A unified framework for multilayer high order CNN

We propose a unified notation for representing any CNN topology. The framework presented here is an attempt to provide a common base for the future development of more general CNN structures, such as multilayer and/or high-order CNNs, which have already been of great interest in many disciplines including 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 derive a vector of ordinary differential equations (ODE) which can be used for mathematical analysis and for computer simulation of the CNN; in the second part (Section 4) some examples show how multilayer structures are required to solve hard learning problems such as the parity problem. © 1998 John Wiley & Sons, Ltd.