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A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…

Numerical Analysis · Mathematics 2020-04-29 Yous van Halder , Benjamin Sanderse , Barry Koren

Deep neural networks have attained remarkable success across diverse classification tasks. Recent empirical studies have shown that deep networks learn features that are linearly separable across classes. However, these findings often lack…

Machine Learning · Computer Science 2026-03-20 Alec S. Xu , Can Yaras , Peng Wang , Qing Qu

Existing Bayesian treatments of neural networks are typically characterized by weak prior and approximate posterior distributions according to which all the weights are drawn independently. Here, we consider a richer prior distribution in…

Machine Learning · Statistics 2018-10-02 Theofanis Karaletsos , Peter Dayan , Zoubin Ghahramani

It has been observed \citep{zhang2016understanding} that deep neural networks can memorize: they achieve 100\% accuracy on training data. Recent theoretical results explained such behavior in highly overparametrized regimes, where the…

Machine Learning · Computer Science 2019-09-27 Rong Ge , Runzhe Wang , Haoyu Zhao

Although deep neural networks are highly effective, their high computational and memory costs severely challenge their applications on portable devices. As a consequence, low-bit quantization, which converts a full-precision neural network…

Computer Vision and Pattern Recognition · Computer Science 2019-12-02 Jiwei Yang , Xu Shen , Jun Xing , Xinmei Tian , Houqiang Li , Bing Deng , Jianqiang Huang , Xiansheng Hua

This paper proposes an architecture for deep neural networks with hidden layer branches that learn targets of lower hierarchy than final layer targets. The branches provide a channel for enforcing useful information in hidden layer which…

Neural and Evolutionary Computing · Computer Science 2016-09-27 Abhinav Tushar

Layer-sequential unit-variance (LSUV) initialization - a simple method for weight initialization for deep net learning - is proposed. The method consists of the two steps. First, pre-initialize weights of each convolution or inner-product…

Machine Learning · Computer Science 2016-02-22 Dmytro Mishkin , Jiri Matas

With the proliferation of mobile devices and the Internet of Things, deep learning models are increasingly deployed on devices with limited computing resources and memory, and are exposed to the threat of adversarial noise. Learning deep…

Computer Vision and Pattern Recognition · Computer Science 2021-12-30 Xian Wei , Yanhui Huang , Yangyu Xu , Mingsong Chen , Hai Lan , Yuanxiang Li , Zhongfeng Wang , Xuan Tang

We develop a new quantum neural network layer designed to run efficiently on a quantum computer but that can be simulated on a classical computer when restricted in the way it entangles input states. We first ask how a classical neural…

Quantum Physics · Physics 2020-11-26 Roberto Bondesan , Max Welling

Recent results in nonparametric regression show that for deep learning, i.e., for neural network estimates with many hidden layers, we are able to achieve good rates of convergence even in case of high-dimensional predictor variables,…

Statistics Theory · Mathematics 2019-12-12 Alina Braun , Michael Kohler , Adam Krzyzak

While transferring a pretrained language model, common approaches conventionally attach their task-specific classifiers to the top layer and adapt all the pretrained layers. We investigate whether one could make a task-specific selection on…

Computation and Language · Computer Science 2022-10-20 Shuo Xie , Jiahao Qiu , Ankita Pasad , Li Du , Qing Qu , Hongyuan Mei

The exponential growth in numbers of parameters of neural networks over the past years has been accompanied by an increase in performance across several fields. However, due to their sheer size, the networks not only became difficult to…

Machine Learning · Computer Science 2022-02-18 Nils Koster , Oliver Grothe , Achim Rettinger

The subject of deep learning has recently attracted users of machine learning from various disciplines, including: medical diagnosis and bioinformatics, financial market analysis and online advertisement, speech and handwriting recognition,…

Machine Learning · Computer Science 2018-03-12 Charles K. Chui , Shao-Bo Lin , Ding-Xuan Zhou

According to conventional neural network theories, the feature of single-hidden-layer feedforward neural networks(SLFNs) resorts to parameters of the weighted connections and hidden nodes. SLFNs are universal approximators when at least the…

Neural and Evolutionary Computing · Computer Science 2014-05-08 Yimin Yang , Q. M. Jonathan Wu , Guangbin Huang , Yaonan Wang

To what extent is the success of deep visualization due to the training? Could we do deep visualization using untrained, random weight networks? To address this issue, we explore new and powerful generative models for three popular deep…

Computer Vision and Pattern Recognition · Computer Science 2016-06-17 Kun He , Yan Wang , John Hopcroft

Neural networks with random weights appear in a variety of machine learning applications, most prominently as the initialization of many deep learning algorithms and as a computationally cheap alternative to fully learned neural networks.…

Machine Learning · Computer Science 2022-11-29 Sjoerd Dirksen , Martin Genzel , Laurent Jacques , Alexander Stollenwerk

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

Machine Learning · Computer Science 2016-03-01 Yixuan Li , Jason Yosinski , Jeff Clune , Hod Lipson , John Hopcroft

This paper presents an algorithm for analytically calculating the weights and thresholds of convolutional neural networks (CNNs) without using standard training procedures. The algorithm enables the determination of CNN parameters based on…

Computer Vision and Pattern Recognition · Computer Science 2025-05-29 Polad Geidarov

We exploit a recently derived inversion scheme for arbitrary deep neural networks to develop a new semi-supervised learning framework that applies to a wide range of systems and problems. The approach outperforms current state-of-the-art…

Machine Learning · Statistics 2017-11-15 Randall Balestriero , Vincent Roger , Herve G. Glotin , Richard G. Baraniuk

The existence of local minima for one-hidden-layer ReLU networks has been investigated theoretically in [8]. Based on the theory, in this paper, we first analyze how big the probability of existing local minima is for 1D Gaussian data and…

Machine Learning · Computer Science 2020-06-17 Bo Liu
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