The power of extra analog neuron

Abstract

In the effort to refine the analysis of computational power of neural nets between integer and rational weights we study a hybrid binary-state network with an extra analog unit. We introduce a finite automaton with a register which is shown to be computationally equivalent to such a network. The main result is a sufficient condition for a language accepted by this automaton to be regular which is based on the new concept of a quasi-periodic power series. These preliminary results suggest an interesting connection with the active research field on the expansions of numbers in non-integer bases which seems to be a fruitful area for further research including many important open problems.