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A unified framework for multilayer high order CNN
Author(s) -
Majorana Salvatore,
Chua Leon O.
Publication year - 1998
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/(sici)1097-007x(199811/12)26:6<567::aid-cta34>3.0.co;2-t
Subject(s) - ode , notation , ordinary differential equation , computer science , theoretical computer science , base (topology) , section (typography) , order (exchange) , topology (electrical circuits) , differential equation , algorithm , mathematics , arithmetic , combinatorics , mathematical analysis , finance , economics , operating system
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.