Artificial neural networks with adaptive multidimensional spline activation functions

This work concerns a new kind of neural structure that involves a multidimensional adaptive activation function. The proposed architecture, based on multi-dimensional cubic spline, allows to collect information from the previous network layer in aggregate form. In other words the number of network connections (structural complexity) can be very low respect to the problem complexity. This fact, as experimentally demonstrated in the paper, improve the network generalization capabilities and speed up the convergence of the learning process. A specific learning algorithm is derived and experimental results, demonstrate the effectiveness of the proposed architecture.