Multi-back-propagation Algorithm for Signal Neural Network Decomposition

In this paper, a novel back-propagation error technique is presented. This neural network structure allows for two fundamental basic modes: (1) To decompose the neurones by transforming their variables, weights, and scalar functions into vectors. This conveys for the decomposition of the transfer fu...

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Veröffentlicht in:Neural processing letters Jg. 56; H. 2; S. 100
Hauptverfasser: Salgado, Paulo, Perdicoúlis, T.-P. Azevedo
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 12.03.2024
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Artificial Intelligence
Back propagation
Back propagation networks
Brain research
Channels
Classification
Complex Systems
Computational Intelligence
Computer Science
Data analysis
Decomposition
Mathematical functions
Neural networks
Orthogonal functions
Orthogonality
Pattern analysis
Pattern recognition
Propagation
Transfer functions
Network decomposition
Back-propagation
Orthogonal decomposition
Fourier series
Multivariable neurone
Network splitting
Neural network training
ISSN:1573-773X, 1370-4621, 1573-773X
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Abstract In this paper, a novel back-propagation error technique is presented. This neural network structure allows for two fundamental basic modes: (1) To decompose the neurones by transforming their variables, weights, and scalar functions into vectors. This conveys for the decomposition of the transfer function of every neurone (where the output variables are the components of the decomposition) and, consequently, to be written as the invariant sum of orthogonal functions, with the safeguard of preserving information This orthogonality is proven using Fourier theory. (2) In a second mode, a tuned neural network that occupies one of the channels of the neural network can see the weights of its supplementary channels adjusted to retain additional information. Only the decomposition algorithm of the network is presented here—Multi-back-propagation algorithm. The adopted methodology is validated step-by-step with some representative examples. Namely, to assess the performance of the splitting method, two different examples have been constructed from scratch: (1) a 2D classification problem and (2) a 3D surface. In both problems, the signal and transfer functions of the neural network are successfully decomposed without information losses. Therefore, since the main contribution of this work is to allow for the organisation of the information stored in neural network structure, through a split process, this promising method shows potential use in various areas—e.g. classification and/or pattern recognition problems, data analysis, modelling and so on. In the future, we expect to work further in the method computational aspects to render it more efficient, versatile and robust.
AbstractList In this paper, a novel back-propagation error technique is presented. This neural network structure allows for two fundamental basic modes: (1) To decompose the neurones by transforming their variables, weights, and scalar functions into vectors. This conveys for the decomposition of the transfer function of every neurone (where the output variables are the components of the decomposition) and, consequently, to be written as the invariant sum of orthogonal functions, with the safeguard of preserving information This orthogonality is proven using Fourier theory. (2) In a second mode, a tuned neural network that occupies one of the channels of the neural network can see the weights of its supplementary channels adjusted to retain additional information. Only the decomposition algorithm of the network is presented here—Multi-back-propagation algorithm. The adopted methodology is validated step-by-step with some representative examples. Namely, to assess the performance of the splitting method, two different examples have been constructed from scratch: (1) a 2D classification problem and (2) a 3D surface. In both problems, the signal and transfer functions of the neural network are successfully decomposed without information losses. Therefore, since the main contribution of this work is to allow for the organisation of the information stored in neural network structure, through a split process, this promising method shows potential use in various areas—e.g. classification and/or pattern recognition problems, data analysis, modelling and so on. In the future, we expect to work further in the method computational aspects to render it more efficient, versatile and robust.
ArticleNumber 100
Author Perdicoúlis, T.-P. Azevedo
Salgado, Paulo
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  surname: Perdicoúlis
  fullname: Perdicoúlis, T.-P. Azevedo
  email: tazevedo@utad.pt
  organization: ISR, University of Coimbra & Department of Engineering, ECT, UTAD
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10.1017/CBO9781139165372
10.1016/j.aml.2012.03.007
10.55630/sjc.2023.17.1-16
10.1093/oso/9780198538493.001.0001
10.24963/ijcai.2021/351
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Keywords Network decomposition
Back-propagation
Orthogonal decomposition
Fourier series
Multivariable neurone
Network splitting
Neural network training
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SubjectTerms Algorithms
Approximation
Artificial Intelligence
Back propagation
Back propagation networks
Brain research
Channels
Classification
Complex Systems
Computational Intelligence
Computer Science
Data analysis
Decomposition
Mathematical functions
Neural networks
Orthogonal functions
Orthogonality
Pattern analysis
Pattern recognition
Propagation
Transfer functions
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