## ABSTRACT

Although some arguments supporting the biomimetic approach to artificial neural networks were given in subsection 2.2.4 of Chapter 2, this chapter strengthens the case for biomimetic neural networks (BNNs). In order to de- fine a truly biomimetic neural network, one requires some knowledge of biological neural networks. It is for this reason that the introduction and first section of this chapter are devoted to acquaint the reader with some basic background of biological neural networks.

Section 8.2 defines the lattice-based biomimetic neural network. Here, “lattice-based” refers to the computational processes that take place at the dendritic receptors of the postsynaptic neurons. Some of the major differences between the current ANNs and the BNNs introduced in this chapter can be summarized as follows:

A biomimetic neuron has dendrites that are capable of doing low-level computations.

A biomimetic neuron can have multiple synaptic sites for the terminal axonal branches of a single presynaptic neuron.

The number of neurons in a hidden layer as well, as the number of synaptic sites and the axonal structures, are not preset but are grown during the learning process.

Another major difference is due to Theorem 8.1 which proves that if X
_{1}, …, X_{k}
is a collection of mutually disjoint and compact subsets of Euclidean n-space, then there exists a positive number δ such that for any E > 0, with E < δ, there exists a single-layer BNN with k output neurons that for any i, with 1 i k, assigns every point of X_{i}
to class C_{i}
and no point x of Euclidean n-space to C_{i}
if the distance from x to X_{i}
is greater than E. The chapter concludes with some very simple examples of BNNs.