Chen T, Chen H, Liu R W
Dept. of Math., Fudan Univ., Shanghai.
IEEE Trans Neural Netw. 1995;6(1):25-30. doi: 10.1109/72.363453.
In this paper, we investigate the capability of approximating functions in C(R (n)) by three-layered neural networks with sigmoidal function in the hidden layer. It is found that the boundedness condition on the sigmoidal function plays an essential role in the approximation, as contrast to continuity or monotonity condition. We point out that in order to prove the neural network in the n-dimensional case, all one needs to do is to prove the case for one dimension. The approximation in L(p)-norm (1<p<infinity) and some related problems are also discussed.
在本文中，我们研究了具有隐藏层中为Sigmoid函数的三层神经网络对(C(R(n)))中函数的逼近能力。结果发现，与连续性或单调性条件不同，Sigmoid函数的有界性条件在逼近中起着至关重要的作用。我们指出，为了证明(n)维情况下的神经网络，只需证明一维情况下的情况即可。还讨论了(L(p))范数（(1 < p < \infty)）下的逼近及一些相关问题。
