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Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…

Machine Learning · Statistics 2022-05-26 Vincent Szolnoky , Viktor Andersson , Balazs Kulcsar , Rebecka Jörnsten

Classical statistical learning theory predicts that overparameterized models should exhibit severe overfitting, yet modern deep neural networks with far more parameters than training samples consistently generalize well. This contradiction…

Machine Learning · Computer Science 2026-04-10 Zeran Johannsen

Regularization techniques such as L2 regularization (Weight Decay) and Dropout are fundamental to training deep neural networks, yet their underlying physical mechanisms regarding feature frequency selection remain poorly understood. In…

Machine Learning · Computer Science 2025-12-30 Jiahao Lu

Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…

Machine Learning · Computer Science 2019-01-21 Navid Azizan , Babak Hassibi

Several works have aimed to explain why overparameterized neural networks generalize well when trained by Stochastic Gradient Descent (SGD). The consensus explanation that has emerged credits the randomized nature of SGD for the bias of the…

Machine Learning · Computer Science 2021-02-24 Shengchao Liu , Dimitris Papailiopoulos , Dimitris Achlioptas

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

Modern machine learning models are often trained in a setting where the number of parameters exceeds the number of training samples. To understand the implicit bias of gradient descent in such overparameterized models, prior work has…

Machine Learning · Statistics 2025-10-29 Hannes Matt , Dominik Stöger

Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient…

Machine Learning · Computer Science 2022-07-20 David G. T. Barrett , Benoit Dherin

Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent…

Machine Learning · Computer Science 2018-11-20 Farzan Farnia , Jesse M. Zhang , David Tse

Understanding the implicit regularization imposed by neural network architectures and gradient based optimization methods is a key challenge in deep learning and AI. In this work we provide sharp results for the implicit regularization…

Machine Learning · Computer Science 2023-07-17 Johan S. Wind , Vegard Antun , Anders C. Hansen

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

Neural networks typically generalize well when fitting the data perfectly, even though they are heavily overparameterized. Many factors have been pointed out as the reason for this phenomenon, including an implicit bias of stochastic…

Machine Learning · Computer Science 2025-02-04 Amit Peleg , Matthias Hein

Spiking Neural Networks (SNNs) have attracted growing interest in both computational neuroscience and artificial intelligence, primarily due to their inherent energy efficiency and compact memory footprint. However, achieving adversarial…

Neural and Evolutionary Computing · Computer Science 2025-12-04 Luu Trong Nhan , Luu Trung Duong , Pham Ngoc Nam , Truong Cong Thang

Recently, there has been significant progress in understanding the convergence and generalization properties of gradient-based methods for training overparameterized learning models. However, many aspects including the role of small random…

Machine Learning · Computer Science 2023-07-04 Mahdi Soltanolkotabi , Dominik Stöger , Changzhi Xie

Regularization can mitigate the generalization gap between training and inference by introducing inductive bias. Existing works have already proposed various inductive biases from diverse perspectives. However, none of them explores…

Machine Learning · Computer Science 2022-11-02 Qiang Fu , Lun Du , Haitao Mao , Xu Chen , Wei Fang , Shi Han , Dongmei Zhang

Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…

Machine Learning · Computer Science 2019-10-23 Xinjie Lan , Kenneth E. Barner

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

For infinitesimal learning rates, stochastic gradient descent (SGD) follows the path of gradient flow on the full batch loss function. However moderately large learning rates can achieve higher test accuracies, and this generalization…

Machine Learning · Computer Science 2021-01-29 Samuel L. Smith , Benoit Dherin , David G. T. Barrett , Soham De

A leading hypothesis for the surprising generalization of neural networks is that the dynamics of gradient descent bias the model towards simple solutions, by searching through the solution space in an incremental order of complexity. We…

Machine Learning · Computer Science 2020-01-01 Daniel Gissin , Shai Shalev-Shwartz , Amit Daniely

Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rules of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the…

Machine Learning · Computer Science 2022-02-21 Tianxiang Gao , Hailiang Liu , Jia Liu , Hridesh Rajan , Hongyang Gao