E. Fiesler, IDIAP, C.P. 592, CH-1920 Martigny, Switzerland, EFiesler@IDIAP.CH

In order to assist the field of neural networks in its maturing, a formalization and a solid foundation are essential. Additionally, to permit the introduction of formal proofs, it is essential to have an all encompassing formal mathematical definition of a neural network.

Most neural networks, even biological ones, exhibit a layered structure. This publication shows that all neural networks can be represented as layered structures. This layeredness is therefore chosen as the basis for a formal neural network framework. This publication offers a neural network formalization consisting of a topological taxonomy, a uniform nomenclature, and an accompanying consistent mnemonic notation. Supported by this formalization, both a flexible hierarchical and a universal mathematical definition are presented.

**Keywords:** (artificial) neural network, neural computing, neurocomputing,
connectionism, formalization, standardization, terminology, nomenclature,
definition, mnemonic notation, topological taxonomy, neural network statics