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Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve…

Neural and Evolutionary Computing · Computer Science 2015-05-25 Ian J. Goodfellow , Oriol Vinyals , Andrew M. Saxe

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible…

Machine Learning · Computer Science 2022-11-15 Colin Ponce , Ruipeng Li , Christina Mao , Panayot Vassilevski

Overparameterized networks trained to convergence have shown impressive performance in domains such as computer vision and natural language processing. Pushing state of the art on salient tasks within these domains corresponds to these…

Machine Learning · Computer Science 2020-08-04 James O' Neill

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Machine Learning · Computer Science 2010-10-19 Sham M. Kakade , Shai Shalev-Shwartz , Ambuj Tewari

Conventional wisdom states that deep linear neural networks benefit from expressiveness and optimization advantages over a single linear layer. This paper suggests that, in practice, the training process of deep linear fully-connected…

Machine Learning · Computer Science 2022-06-10 Oriel BenShmuel

Pruning is a compression method which aims to improve the efficiency of neural networks by reducing their number of parameters while maintaining a good performance, thus enhancing the performance-to-cost ratio in nontrivial ways. Of…

Neural and Evolutionary Computing · Computer Science 2023-09-25 Hugo Tessier , Ghouti Boukli Hacene , Vincent Gripon

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

Deep learning has been wildly successful in practice and most state-of-the-art machine learning methods are based on neural networks. Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of…

Machine Learning · Statistics 2023-10-03 Rahul Parhi , Robert D. Nowak

Neural networks are more expressive when they have multiple layers. In turn, conventional training methods are only successful if the depth does not lead to numerical issues such as exploding or vanishing gradients, which occur less…

Machine Learning · Computer Science 2022-06-07 Carles Riera , Camilo Rey , Thiago Serra , Eloi Puertas , Oriol Pujol

In Machine Learning, Artificial Neural Networks (ANNs) are a very powerful tool, broadly used in many applications. Often, the selected (deep) architectures include many layers, and therefore a large amount of parameters, which makes…

Machine Learning · Computer Science 2022-06-29 Matteo Cacciola , Antonio Frangioni , Xinlin Li , Andrea Lodi

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

Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…

Machine Learning · Computer Science 2020-05-22 Michele Lombardi , Federico Baldo , Andrea Borghesi , Michela Milano

Large-scale supervised classification algorithms, especially those based on deep convolutional neural networks (DCNNs), require vast amounts of training data to achieve state-of-the-art performance. Decreasing this data requirement would…

Computer Vision and Pattern Recognition · Computer Science 2016-06-15 Maya Kabkab , Azadeh Alavi , Rama Chellappa

Current deep neural networks suffer from two problems; first, they are hard to interpret, and second, they suffer from overfitting. There have been many attempts to define interpretability in neural networks, but they typically lack…

Machine Learning · Computer Science 2019-08-15 Sean Tao

The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…

Optimization and Control · Mathematics 2024-05-06 Corrado Coppola , Lorenzo Papa , Marco Boresta , Irene Amerini , Laura Palagi

Much as replacing hand-designed features with learned functions has revolutionized how we solve perceptual tasks, we believe learned algorithms will transform how we train models. In this work we focus on general-purpose learned optimizers…

Machine Learning · Computer Science 2020-09-24 Luke Metz , Niru Maheswaranathan , C. Daniel Freeman , Ben Poole , Jascha Sohl-Dickstein

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

The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…

Machine Learning · Computer Science 2025-11-20 Jörg K. H. Franke , Urs Spiegelhalter , Marianna Nezhurina , Jenia Jitsev , Frank Hutter , Michael Hefenbrock

Efficiently executing convolutional neural nets (CNNs) is important in many machine-learning tasks. Since the cost of moving a word of data, either between levels of a memory hierarchy or between processors over a network, is much higher…

Data Structures and Algorithms · Computer Science 2018-04-25 James Demmel , Grace Dinh

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

Numerical Analysis · Mathematics 2020-06-09 Markus Haltmeier , Linh V. Nguyen