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Related papers: Flatness After All?

200 papers

Sharpness of minima is a promising quantity that can correlate with generalization in deep networks and, when optimized during training, can improve generalization. However, standard sharpness is not invariant under reparametrizations of…

Machine Learning · Computer Science 2023-06-08 Maksym Andriushchenko , Francesco Croce , Maximilian Müller , Matthias Hein , Nicolas Flammarion

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

Flatness of the loss curve is conjectured to be connected to the generalization ability of machine learning models, in particular neural networks. While it has been empirically observed that flatness measures consistently correlate strongly…

Machine Learning · Computer Science 2021-11-05 Henning Petzka , Michael Kamp , Linara Adilova , Cristian Sminchisescu , Mario Boley

Empirical evidence suggests that for a variety of overparameterized nonlinear models, most notably in neural network training, the growth of the loss around a minimizer strongly impacts its performance. Flat minima -- those around which the…

Machine Learning · Computer Science 2023-02-20 Lijun Ding , Dmitriy Drusvyatskiy , Maryam Fazel , Zaid Harchaoui

Recent studies showed that the generalization of neural networks is correlated with the sharpness of the loss landscape, and flat minima suggests a better generalization ability than sharp minima. In this paper, we propose a novel method…

Machine Learning · Computer Science 2024-05-24 Yuyan Zhou , Ye Li , Lei Feng , Sheng-Jun Huang

In this paper we study the generalization capabilities of fully-connected neural networks trained in the context of time series forecasting. Time series do not satisfy the typical assumption in statistical learning theory of the data being…

Machine Learning · Statistics 2019-07-30 Anastasia Borovykh , Cornelis W. Oosterlee , Sander M. Bohte

Recently, there has been a surge in interest in developing optimization algorithms for overparameterized models as achieving generalization is believed to require algorithms with suitable biases. This interest centers on minimizing…

Machine Learning · Computer Science 2026-02-05 Behrooz Tahmasebi , Ashkan Soleymani , Dara Bahri , Stefanie Jegelka , Patrick Jaillet

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the…

Machine Learning · Computer Science 2023-11-15 Van-Anh Nguyen , Tung-Long Vuong , Hoang Phan , Thanh-Toan Do , Dinh Phung , Trung Le

Existing generalization measures that aim to capture a model's simplicity based on parameter counts or norms fail to explain generalization in overparameterized deep neural networks. In this paper, we introduce a new, theoretically…

Machine Learning · Computer Science 2021-03-11 Lorenz Kuhn , Clare Lyle , Aidan N. Gomez , Jonas Rothfuss , Yarin Gal

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

The training of over-parameterized neural networks has received much study in recent literature. An important consideration is the regularization of over-parameterized networks due to their highly nonconvex and nonlinear geometry. In this…

Machine Learning · Computer Science 2024-09-24 Hongyang R. Zhang , Dongyue Li , Haotian Ju

The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. First, we discuss…

Over-parameterized neural networks generalize well in practice without any explicit regularization. Although it has not been proven yet, empirical evidence suggests that implicit regularization plays a crucial role in deep learning and…

Machine Learning · Computer Science 2019-03-07 Masayoshi Kubo , Ryotaro Banno , Hidetaka Manabe , Masataka Minoji

It is important to understand how the popular regularization method dropout helps the neural network training find a good generalization solution. In this work, we show that the training with dropout finds the neural network with a flatter…

Machine Learning · Computer Science 2022-05-24 Zhongwang Zhang , Hanxu Zhou , Zhi-Qin John Xu

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

Understanding the geometry of the loss landscape near a minimum is key to explaining the implicit bias of gradient-based methods in non-convex optimization problems such as deep neural network training and deep matrix factorization. A…

Machine Learning · Statistics 2026-02-05 Anil Kamber , Rahul Parhi

It is widely observed that deep learning models with learned parameters generalize well, even with much more model parameters than the number of training samples. We systematically investigate the underlying reasons why deep neural networks…

Machine Learning · Computer Science 2017-11-29 Lei Wu , Zhanxing Zhu , Weinan E

We consider the problem of generalization of arbitrarily overparameterized two-layer ReLU Neural Networks with univariate input. Recent work showed that under square loss, flat solutions (motivated by flat / stable minima and Edge of…

Machine Learning · Computer Science 2025-12-02 Dan Qiao , Yu-Xiang Wang

Deep Neural Networks (DNNs) generalization is known to be closely related to the flatness of minima, leading to the development of Sharpness-Aware Minimization (SAM) for seeking flatter minima and better generalization. In this paper, we…

Machine Learning · Computer Science 2024-12-06 Yun Yue , Jiadi Jiang , Zhiling Ye , Ning Gao , Yongchao Liu , Ke Zhang

We consider fine-tuning a pretrained deep neural network on a target task. We study the generalization properties of fine-tuning to understand the problem of overfitting, which has often been observed (e.g., when the target dataset is small…

Machine Learning · Computer Science 2023-12-27 Haotian Ju , Dongyue Li , Hongyang R. Zhang