Generalized backpropagation algorithm for training second‐order neural networks

The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to second‐order counterparts, in which the linear operation between inputs to a neuron and the associated weights is repla...

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Published in:	International journal for numerical methods in biomedical engineering Vol. 34; no. 5; pp. e2956 - n/a
Main Authors:	Fan, Fenglei, Cong, Wenxiang, Wang, Ge
Format:	Journal Article
Language:	English
Published:	England Wiley Subscription Services, Inc 01.05.2018
Subjects:	Algorithms artificial neural network Artificial neural networks Back propagation backpropagation (BP) Fuzzy Logic Learning algorithms Machine Learning Mathematical models Neural networks Neural Networks (Computer) Neurons second‐order neurons artificial neural network second-order neurons backpropagation (BP)
ISSN:	2040-7939, 2040-7947, 2040-7947
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Abstract	The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to second‐order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear quadratic operation. A single second‐order neurons already have a strong nonlinear modeling ability, such as implementing basic fuzzy logic operations. In this paper, we develop a general backpropagation algorithm to train the network consisting of second‐order neurons. The numerical studies are performed to verify the generalized backpropagation algorithm. The main contribution of this paper is to propose deep neural networks consisting of quadratic artificial neurons and an associated generalized backpropagation algorithm and illustrate such networks with a number of examples. Interestingly, each quadratic neuron can be interpreted as a fuzzy logic gate, and a neural network of quadratic neurons can be naturally interpreted as a deep fuzzy logic system. Hence, we suggest to understand and develop quadratic neural networks in light of fuzzy logic theory and techniques for applications in which fuzzy logic is relevant.
AbstractList	The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to second-order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear quadratic operation. A single second-order neurons already have a strong nonlinear modeling ability, such as implementing basic fuzzy logic operations. In this paper, we develop a general backpropagation algorithm to train the network consisting of second-order neurons. The numerical studies are performed to verify the generalized backpropagation algorithm.The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to second-order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear quadratic operation. A single second-order neurons already have a strong nonlinear modeling ability, such as implementing basic fuzzy logic operations. In this paper, we develop a general backpropagation algorithm to train the network consisting of second-order neurons. The numerical studies are performed to verify the generalized backpropagation algorithm. The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to second‐order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear quadratic operation. A single second‐order neurons already have a strong nonlinear modeling ability, such as implementing basic fuzzy logic operations. In this paper, we develop a general backpropagation algorithm to train the network consisting of second‐order neurons. The numerical studies are performed to verify the generalized backpropagation algorithm. The main contribution of this paper is to propose deep neural networks consisting of quadratic artificial neurons and an associated generalized backpropagation algorithm and illustrate such networks with a number of examples. Interestingly, each quadratic neuron can be interpreted as a fuzzy logic gate, and a neural network of quadratic neurons can be naturally interpreted as a deep fuzzy logic system. Hence, we suggest to understand and develop quadratic neural networks in light of fuzzy logic theory and techniques for applications in which fuzzy logic is relevant. The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons could be upgraded to second‐order counterparts, in which the linear operation between inputs to a neuron and the associated weights is replaced with a nonlinear quadratic operation. A single second‐order neurons already have a strong nonlinear modeling ability, such as implementing basic fuzzy logic operations. In this paper, we develop a general backpropagation algorithm to train the network consisting of second‐order neurons. The numerical studies are performed to verify the generalized backpropagation algorithm.
Author	Cong, Wenxiang Wang, Ge Fan, Fenglei
Author_xml	– sequence: 1 givenname: Fenglei orcidid: 0000-0003-3691-5141 surname: Fan fullname: Fan, Fenglei organization: Rensselaer Polytechnic Institute – sequence: 2 givenname: Wenxiang surname: Cong fullname: Cong, Wenxiang organization: Rensselaer Polytechnic Institute – sequence: 3 givenname: Ge orcidid: 0000-0002-2656-7705 surname: Wang fullname: Wang, Ge email: wangg6@rpi.edu organization: Rensselaer Polytechnic Institute
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Snippet	The artificial neural network is a popular framework in machine learning. To empower individual neurons, we recently suggested that the current type of neurons...
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SubjectTerms	Algorithms artificial neural network Artificial neural networks Back propagation backpropagation (BP) Fuzzy Logic Learning algorithms Machine Learning Mathematical models Neural networks Neural Networks (Computer) Neurons second‐order neurons
Title	Generalized backpropagation algorithm for training second‐order neural networks
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