關(guān)于前饋多層神經(jīng)網(wǎng)絡(luò)多維函數(shù)逼近能力的一個(gè)定理
A NOVEL THEOREM ON THE MULTI-DIMENSIONAL FUNCTION APPROXIMATION ABILITY OF FEED FORWARD MULTI-LAYER NEURAL NETWORKS
-
摘要: 本文首次證明了前饋神經(jīng)網(wǎng)絡(luò)多維函數(shù)逼近能力的一個(gè)重要定理:當(dāng)隱層神經(jīng)元數(shù)目足夠多時(shí),其多維函數(shù)逼近能力與維數(shù)無關(guān).也就是說我們只需研究其一維函數(shù)逼近能力,所得的結(jié)論完全適合于多維情形,該定理大大簡化了前饋多層神經(jīng)網(wǎng)絡(luò)函數(shù)逼近問題的分析難度。本文還給出了該定理的一個(gè)應(yīng)用。Abstract: This paper presents a novel theorem on the multi-dimensional function approximation ability of feed forward multi-layer neural networks (FFMLNN), which states that the function approximation ability of FFMLNN is independent of the dimension of the function to be approximated when the number of the hidden units is sufficiently large. This theorem simplifies greatly the analysis of the function approximation ability of FFMLNN because one needs only to study the one dimensional function approximation ability of FFMLNN. An application of the proposed theorem is given.
-
韋崗,賀前華.神經(jīng)網(wǎng)絡(luò)模型學(xué)習(xí)及應(yīng)用,北京:電子工業(yè)出版社,1994，第三章.[2]Sam Kwong, Wei Gang, Ouyang Jing-zheng. Discrete utterance recognition based on nonlinear[3]model identification with single layer neural networks. Proc. IEEE Int. Conf. Circuits and Systems, USA:1993, 2419-2422.[4]Wei Gang, Ouyang Jing-zheng. On the bound of the approximation capacity of multi-layer neural[5]networks. Proc. Int. Joint. Conf. Neural Networks, Singapore:1991, 2299-2304.[6]Cybenko G. Approximation勿superposition of a sigmoidal function[J].Math. Control, Signals, Syst.1989, 2(4):303-314[7]Hartman E J, Keeler J D, Kowalski J M. Layered neural networks with Gaussian hidden units as universal approximations[J].Neural Comp.1991, 2(3):210-215[8]Hornik K. Approximation capacities of multilayer feedforward networks[J].Neural Networks.1991, 4(3):251-257[9]Park J, Sandberg I W. Universal approximation using radial-basis-function networks[J].Neural Comp.1991, 3(3):246-257[10]Park J, Sanberg I W. Approximation and radial-basis-function networks[J].Neural Comp.1993, 5(4):305-316 -
計(jì)量
- 文章訪問數(shù): 2471
- HTML全文瀏覽量: 117
- PDF下載量: 391
- 被引次數(shù): 0
下載:
