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This paper explores the complexity of deep feedforward networks with linear pre-synaptic couplings and rectified linear activations. This is a contribution to the growing body of work contrasting the representational power of deep and…

Machine Learning · Computer Science 2014-02-17 Razvan Pascanu , Guido Montufar , Yoshua Bengio

Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals. However, training them to capture fine details in multi-scale signals is difficult and…

Machine Learning · Computer Science 2022-10-06 Sifan Wang , Hanwen Wang , Jacob H. Seidman , Paris Perdikaris

Benefiting from the joint learning of the multiple tasks in the deep multi-task networks, many applications have shown the promising performance comparing to single-task learning. However, the performance of multi-task learning framework is…

Computer Vision and Pattern Recognition · Computer Science 2019-11-11 Zuheng Ming , Junshi Xia , Muhammad Muzzamil Luqman , Jean-Christophe Burie , Kaixing Zhao

The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable physics-informed neural network consisting of neural networks…

Numerical Analysis · Mathematics 2025-07-08 Vasiliy A. Es'kin , Alexey O. Malkhanov , Mikhail E. Smorkalov

The paper discusses the capabilities of multilayer perceptron neural networks implementing metric recognition methods, for which the values of the weights are calculated analytically by formulas. Comparative experiments in training a neural…

Machine Learning · Computer Science 2025-06-02 Polad Geidarov

We propose a new computationally efficient method for quantizing the weights of pre- trained neural networks that is general enough to handle both multi-layer perceptrons and convolutional neural networks. Our method deterministically…

Machine Learning · Computer Science 2021-08-17 Eric Lybrand , Rayan Saab

The choice of architecture of a neural network influences which functions will be realizable by that neural network and, as a result, studying the expressiveness of a chosen architecture has received much attention. In ReLU neural networks,…

Machine Learning · Computer Science 2024-12-18 Natalie Brownlowe , Christopher R. Cornwell , Ethan Montes , Gabriel Quijano , Grace Stulman , Na Zhang

It is well known that Artificial Neural Networks are universal approximators. The classical result proves that, given a continuous function on a compact set on an n-dimensional space, then there exists a one-hidden-layer feedforward network…

Machine Learning · Computer Science 2020-07-23 Rocio Gonzalez-Diaz , Miguel A. Gutiérrez-Naranjo , Eduardo Paluzo-Hidalgo

Recent Progress has shown that exploitation of hidden layer neurons in convolution neural networks incorporating with a carefully designed activation function can yield better classification results in the field of computer vision. The…

Computer Vision and Pattern Recognition · Computer Science 2018-07-10 Zhi Chen , Pin-han Ho

In this paper, we study 1-bit convolutional neural networks (CNNs), of which both the weights and activations are binary. While efficient, the lacking of representational capability and the training difficulty impede 1-bit CNNs from…

Computer Vision and Pattern Recognition · Computer Science 2019-09-05 Zechun Liu , Wenhan Luo , Baoyuan Wu , Xin Yang , Wei Liu , Kwang-Ting Cheng

Deep neural networks (DNNs) are quantized for efficient inference on resource-constrained platforms. However, training deep learning models with low-precision weights and activations involves a demanding optimization task, which calls for…

Machine Learning · Computer Science 2021-05-25 Ziang Long , Penghang Yin , Jack Xin

Restricted Boltzmann Machines are simple yet powerful neural networks. They can be used for learning structure in data, and are used as a building block of more complex neural architectures. At the same time, their simplicity makes them…

Disordered Systems and Neural Networks · Physics 2025-01-09 Giovanni di Sarra , Barbara Bravi , Yasser Roudi

Interpreting neural networks is a crucial and challenging task in machine learning. In this paper, we develop a novel framework for detecting statistical interactions captured by a feedforward multilayer neural network by directly…

Machine Learning · Statistics 2018-02-28 Michael Tsang , Dehua Cheng , Yan Liu

Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…

Machine Learning · Computer Science 2016-05-03 Ewout van den Berg

Learning automatically the best activation function for the task is an active topic in neural network research. At the moment, despite promising results, it is still difficult to determine a method for learning an activation function that…

Machine Learning · Computer Science 2019-10-29 Andrea Apicella , Francesco Isgrò , Roberto Prevete

We present a method for constructing a special type of shallow neural network that learns univariate meromorphic functions with pole-type singularities. Our method is based on using a finite set of Laurent coefficients as input information,…

Numerical Analysis · Mathematics 2025-09-15 Nadiia Derevianko , Ioannis G. Kevrekidis , Felix Dietrich

The activation functions are fundamental to neural networks as they introduce non-linearity into data relationships, thereby enabling deep networks to approximate complex data relations. Existing efforts to enhance neural network…

Machine Learning · Computer Science 2024-09-26 Jiayu Li , Zilong Zhao , Kevin Yee , Uzair Javaid , Biplab Sikdar

Activation functions play a vital role in the training of Convolutional Neural Networks. For this reason, to develop efficient and performing functions is a crucial problem in the deep learning community. Key to these approaches is to…

Computer Vision and Pattern Recognition · Computer Science 2020-09-23 Gianluca Maguolo , Loris Nanni , Stefano Ghidoni

While the optimization problem behind deep neural networks is highly non-convex, it is frequently observed in practice that training deep networks seems possible without getting stuck in suboptimal points. It has been argued that this is…

Machine Learning · Computer Science 2017-06-14 Quynh Nguyen , Matthias Hein

We demonstrate that, hidden within one-layer randomly weighted neural networks, there exist subnetworks that can achieve impressive performance, without ever modifying the weight initializations, on machine translation tasks. To find…

Computation and Language · Computer Science 2021-09-10 Sheng Shen , Zhewei Yao , Douwe Kiela , Kurt Keutzer , Michael W. Mahoney