A unified framework for multilayer high order CNN

We propose a unified notation for representing any CNN topology. The framew ork presented here is an attempt to provide a common base for the future de velopment of more general CNN structures, such as multilayer and/or high-or der CNNs, which have already been of great interest in many disciplines inc luding biology, chemistry, ecology, physics, etc. The paper is divided in two parts: first (Sections 1-3) it is shown how to cast any CNN structure into a so called 'compact form', from which we can d erive a vector of ordinary differential equations (ODE) which can be used f or mathematical analysis and for computer simulation of the CNN; in the sec ond part (Section 4) some examples show how multilayer structures are requi red to solve hard learning problems such as the parity problem. (C) 1998 Jo hn Wiley & Sons, Ltd.