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Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

Machine Learning · Statistics 2026-05-15 Hubert Leroux , Jean Marcus , Julien Roger

Recently, metric learning and similarity learning have attracted a large amount of interest. Many models and optimisation algorithms have been proposed. However, there is relatively little work on the generalization analysis of such…

Machine Learning · Computer Science 2013-03-19 Qiong Cao , Zheng-Chu Guo , Yiming Ying

Established approaches to obtain generalization bounds in data-driven optimization and machine learning mostly build on solutions from empirical risk minimization (ERM), which depend crucially on the functional complexity of the hypothesis…

Optimization and Control · Mathematics 2022-10-14 Yibo Zeng , Henry Lam

In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate. We consider the standard (non-periodic) DNNs as well as…

Numerical Analysis · Mathematics 2026-03-04 Alexander Keller , Frances Y. Kuo , Dirk Nuyens , Ian H. Sloan

Training of deep neural networks heavily depends on the data distribution. In particular, the networks easily suffer from class imbalance. The trained networks would recognize the frequent classes better than the infrequent classes. To…

Computer Vision and Pattern Recognition · Computer Science 2020-03-12 Byungju Kim , Junmo Kim

A key challenge facing deep learning is that neural networks are often not robust to shifts in the underlying data distribution. We study this problem from the perspective of the statistical concept of parameter identification.…

Machine Learning · Computer Science 2022-02-18 Kan Xu , Hamsa Bastani , Osbert Bastani

A main puzzle of deep neural networks (DNNs) revolves around the apparent absence of "overfitting", defined in this paper as follows: the expected error does not get worse when increasing the number of neurons or of iterations of gradient…

Machine Learning · Computer Science 2018-07-02 Tomaso Poggio , Qianli Liao , Brando Miranda , Andrzej Banburski , Xavier Boix , Jack Hidary

We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted…

Statistics Theory · Mathematics 2007-06-13 Yoav Freund , Yishay Mansour , Robert E. Schapire

Many fundamental machine learning tasks can be formulated as a problem of learning with vector-valued functions, where we learn multiple scalar-valued functions together. Although there is some generalization analysis on different specific…

Machine Learning · Computer Science 2021-04-30 Liang Wu , Antoine Ledent , Yunwen Lei , Marius Kloft

Algorithm-dependent generalization error bounds are central to statistical learning theory. A learning algorithm may use a large hypothesis space, but the limited number of iterations controls its model capacity and generalization error.…

Machine Learning · Computer Science 2017-07-20 Wenlong Mou , Liwei Wang , Xiyu Zhai , Kai Zheng

We propose a new bound for generalization of neural networks using Koopman operators. Whereas most of existing works focus on low-rank weight matrices, we focus on full-rank weight matrices. Our bound is tighter than existing norm-based…

Machine Learning · Computer Science 2024-03-19 Yuka Hashimoto , Sho Sonoda , Isao Ishikawa , Atsushi Nitanda , Taiji Suzuki

We carry out an information-theoretical analysis of a two-layer neural network trained from input-output pairs generated by a teacher network with matching architecture, in overparametrized regimes. Our results come in the form of bounds…

Machine Learning · Computer Science 2023-07-13 Francesco Camilli , Daria Tieplova , Jean Barbier

Recent results suggest that reinitializing a subset of the parameters of a neural network during training can improve generalization, particularly for small training sets. We study the impact of different reinitialization methods in several…

Machine Learning · Computer Science 2021-09-02 Ibrahim Alabdulmohsin , Hartmut Maennel , Daniel Keysers

This paper proposes a novel regularization approach to bias Convolutional Neural Networks (CNNs) toward utilizing edge and line features in their hidden layers. Rather than learning arbitrary kernels, we constrain the convolution layers to…

Computer Vision and Pattern Recognition · Computer Science 2024-10-23 Christoph Linse , Beatrice Brückner , Thomas Martinetz

A recently-proposed technique called self-adaptive training augments modern neural networks by allowing them to adjust training labels on the fly, to avoid overfitting to samples that may be mislabeled or otherwise non-representative. By…

Machine Learning · Computer Science 2020-06-16 Daniel Chiu , Franklyn Wang , Scott Duke Kominers

In recent years, several results in the supervised learning setting suggested that classical statistical learning-theoretic measures, such as VC dimension, do not adequately explain the performance of deep learning models which prompted a…

Machine Learning · Computer Science 2021-12-09 Pascal Mattia Esser , Leena Chennuru Vankadara , Debarghya Ghoshdastidar

Training deep neural networks results in strong learned representations that show good generalization capabilities. In most cases, training involves iterative modification of all weights inside the network via back-propagation. In Extreme…

Machine Learning · Computer Science 2018-02-06 Amir Rosenfeld , John K. Tsotsos

A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we…

While deep learning models and techniques have achieved great empirical success, our understanding of the source of success in many aspects remains very limited. In an attempt to bridge the gap, we investigate the decision boundary of a…

Neural and Evolutionary Computing · Computer Science 2019-01-03 Yu Li , Lizhong Ding , Xin Gao

This paper studies the approximation capacity of ReLU neural networks with norm constraint on the weights. We prove upper and lower bounds on the approximation error of these networks for smooth function classes. The lower bound is derived…

Machine Learning · Computer Science 2023-03-31 Yuling Jiao , Yang Wang , Yunfei Yang