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We study the properties of alignment, a form of implicit regularization, in linear neural networks under gradient descent. We define alignment for fully connected networks with multidimensional outputs and show that it is a natural…

Machine Learning · Computer Science 2020-06-18 Adityanarayanan Radhakrishnan , Eshaan Nichani , Daniel Bernstein , Caroline Uhler

Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target…

Machine Learning · Computer Science 2022-05-04 Kensuke Nakamura , Bong-Soo Sohn , Kyoung-Jae Won , Byung-Woo Hong

Handling the ever-increasing scale of contemporary deep learning and transformer-based models poses a significant challenge. Overparameterized Transformer networks outperform prior art in Natural Language processing and Computer Vision.…

Machine Learning · Computer Science 2024-11-05 Soheil Zibakhsh Shabgahi , Mohammad Sohail Shariff , Farinaz Koushanfar

Dropout is a regularisation technique in neural network training where unit activations are randomly set to zero with a given probability \emph{independently}. In this work, we propose a generalisation of dropout and other multiplicative…

Machine Learning · Statistics 2019-09-24 Beyrem Khalfaoui , Joseph Boyd , Jean-Philippe Vert

The regularization and output consistency behavior of dropout and layer-wise pretraining for learning deep networks have been fairly well studied. However, our understanding of how the asymptotic convergence of backpropagation in deep…

Machine Learning · Computer Science 2017-02-23 Vamsi K Ithapu , Sathya N Ravi , Vikas Singh

Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE),…

Machine Learning · Computer Science 2020-06-29 Viktor Oganesyan , Alexandra Volokhova , Dmitry Vetrov

Contrary to most machine learning models, modern deep artificial neural networks typically include multiple components that contribute to regularization. Despite the fact that some (explicit) regularization techniques, such as weight decay…

Computer Vision and Pattern Recognition · Computer Science 2020-11-13 Alex Hernández-García , Peter König

The paper presents a novel, principled approach to train recurrent neural networks from the Reservoir Computing family that are robust to missing part of the input features at prediction time. By building on the ensembling properties of…

Machine Learning · Computer Science 2017-05-09 Davide Bacciu , Francesco Crecchi , Davide Morelli

Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical…

Machine Learning · Computer Science 2025-09-24 Steffen Schotthöfer , H. Lexie Yang , Stefan Schnake

In convolutional neural network (CNN), dropout cannot work well because dropped information is not entirely obscured in convolutional layers where features are correlated spatially. Except randomly discarding regions or channels, many…

Computer Vision and Pattern Recognition · Computer Science 2021-03-30 Tianshu Xie , Minghui Liu , Jiali Deng , Xuan Cheng , Xiaomin Wang , Ming Liu

This paper shows that dropout training in Generalized Linear Models is the minimax solution of a two-player, zero-sum game where an adversarial nature corrupts a statistician's covariates using a multiplicative nonparametric…

Machine Learning · Statistics 2021-04-15 Jose Blanchet , Yang Kang , Jose Luis Montiel Olea , Viet Anh Nguyen , Xuhui Zhang

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Machine Learning · Computer Science 2023-11-08 Edith Heiter , Robin Vandaele , Tijl De Bie , Yvan Saeys , Jefrey Lijffijt

Recently, the training with adversarial examples, which are generated by adding a small but worst-case perturbation on input examples, has been proved to improve generalization performance of neural networks. In contrast to the individually…

Machine Learning · Computer Science 2017-09-19 Sungrae Park , Jun-Keon Park , Su-Jin Shin , Il-Chul Moon

Deep neural networks often consist of a great number of trainable parameters for extracting powerful features from given datasets. On one hand, massive trainable parameters significantly enhance the performance of these deep networks. On…

Machine Learning · Computer Science 2020-02-26 Yehui Tang , Yunhe Wang , Yixing Xu , Boxin Shi , Chao Xu , Chunjing Xu , Chang Xu

Dropout is an effective strategy for the regularization of deep neural networks. Applying tabu to the units that have been dropped in the recent epoch and retaining them for training ensures diversification in dropout. In this paper, we…

In this paper we explore the relation between distributionally robust learning and different forms of regularization to enforce robustness of deep neural networks. In particular, starting from a concrete min-max distributionally robust…

Optimization and Control · Mathematics 2022-03-29 Camilo Garcia Trillos , Nicolas Garcia Trillos

Deep convolutional neural networks have shown remarkable performance on various computer vision tasks, and yet, they are susceptible to picking up spurious correlations from the training signal. So called `shortcuts' can occur during…

Computer Vision and Pattern Recognition · Computer Science 2022-09-21 Mobarakol Islam , Ben Glocker

We provide a general framework for studying recurrent neural networks (RNNs) trained by injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as discretizations of stochastic differential equations driven by…

Machine Learning · Statistics 2021-12-02 Soon Hoe Lim , N. Benjamin Erichson , Liam Hodgkinson , Michael W. Mahoney

Underpinning the success of deep learning is effective regularizations that allow a variety of priors in data to be modeled. For example, robustness to adversarial perturbations, and correlations between multiple modalities. However, most…

Machine Learning · Computer Science 2020-06-16 Mao Li , Yingyi Ma , Xinhua Zhang

Mixup is a popular regularization technique for training deep neural networks that improves generalization and increases robustness to certain distribution shifts. It perturbs input training data in the direction of other randomly-chosen…

Machine Learning · Computer Science 2023-10-10 Kristjan Greenewald , Anming Gu , Mikhail Yurochkin , Justin Solomon , Edward Chien