距离空间中的神经网络插值与逼近

Interpolation and Approximation by Neural Networks in Distance Space

已有的关于插值神经网络的研究大多是在欧氏空间中进行的,但实际应用中的许多问题往往需要用非欧氏尺度进行度量.本文研究一般距离空间中的神经网络插值与逼近问题,即先在距离空间中构造新的插值网络,然后在此基础上构造近似插值网络,最后研究近似插值网络对连续泛函的逼近.

There have been many studies on interpolation by neural networks in Euclidean spaces. However, there are plentiful concrete problems which must be measured by using non-Euclidean metrics. This paper deals with the interpolation and approximation of neural networks in general non-Euclidean spaces. That is, first construct interpolation networks in general spaces, and then construct approximate interpolation networks, finally, study the approximation of continuous functional with approximating network.