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Many machine learning algorithms have been developed under the assumption that data sets are already available in batch form. Yet in many application domains data is only available sequentially overtime via compute nodes in different…

Optimization and Control · Mathematics 2020-09-10 Alfredo Garcia , Luochao Wang , Jeff Huang , Lingzhou Hong

Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…

Optimization and Control · Mathematics 2021-06-08 Yong Sheng Soh , Venkat Chandrasekaran

We propose a novel regularization method, called \textit{volumization}, for neural networks. Inspired by physics, we define a physical volume for the weight parameters in neural networks, and we show that this method is an effective way of…

Machine Learning · Computer Science 2020-04-02 Liu Ziyin , Zihao Wang , Makoto Yamada , Masahito Ueda

We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…

Computer Vision and Pattern Recognition · Computer Science 2017-07-11 Marco Loog , François Lauze

Deep neural networks have achieved remarkable results across many language processing tasks, however these methods are highly sensitive to noise and adversarial attacks. We present a regularization based method for limiting network…

Computation and Language · Computer Science 2016-09-21 Yitong Li , Trevor Cohn , Timothy Baldwin

Dropout is a regularization technique widely used in training artificial neural networks to mitigate overfitting. It consists of dynamically deactivating subsets of the network during training to promote more robust representations. Despite…

Machine Learning · Statistics 2025-09-10 Francesco Mori , Francesca Mignacco

Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping…

Machine Learning · Computer Science 2025-03-05 Ali Hasan , Haoming Yang , Yuting Ng , Vahid Tarokh

Dropout is a very effective way of regularizing neural networks. Stochastically "dropping out" units with a certain probability discourages over-specific co-adaptations of feature detectors, preventing overfitting and improving network…

Neural and Evolutionary Computing · Computer Science 2017-08-04 Pietro Morerio , Jacopo Cavazza , Riccardo Volpi , Rene Vidal , Vittorio Murino

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

Numerical Analysis · Mathematics 2024-06-05 Martin Burger , Samira Kabri

The widespread use of diffusion models has led to an abundance of AI-generated data, raising concerns about model collapse -- a phenomenon in which recursive iterations of training on synthetic data lead to performance degradation. Prior…

Machine Learning · Computer Science 2025-12-29 Lianghe Shi , Meng Wu , Huijie Zhang , Zekai Zhang , Molei Tao , Qing Qu

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…

Machine Learning · Statistics 2023-01-02 Hongkang Yang

In this paper, we study the dynamics of temporal difference learning with neural network-based value function approximation over a general state space, namely, \emph{Neural TD learning}. We consider two practically used algorithms,…

Machine Learning · Computer Science 2021-08-09 Semih Cayci , Siddhartha Satpathi , Niao He , R. Srikant

Convolution neural networks have achieved remarkable performance in many tasks of computing vision. However, CNN tends to bias to low frequency components. They prioritize capturing low frequency patterns which lead them fail when suffering…

Machine Learning · Computer Science 2020-07-08 Weiyu Guo , Yidong Ouyang

How to extract more and useful information for single image super resolution is an imperative and difficult problem. Learning-based method is a representative method for such task. However, the results are not so stable as there may exist…

Image and Video Processing · Electrical Eng. & Systems 2020-03-25 Hu Liang , Shengrong Zhao

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…

Numerical Analysis · Mathematics 2025-11-12 Markus Juvonen , Bjørn Jensen , Ilmari Pohjola , Yiqiu Dong , Samuli Siltanen

We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…

Numerical Analysis · Mathematics 2020-10-02 Weinan E , Chao Ma , Lei Wu

Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…

Machine Learning · Statistics 2021-03-18 Zhenyu Liao , Romain Couillet

During the last decade, the deluge of multimedia data has impacted a wide range of research areas, including multimedia retrieval, 3D tracking, database management, data mining, machine learning, social media analysis, medical imaging, and…

Computer Vision and Pattern Recognition · Computer Science 2017-07-11 Lianli Gao , Jingkuan Song , Xingyi Liu , Junming Shao , Jiajun Liu , Jie Shao

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Machine Learning · Statistics 2016-10-18 Li Wang

Deep learning using multi-layer neural networks (NNs) architecture manifests superb power in modern machine learning systems. The trained Deep Neural Networks (DNNs) are typically large. The question we would like to address is whether it…

Computer Vision and Pattern Recognition · Computer Science 2016-07-05 Wei Pan , Hao Dong , Yike Guo