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We present a simple regularization technique for Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM) units. Dropout, the most successful technique for regularizing neural networks, does not work well with RNNs and LSTMs. In…

Neural and Evolutionary Computing · Computer Science 2015-02-20 Wojciech Zaremba , Ilya Sutskever , Oriol Vinyals

Deep neural networks have become a staple in solving intricate problems, proving their mettle in a wide array of applications. However, their training process is often hampered by shifting activation distributions during backpropagation,…

Machine Learning · Computer Science 2024-09-10 Bilal Faye , Hanane Azzag , Mustapha Lebbah , Fangchen Fang

We propose a simple neural network model to deal with the domain adaptation problem in object recognition. Our model incorporates the Maximum Mean Discrepancy (MMD) measure as a regularization in the supervised learning to reduce the…

Computer Vision and Pattern Recognition · Computer Science 2016-07-28 Muhammad Ghifary , W. Bastiaan Kleijn , Mengjie Zhang

Solid results from Transformers have made them prevailing architectures in various natural language and vision tasks. As a default component in Transformers, Layer Normalization (LN) normalizes activations within each token to boost the…

Computer Vision and Pattern Recognition · Computer Science 2022-08-03 Qiming Yang , Kai Zhang , Chaoxiang Lan , Zhi Yang , Zheyang Li , Wenming Tan , Jun Xiao , Shiliang Pu

Current unsupervised anomaly localization approaches rely on generative models to learn the distribution of normal images, which is later used to identify potential anomalous regions derived from errors on the reconstructed images. However,…

Image and Video Processing · Electrical Eng. & Systems 2022-07-13 Julio Silva-Rodríguez , Valery Naranjo , Jose Dolz

In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…

Numerical Analysis · Mathematics 2025-11-21 Lan Wang , Qiao Zhu , Bangti Jin , Ye Zhang

From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models. However, the impressive generalization performance of neural networks…

Machine Learning · Computer Science 2021-02-09 Taejong Joo , Uijung Chung

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

The core challenge in unsupervised anomaly detection is identifying abnormal patterns without prior knowledge of their characteristics. While existing methods have addressed aspects of this problem, they often struggle to learn a robust…

Machine Learning · Computer Science 2026-05-12 Prithul Sarker , Sushmita Sarker , Nicholas G. Murray , Alireza Tavakkoli

We derive a new margin-based regularization formulation, termed multi-margin regularization (MMR), for deep neural networks (DNNs). The MMR is inspired by principles that were applied in margin analysis of shallow linear classifiers, e.g.,…

Machine Learning · Computer Science 2020-09-15 Berry Weinstein , Shai Fine , Yacov Hel-Or

In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…

Numerical Analysis · Mathematics 2021-04-15 Babak Maboudi Afkham , Julianne Chung , Matthias Chung

Normalization techniques have only recently begun to be exploited in supervised learning tasks. Batch normalization exploits mini-batch statistics to normalize the activations. This was shown to speed up training and result in better…

Machine Learning · Computer Science 2017-03-08 Mengye Ren , Renjie Liao , Raquel Urtasun , Fabian H. Sinz , Richard S. Zemel

Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks.…

Machine Learning · Computer Science 2021-11-17 Weiyang Liu , Rongmei Lin , Zhen Liu , Li Xiong , Bernhard Schölkopf , Adrian Weller

Continual learning of deep neural networks is a key requirement for scaling them up to more complex applicative scenarios and for achieving real lifelong learning of these architectures. Previous approaches to the problem have considered…

Machine Learning · Computer Science 2020-06-25 Jary Pomponi , Simone Scardapane , Vincenzo Lomonaco , Aurelio Uncini

In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal…

Machine Learning · Computer Science 2024-02-21 Elena Agliari , Francesco Alemanno , Miriam Aquaro , Alberto Fachechi

Batch Normalization (BN) improves both convergence and generalization in training neural networks. This work understands these phenomena theoretically. We analyze BN by using a basic block of neural networks, consisting of a kernel layer, a…

Machine Learning · Computer Science 2019-04-25 Ping Luo , Xinjiang Wang , Wenqi Shao , Zhanglin Peng

Recently, model-driven deep learning unrolls a certain iterative algorithm of a regularization model into a cascade network by replacing the first-order information (i.e., (sub)gradient or proximal operator) of the regularizer with a…

Machine Learning · Computer Science 2021-12-24 Zhuo-Xu Cui , Jing Cheng , Qingyong Zhu , Yuanyuan Liu , Sen Jia , Kankan Zhao , Ziwen Ke , Wenqi Huang , Haifeng Wang , Yanjie Zhu , Dong Liang

We present a novel optimization strategy for training neural networks which we call "BitNet". The parameters of neural networks are usually unconstrained and have a dynamic range dispersed over all real values. Our key idea is to limit the…

Machine Learning · Computer Science 2018-11-20 Aswin Raghavan , Mohamed Amer , Sek Chai , Graham Taylor

Overfitting is one of the most critical challenges in deep neural networks, and there are various types of regularization methods to improve generalization performance. Injecting noises to hidden units during training, e.g., dropout, is…

Machine Learning · Computer Science 2017-11-10 Hyeonwoo Noh , Tackgeun You , Jonghwan Mun , Bohyung Han

Regularization plays a vital role in the context of deep learning by preventing deep neural networks from the danger of overfitting. This paper proposes a novel deep learning regularization method named as DL-Reg, which carefully reduces…

Machine Learning · Computer Science 2020-11-05 Maryam Dialameh , Ali Hamzeh , Hossein Rahmani