Regularising neural networks using flexible multivariate activation function

This paper presents a new general neural structure based on nonlinear flexible multivariate function that can be viewed in the framework of the generalised regularisation net-works theory. The proposed architecture is based on multi-dimensional adaptive cubic spline basis activation function that collects information from the previous network layer in aggregate form. In other words, each activation function represents a spline function of a subset of previous layer outputs so the number of network connections (structural complexity) can be very low with respect to the problem complexity. A specific learning algorithm, based on the adaptation of local parameters of the activation function, is derived. This fact improve the network generalisation capabilities and speed up the convergence of the learning process. At last, some experimental results demonstrating the effectiveness of the proposed architecture, are presented. (C) 2003 Elsevier Ltd. All rights reserved.