LORENTZIAN NEURAL NETS

We consider neural units whose response functions are Lorentzians rather than the usual sigmoids or steps. This consideration ir justified by the fact that neurons can be paired and that a suitable difference of the sigmoids of the paired neurons can create a window response function. Lorentzians are special cases of such windows and we take advantage of their simplicity to generate polynomial equations for several problems such as: i) fixed points of completely connected net, ii) classification of operational modes, iii) training of a feedforward net, iv) process signals represented by complex numbers.