Bounds on the number of hidden neurons in three-layer binary neural networks
文献类型：期刊论文
| 作者 | Zhang, ZZ; Ma, XM; Yang, YX |
| 刊名 | NEURAL NETWORKS
 |
| 出版日期 | 2003-09-01 |
| 卷号 | 16期号:7页码:995-1002 |
| 关键词 | three-layer binary neural network Boolean function set covering algorithm unit sphere covering Hamming space weighted distance sphere |
| ISSN号 | 0893-6080 |
| DOI | 10.1016/S0893-6080(03)00006-6 |
| 英文摘要 | This 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. |
| WOS研究方向 | Computer Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000185078700005 |
| 出版者 | PERGAMON-ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/18391]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Ma, XM |
| 作者单位 | 1.Oral Roberts Univ, Engn & Phys Dept, Tulsa, OK 74171 USA 2.Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。