Functionally weighted neural networks: frugal models with high accuracy

In this article, we introduce the “functionally weighted neural network,” a new addition to the rich collection of artificial neural networks. Instead of a finite number of discrete nodes, we consider an infinite number of continuously distributed nodes. The weights assume a functional form, and the sum over the nodes becomes an integral. The gain is a significant reduction in the number of adjustable parameters, accompanied by an enhanced generalization performance. To quantitatively assess the quality of this new network, we have performed numerical experiments on a number of benchmark datasets. Comparison with state-of-the-art techniques reveals the advantages of the proposed method and emphasizes its modeling potential.