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Sharpness-Aware Minimization (SAM) has attracted considerable attention for its effectiveness in improving generalization in deep neural network training by explicitly minimizing sharpness in the loss landscape. Its success, however, relies…

Machine Learning · Computer Science 2025-06-16 Sungbin Shin , Dongyeop Lee , Maksym Andriushchenko , Namhoon Lee

We analyze the landscape and training dynamics of diagonal linear networks in a linear regression task, with the network parameters being perturbed by small isotropic normal noise. The addition of such noise may be interpreted as a…

Machine Learning · Computer Science 2025-03-18 Gabriel Clara , Sophie Langer , Johannes Schmidt-Hieber

The Fisher information matrix (FIM) is a fundamental quantity to represent the characteristics of a stochastic model, including deep neural networks (DNNs). The present study reveals novel statistics of FIM that are universal among a wide…

Machine Learning · Statistics 2019-10-10 Ryo Karakida , Shotaro Akaho , Shun-ichi Amari

Sharpness-Aware Minimization (SAM) enhances generalization by reducing a Max-Sharpness (MaxS). Despite the practical success, we empirically found that the MAxS behind SAM's generalization enhancements face the "Flatness Indicator Problem"…

Computer Vision and Pattern Recognition · Computer Science 2024-09-23 Jiaxin Deng , Junbiao Pang , Baochang Zhang , Qingming Huang

We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to…

Machine Learning · Statistics 2017-06-01 Yuichi Yoshida , Takeru Miyato

Sharpness-Aware Minimization (SAM) has proven highly effective in improving model generalization in machine learning tasks. However, SAM employs a fixed hyperparameter associated with the regularization to characterize the sharpness of the…

Machine Learning · Computer Science 2024-12-24 Jinping Zou , Xiaoge Deng , Tao Sun

We argue that the optimization plays a crucial role in generalization of deep learning models through implicit regularization. We do this by demonstrating that generalization ability is not controlled by network size but rather by some…

Machine Learning · Computer Science 2017-05-10 Behnam Neyshabur , Ryota Tomioka , Ruslan Salakhutdinov , Nathan Srebro

Batch Normalization (BN) improves both convergence and generalization in training neural networks. This work understands these phenomena theoretically. We analyze BN by using a basic block of neural networks, consisting of a kernel layer, a…

Machine Learning · Computer Science 2019-04-25 Ping Luo , Xinjiang Wang , Wenqi Shao , Zhanglin Peng

While modern convolutional neural networks achieve outstanding accuracy on many image classification tasks, they are, compared to humans, much more sensitive to image degradation. Here, we describe a variant of Batch Normalization,…

Computer Vision and Pattern Recognition · Computer Science 2019-03-05 Bojian Yin , Siebren Schaafsma , Henk Corporaal , H. Steven Scholte , Sander M. Bohte

In this paper, we address monocular depth estimation with deep neural networks. To enable training of deep monocular estimation models with various sources of datasets, state-of-the-art methods adopt image-level normalization strategies to…

Computer Vision and Pattern Recognition · Computer Science 2022-10-19 Chi Zhang , Wei Yin , Zhibin Wang , Gang Yu , Bin Fu , Chunhua Shen

Modern deep learning architecture utilize batch normalization (BN) to stabilize training and improve accuracy. It has been shown that the BN layers alone are surprisingly expressive. In the context of robustness against adversarial…

Machine Learning · Computer Science 2022-04-27 Nils Philipp Walter , David Stutz , Bernt Schiele

Batch normalization was introduced in 2015 to speed up training of deep convolution networks by normalizing the activations across the current batch to have zero mean and unity variance. The results presented here show an interesting aspect…

Computer Vision and Pattern Recognition · Computer Science 2018-02-22 Mohamed Hajaj , Duncan Gillies

The strong correlation between neurons or filters can significantly weaken the generalization ability of neural networks. Inspired by the well-known Tammes problem, we propose a novel diversity regularization method to address this issue,…

Machine Learning · Computer Science 2021-03-24 Zhennan Wang , Canqun Xiang , Wenbin Zou , Chen Xu

We introduce a Normalized Convolutional Neural Layer, a novel approach to normalization in convolutional networks. Unlike conventional methods, this layer normalizes the rows of the im2col matrix during convolution, making it inherently…

Computer Vision and Pattern Recognition · Computer Science 2025-04-03 Dongsuk Kim , Geonhee Lee , Myungjae Lee , Shin Uk Kang , Dongmin Kim

Deep neural networks (DNNs) play an important role in machine learning due to its outstanding performance compared to other alternatives. However, DNNs are not suitable for safety-critical applications since DNNs can be easily fooled by…

Machine Learning · Computer Science 2021-03-26 Zhixin Pan , Prabhat Mishra

Modern deep learning models are over-parameterized, where the optimization setup strongly affects the generalization performance. A key element of reliable optimization for these systems is the modification of the loss function.…

Machine Learning · Computer Science 2022-12-09 Kayhan Behdin , Qingquan Song , Aman Gupta , David Durfee , Ayan Acharya , Sathiya Keerthi , Rahul Mazumder

Despite their overwhelming capacity to overfit, deep learning architectures tend to generalize relatively well to unseen data, allowing them to be deployed in practice. However, explaining why this is the case is still an open area of…

Machine Learning · Computer Science 2017-11-15 Laurent Dinh , Razvan Pascanu , Samy Bengio , Yoshua Bengio

Deep feedforward neural networks with piecewise linear activations are currently producing the state-of-the-art results in several public datasets. The combination of deep learning models and piecewise linear activation functions allows for…

Computer Vision and Pattern Recognition · Computer Science 2015-11-03 Zhibin Liao , Gustavo Carneiro

Sharpness-aware minimization (SAM) is a recently proposed method that minimizes the sharpness of the training loss of a neural network. While its generalization improvement is well-known and is the primary motivation, we uncover an…

Machine Learning · Computer Science 2023-10-31 Maksym Andriushchenko , Dara Bahri , Hossein Mobahi , Nicolas Flammarion

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been…

Machine Learning · Statistics 2018-01-03 Elad Hoffer , Itay Hubara , Daniel Soudry