A hyperbolic multilayer perceptron

Abstract

We present a novel MLP-type neural network based on hyperbolic numbers $the hyperbolic multilayer perceptron (HMLP). The neurons of the HMLP compute 2D-hyperbolic orthogonal transformations as weight propagation functions. The HMLP can therefore be seen as the hyperbolic counterpart of the known complex MLP. The HMLP is proven to be a universal approximator. Furthermore, a suitable backpropagation algorithm for it is derived. It is shown by experiments that the HMLP can learn tasks with underlying hyperbolic properties much more accurately and efficiently than a complex MLP and an ordinary MLP.