Bounds on the number of hidden neurons in three-layer binary neural networks
Zhang, ZZ; Ma, XM; Yang, YX
Source PublicationNEURAL NETWORKS
AbstractThis paper investigates an important problem concerning the complexity of three-layer binary neural networks (BNNs) with one hidden layer. The neuron in the studied BNNs employs a hard limiter activation function with only integer weights and an integer threshold. The studies are focused on implementations of arbitrary Boolean functions which map from {0,1}(n) into {0,1}. A deterministic algorithm called set covering algorithm (SCA) is proposed for the construction of a three-layer BNN to implement an arbitrary Boolean function. The SCA is based on a unit sphere covering (USC) of the Hamming space (HS) which is chosen in advance. It is proved that for the implementation of an arbitrary Boolean function of n-variables (n greater than or equal to 3) by using SCA, [3L/2] hidden neurons are necessary and sufficient, where L is the number of unit spheres contained in the chosen USC of the n-dimensional HS. It is shown that by using SCA, the number of hidden neurons required is much less than that by using a two-parallel hyperplane method. In order to indicate the potential ability of three-layer BNNs, a lower bound on the required number of hidden neurons which is derived by using the method of estimating the Vapnik-Chervonenkis (VC) dimension is also given. (C) 2003 Elsevier Science Ltd. All rights reserved.
Keywordthree-layer binary neural network Boolean function set covering algorithm unit sphere covering Hamming space weighted distance sphere
WOS Research AreaComputer Science
WOS SubjectComputer Science, Artificial Intelligence
WOS IDWOS:000185078700005
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Document Type期刊论文
Corresponding AuthorMa, XM
Affiliation1.Oral Roberts Univ, Engn & Phys Dept, Tulsa, OK 74171 USA
2.Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China
Recommended Citation
GB/T 7714
Zhang, ZZ,Ma, XM,Yang, YX. Bounds on the number of hidden neurons in three-layer binary neural networks[J]. NEURAL NETWORKS,2003,16(7):995-1002.
APA Zhang, ZZ,Ma, XM,&Yang, YX.(2003).Bounds on the number of hidden neurons in three-layer binary neural networks.NEURAL NETWORKS,16(7),995-1002.
MLA Zhang, ZZ,et al."Bounds on the number of hidden neurons in three-layer binary neural networks".NEURAL NETWORKS 16.7(2003):995-1002.
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