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Deep neural networks generalize well despite being exceedingly overparameterized and being trained without explicit regularization. This curious phenomenon has inspired extensive research activity in establishing its statistical principles:…

Machine Learning · Statistics 2021-09-16 Ke Wang , Christos Thrampoulidis

Logit regularization, the addition of a convex penalty directly in logit space, is widely used in modern classifiers, with label smoothing as a prominent example. While such methods often improve calibration and generalization, their…

Machine Learning · Statistics 2026-02-16 Alon Beck , Yohai Bar Sinai , Noam Levi

To learn and reason in the presence of uncertainty, the brain must be capable of imposing some form of regularization. Here we suggest, through theoretical and computational arguments, that the combination of noise with synchronization…

Neurons and Cognition · Quantitative Biology 2013-12-06 Jake Bouvrie , Jean-Jacques Slotine

Noise injection is a fundamental tool for data augmentation, and yet there is no widely accepted procedure to incorporate it with learning frameworks. This study analyzes the effects of adding or applying different noise models of varying…

Computer Vision and Pattern Recognition · Computer Science 2023-07-14 M. Eren Akbiyik

In this work, we investigate the use of sparsity-inducing regularizers during training of Convolution Neural Networks (CNNs). These regularizers encourage that fewer connections in the convolution and fully connected layers take non-zero…

Computer Vision and Pattern Recognition · Computer Science 2014-12-04 Maxwell D. Collins , Pushmeet Kohli

Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit…

Machine Learning · Computer Science 2019-10-29 Sanjeev Arora , Nadav Cohen , Wei Hu , Yuping Luo

Dropout-based regularization methods can be regarded as injecting random noise with pre-defined magnitude to different parts of the neural network during training. It was recently shown that Bayesian dropout procedure not only improves…

Machine Learning · Statistics 2017-11-07 Kirill Neklyudov , Dmitry Molchanov , Arsenii Ashukha , Dmitry Vetrov

Normalization techniques play an important role in supporting efficient and often more effective training of deep neural networks. While conventional methods explicitly normalize the activations, we suggest to add a loss term instead. This…

Machine Learning · Computer Science 2018-11-22 Etai Littwin , Lior Wolf

We construct custom regularization functions for use in supervised training of deep neural networks. Our technique is applicable when the ground-truth labels themselves exhibit internal structure; we derive a regularizer by learning an…

Computer Vision and Pattern Recognition · Computer Science 2018-04-09 Mohammadreza Mostajabi , Michael Maire , Gregory Shakhnarovich

Fast Gradient Sign Method (FGSM) is a popular method to generate adversarial examples that make neural network models robust against perturbations. Despite its empirical success, its theoretical property is not well understood. This paper…

Machine Learning · Statistics 2018-10-31 Chandler Zuo

Consistency regularization is a commonly-used technique for semi-supervised and self-supervised learning. It is an auxiliary objective function that encourages the prediction of the network to be similar in the vicinity of the observed…

Machine Learning · Computer Science 2021-10-05 Erik Englesson , Hossein Azizpour

Previous work has examined the ability of larger capacity neural networks to generalize better than smaller ones, even without explicit regularizers, by analyzing gradient based algorithms such as GD and SGD. The presence of noise and its…

Machine Learning · Computer Science 2020-05-27 Arushi Gupta

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…

Computer Vision and Pattern Recognition · Computer Science 2025-03-03 Zahra Kadkhodaie , Florentin Guth , Eero P. Simoncelli , Stéphane Mallat

The gradient noise of SGD is considered to play a central role in the observed strong generalization abilities of deep learning. While past studies confirm that the magnitude and the covariance structure of gradient noise are critical for…

Machine Learning · Computer Science 2020-06-22 Jingfeng Wu , Wenqing Hu , Haoyi Xiong , Jun Huan , Vladimir Braverman , Zhanxing Zhu

Stochastic regularisation is an important weapon in the arsenal of a deep learning practitioner. However, despite recent theoretical advances, our understanding of how noise influences signal propagation in deep neural networks remains…

Machine Learning · Statistics 2018-12-03 Arnu Pretorius , Elan Van Biljon , Steve Kroon , Herman Kamper

In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient…

Machine Learning · Computer Science 2022-10-21 Alberto Lanconelli , Christopher S. A. Lauria

The phenomenon of implicit regularization has attracted interest in recent years as a fundamental aspect of the remarkable generalizing ability of neural networks. In a nutshell, it entails that gradient descent dynamics in many neural…

Machine Learning · Computer Science 2024-02-28 Hong T. M. Chu , Subhro Ghosh , Chi Thanh Lam , Soumendu Sundar Mukherjee

Regularization plays an important role in generalization of deep neural networks, which are often prone to overfitting with their numerous parameters. L1 and L2 regularizers are common regularization tools in machine learning with their…

Machine Learning · Computer Science 2019-10-21 Dae Hoon Park , Chiu Man Ho , Yi Chang , Huaqing Zhang

Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…

Machine Learning · Computer Science 2026-03-17 Jonathan Wenger , Beau Coker , Juraj Marusic , John P. Cunningham

Deep neural networks (DNNs) experience significant performance degradation when processing noisy labels, primarily due to overfitting on mislabeled data. Current mainstream approaches attempt to mitigate this issue by passively filtering…

Computer Vision and Pattern Recognition · Computer Science 2026-05-21 Ningkang Peng , Jingyang Mao , Xiaoqian Peng , Peirong Ma , Xichen Yang , Weiguang Qu , Yanhui Gu
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