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The foundations of deep learning are supported by the seemingly opposing perspectives of approximation or learning theory. The former advocates for large/expressive models that need not generalize, while the latter considers classes that…

Machine Learning · Computer Science 2025-06-27 Ruiyang Hong , Anastasis Kratsios

Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However,…

Machine Learning · Computer Science 2016-12-06 Zhe Li , Boqing Gong , Tianbao Yang

Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…

Machine Learning · Computer Science 2022-09-20 R. Gentile , G. Welper

We explore techniques to significantly improve the compute efficiency and performance of Deep Convolution Networks without impacting their accuracy. To improve the compute efficiency, we focus on achieving high accuracy with extremely…

Machine Learning · Computer Science 2016-10-04 Ganesh Venkatesh , Eriko Nurvitadhi , Debbie Marr

Homomorphic encryption is one of the representative solutions to privacy-preserving machine learning (PPML) classification enabling the server to classify private data of clients while guaranteeing privacy. This work focuses on PPML using…

Cryptography and Security · Computer Science 2021-06-15 Junghyun Lee , Eunsang Lee , Joon-Woo Lee , Yongjune Kim , Young-Sik Kim , Jong-Seon No

We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the…

Machine Learning · Computer Science 2020-06-23 Guy Bresler , Dheeraj Nagaraj

We discuss the expressive power of neural networks which use the non-smooth ReLU activation function $\varrho(x) = \max\{0,x\}$ by analyzing the approximation theoretic properties of such networks. The existing results mainly fall into two…

Functional Analysis · Mathematics 2019-04-10 Felix Voigtlaender , Philipp Petersen

This work explores the neural network approximation capabilities for functions within the spectral Barron space $\mathscr{B}^s$, where $s$ is the smoothness index. We demonstrate that for functions in $\mathscr{B}^{1/2}$, a shallow neural…

Numerical Analysis · Mathematics 2025-07-10 Yulei Liao , Pingbing Ming , Hao Yu

In this paper, we propose a novel multi-task learning method based on the deep convolutional network. The proposed deep network has four convolutional layers, three max-pooling layers, and two parallel fully connected layers. To adjust the…

Machine Learning · Computer Science 2019-04-17 Fang Su , Hai-Yang Shang , Jing-Yan Wang

To accelerate DNNs inference, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank…

Computer Vision and Pattern Recognition · Computer Science 2020-01-27 Yuhui Xu , Yuxi Li , Shuai Zhang , Wei Wen , Botao Wang , Wenrui Dai , Yingyong Qi , Yiran Chen , Weiyao Lin , Hongkai Xiong

Deep convolutional neural networks contain tens of millions of parameters, making them impossible to work efficiently on embedded devices. We propose iterative approach of applying low-rank approximation to compress deep convolutional…

Computer Vision and Pattern Recognition · Computer Science 2019-11-18 Maksym Kholiavchenko

Neural networks are effective function approximators, but hard to train in the reinforcement learning (RL) context mainly because samples are correlated. For years, scholars have got around this by employing experience replay or an…

Machine Learning · Computer Science 2020-05-06 Budi Kurniawan , Peter Vamplew , Michael Papasimeon , Richard Dazeley , Cameron Foale

D-Adaptation is an approach to automatically setting the learning rate which asymptotically achieves the optimal rate of convergence for minimizing convex Lipschitz functions, with no back-tracking or line searches, and no additional…

Machine Learning · Computer Science 2023-07-11 Aaron Defazio , Konstantin Mishchenko

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

Optimization and Control · Mathematics 2020-02-27 V. Peiris , N. Sharon , N. Sukhorukova J. Ugon

We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…

Machine Learning · Computer Science 2021-04-08 Philipp Grohs , Felix Voigtlaender

This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…

Probability · Mathematics 2021-09-21 Côme Huré , Huyên Pham , Achref Bachouch , Nicolas Langrené

To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a…

Machine Learning · Computer Science 2020-05-01 Yuhui Xu , Yuxi Li , Shuai Zhang , Wei Wen , Botao Wang , Yingyong Qi , Yiran Chen , Weiyao Lin , Hongkai Xiong

In this paper, we study neural networks from the point of view of nonsmooth optimisation, namely, quasidifferential calculus. We restrict ourselves to the case of uniform approximation by a neural network without hidden layers, the…

Optimization and Control · Mathematics 2025-03-05 Vinesha Peiris , Nadezda Sukhorukova

Recently, dropout has seen increasing use in deep learning. For deep convolutional neural networks, dropout is known to work well in fully-connected layers. However, its effect in convolutional and pooling layers is still not clear. This…

Machine Learning · Computer Science 2015-12-02 Haibing Wu , Xiaodong Gu

In this paper, we prove the universal consistency of wide and deep ReLU neural network classifiers trained on the logistic loss. We also give sufficient conditions for a class of probability measures for which classifiers based on neural…

Machine Learning · Statistics 2024-02-01 Hyunouk Ko , Xiaoming Huo