently, information theoretic analysis has become a popular framework for understanding the generalization behavior of deep neural networks. It allows a direct analysis for stochastic gradient/Langevin descent (SGD/SGLD) learning…

Machine Learning · Statistics 2023-05-03 Yuxin Dong , Tieliang Gong , Hong Chen , Chen Li

Flatness of the loss curve around a model at hand has been shown to empirically correlate with its generalization ability. Optimizing for flatness has been proposed as early as 1994 by Hochreiter and Schmidthuber, and was followed by more…

Machine Learning · Computer Science 2023-07-06 Linara Adilova , Amr Abourayya , Jianning Li , Amin Dada , Henning Petzka , Jan Egger , Jens Kleesiek , Michael Kamp

Sharpness-Aware Minimization (SAM) has attracted significant attention for its effectiveness in improving generalization across various tasks. However, its underlying principles remain poorly understood. In this work, we analyze SAM's…

Machine Learning · Computer Science 2025-01-23 Haocheng Luo , Tuan Truong , Tung Pham , Mehrtash Harandi , Dinh Phung , Trung Le