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The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Numerical Analysis · Mathematics 2023-08-23 Ziad Aldirany , Régis Cottereau , Marc Laforest , Serge Prudhomme

Batch normalization (BN) is a popular and ubiquitous method in deep learning that has been shown to decrease training time and improve generalization performance of neural networks. Despite its success, BN is not theoretically well…

Machine Learning · Computer Science 2022-01-21 Susanna Lange , Kyle Helfrich , Qiang Ye

Label noise may affect the generalization of classifiers, and the effective learning of main patterns from samples with noisy labels is an important challenge. Recent studies have shown that deep neural networks tend to prioritize the…

Machine Learning · Computer Science 2019-12-06 Yi Sun , Yan Tian , Yiping Xu , Jianxiang Li

We propose a new regularization method to alleviate over-fitting in deep neural networks. The key idea is utilizing randomly transformed training samples to regularize a set of sub-networks, which are originated by sampling the width of the…

Computer Vision and Pattern Recognition · Computer Science 2020-10-14 Taojiannan Yang , Sijie Zhu , Chen Chen

In this work, we propose a simple yet effective meta-learning algorithm in semi-supervised learning. We notice that most existing consistency-based approaches suffer from overfitting and limited model generalization ability, especially when…

Machine Learning · Computer Science 2021-03-18 Xin-Yu Zhang , Taihong Xiao , Haolin Jia , Ming-Ming Cheng , Ming-Hsuan Yang

Although application examples of multilevel optimization have already been discussed since the 1990s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine…

Optimization and Control · Mathematics 2021-10-27 Ryo Sato , Mirai Tanaka , Akiko Takeda

Recently deep neural networks have been successfully used for various classification tasks, especially for problems with massive perfectly labeled training data. However, it is often costly to have large-scale credible labels in real-world…

Machine Learning · Computer Science 2019-01-15 Mingxiao An , Yongzhou Chen , Qi Liu , Chuanren Liu , Guangyi Lv , Fangzhao Wu , Jianhui Ma

An open question in the Deep Learning community is why neural networks trained with Gradient Descent generalize well on real datasets even though they are capable of fitting random data. We propose an approach to answering this question…

Machine Learning · Computer Science 2020-02-26 Satrajit Chatterjee

In this paper we introduce a novel method of gradient normalization and decay with respect to depth. Our method leverages the simple concept of normalizing all gradients in a deep neural network, and then decaying said gradients with…

Machine Learning · Computer Science 2018-03-01 Robert Kwiatkowski , Oscar Chang

We study gradient-based regularization methods for neural networks. We mainly focus on two regularization methods: the total variation and the Tikhonov regularization. Applying these methods is equivalent to using neural networks to solve…

Machine Learning · Computer Science 2022-11-09 Lingfeng Li , Xue-Cheng Tai , Jiang Yang

Learning meaningful representations using deep neural networks involves designing efficient training schemes and well-structured networks. Currently, the method of stochastic gradient descent that has a momentum with dropout is one of the…

Machine Learning · Computer Science 2016-01-15 Taehoon Lee , Minsuk Choi , Sungroh Yoon

We introduce a general theoretical framework, designed for the study of gradient optimisation of deep neural networks, that encompasses ubiquitous architecture choices including batch normalisation, weight normalisation and skip…

Machine Learning · Computer Science 2023-12-05 Lachlan Ewen MacDonald , Jack Valmadre , Hemanth Saratchandran , Simon Lucey

Neural network models and deep models are one of the leading and state of the art models in machine learning. Most successful deep neural models are the ones with many layers which highly increases their number of parameters. Training such…

Machine Learning · Computer Science 2018-07-17 Soufiane Belharbi

This paper formalizes the binarization operations over neural networks from a learning perspective. In contrast to classical hand crafted rules (\eg hard thresholding) to binarize full-precision neurons, we propose to learn a mapping from…

Computer Vision and Pattern Recognition · Computer Science 2020-10-13 Kai Han , Yunhe Wang , Yixing Xu , Chunjing Xu , Enhua Wu , Chang Xu

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

The current deep learning model is of a single-grade, that is, it learns a deep neural network by solving a single nonconvex optimization problem. When the layer number of the neural network is large, it is computationally challenging to…

Machine Learning · Computer Science 2023-02-02 Yuesheng Xu

We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…

Machine Learning · Computer Science 2019-10-04 Wonpyo Park , Paul Hongsuck Seo , Bohyung Han , Minsu Cho

Despite their massive size, successful deep artificial neural networks can exhibit a remarkably small difference between training and test performance. Conventional wisdom attributes small generalization error either to properties of the…

Machine Learning · Computer Science 2017-02-28 Chiyuan Zhang , Samy Bengio , Moritz Hardt , Benjamin Recht , Oriol Vinyals

Training a deep neural network with noisy labels could reduce data annotation cost but may introduce noise into the learned model. In meta label correction approaches, an additional meta model besides the main model is trained with a small,…

Machine Learning · Computer Science 2026-05-19 Ba Hoang Anh Nguyen , Viet Cuong Ta

Deep learning systems are known to exhibit implicit regularization (alt. implicit bias), favoring simple solutions instead of merely minimizing the loss function. In some cases, we can analytically derive the implicit regularization --…

Machine Learning · Statistics 2026-05-08 Joseph H. Rudoler , Kevin Tan , Giles Hooker , Konrad P. Kording