AppART: An ART Hybrid Stable Learning Neural Network for Universal Function Approximation

2002 ◽  
pp. 93-119 ◽  
Author(s):  
Luis Martí ◽  
Alberto Policriti ◽  
Luciano García
Keyword(s):  
Neural Network ◽  
Function Approximation ◽  
Universal Function ◽  
Stable Learning

Function approximation using a sinc neural network

1996 ◽  
Author(s):  
Wael R. Elwasif ◽  
Laurene V. Fausett
Keyword(s):  
Neural Network ◽  
Function Approximation

scholarly journals Chaos and complexity from quantum neural network. A study with diffusion metric in machine learning

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sayantan Choudhury ◽  
Ankan Dutta ◽  
Debisree Ray
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Quantum Chaos ◽  
Geometric Approach ◽  
Universal Function ◽  
Stochastic Gradient Descent ◽  
Generalization Capability ◽  
Steady State Condition ◽  
Quantum Neural Network ◽  
Function Approximator

Abstract In this work, our prime objective is to study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN). A Parameterized Quantum Circuits (PQCs) in the hybrid quantum-classical framework is introduced as a universal function approximator to perform optimization with Stochastic Gradient Descent (SGD). We employ a statistical and differential geometric approach to study the learning theory of QNN. The evolution of parametrized unitary operators is correlated with the trajectory of parameters in the Diffusion metric. We establish the parametrized version of Quantum Complexity and Quantum Chaos in terms of physically relevant quantities, which are not only essential in determining the stability, but also essential in providing a very significant lower bound to the generalization capability of QNN. We explicitly prove that when the system executes limit cycles or oscillations in the phase space, the generalization capability of QNN is maximized. Finally, we have determined the generalization capability bound on the variance of parameters of the QNN in a steady state condition using Cauchy Schwartz Inequality.

scholarly journals Kernel-blending connection approximated by a neural network for image classification

2020 ◽  
Vol 6 (4) ◽  
pp. 467-476
Author(s):  
Xinxin Liu ◽  
Yunfeng Zhang ◽  
Fangxun Bao ◽  
Kai Shao ◽  
Ziyi Sun ◽  
...  
Keyword(s):  
Neural Network ◽  
Image Classification ◽  
Function Approximation ◽  
Feature Space ◽  
Neural Network Learning ◽  
Network Learning ◽  
Hinge Loss ◽  
The Neural Network ◽  
Good Classification ◽  
Kernel Mapping

AbstractThis paper proposes a kernel-blending connection approximated by a neural network (KBNN) for image classification. A kernel mapping connection structure, guaranteed by the function approximation theorem, is devised to blend feature extraction and feature classification through neural network learning. First, a feature extractor learns features from the raw images. Next, an automatically constructed kernel mapping connection maps the feature vectors into a feature space. Finally, a linear classifier is used as an output layer of the neural network to provide classification results. Furthermore, a novel loss function involving a cross-entropy loss and a hinge loss is proposed to improve the generalizability of the neural network. Experimental results on three well-known image datasets illustrate that the proposed method has good classification accuracy and generalizability.

A CONSTRUCTIVE NEURAL NETWORK ALGORITHM FOR FUNCTION APPROXIMATION USING LOCALLY FIT SIGMOIDS

1998 ◽  
Vol 07 (03) ◽  
pp. 373-398
Author(s):  
TIM DRAELOS ◽  
DON HUSH
Keyword(s):  
Neural Network ◽  
Function Approximation ◽  
Piecewise Linear ◽  
Target Function ◽  
Approximation Problem ◽  
Sigmoidal Functions ◽  
Network Algorithm ◽  
Neural Network Algorithm ◽  
Training Error ◽  
Hidden Layer

A study of the function approximation capabilities of single hidden layer neural networks strongly motivates the investigation of constructive learning techniques as a means of realizing established error bounds. Learning characteristics employed by constructive algorithms provide ideas for development of new algorithms applicable to the function approximation problem. In addition, constructive techniques offer efficient methods for network construction and weight determination. The development of a novel neural network algorithm, the Constructive Locally Fit Sigmoids (CLFS) function approximation algorithm, is presented in detail. Basis functions of global extent (piecewise linear sigmoidal functions) are locally fit to the target function, resulting in a pool of candidate hidden layer nodes from which a function approximation is obtained. This algorithm provides a methodology of selecting nodes in a meaningful way from the infinite set of possibilities and synthesizes an n node single hidden layer network with empirical and analytical results that strongly indicate an O(1/n) mean squared training error bound under certain assumptions. The algorithm operates in polynomial time in the number of network nodes and the input dimension. Empirical results demonstrate its effectiveness on several multidimensional function approximate problems relative to contemporary constructive and nonconstructive algorithms.

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