Translated Multiplicative Neuron: An Extended Multiplicative Neuron that can Translate Decision Surfaces

A multiplicative neuron model called translated multiplicative neuron (π_t-neuron) is proposed. Compared to the traditional π-neuron, the π_t-neuron presents 2 advantages: (1) it can generate decision surfaces centered at any point of its input space; and (2) π_t-neuron has a meaningful set of adjustable parameters. Learning rules for π_t-neurons are derived using the error backpropagation procedure. It is shown that the XOR and N-bit parity problems can be perfectly solved using only 1 π_t-neuron, with no need for hidden neurons. The π_t-neuron is also evaluated in Hwang’s regression benchmark problems, in which neural networks composed of π_t-neurons in the hidden layer can perform better than conventional multilayer perceptrons (MLP) in almost all cases: Errors are reduced an average of 58% using about 33% fewer hidden neurons than MLP.