# 3

# Associative neural networks

## 3.1 BASIC CIRCUITS

### 3.1.1 The associative function

Association is one of the basic mechanisms of cognition. Association connects two entities with each other so that one of these entities may be evoked by the other one. The entities to be associated with each other may be represented by signals and arrays of signals' signal vectors. An algorithm or a device that associates signals or signal vectors with each other is called an associator. An associative memory associates two vectors with each other so that the presentation of the first vector will evoke the second vector. In an autoassociative memory the evoking vector is a part of the evoked vector. In a heteroassociative memory the associated vectors are arbitrary. ‘Associative learning’ refers to mechanisms and algorithms that execute association automatically when certain criteria are met. In the following, artificial neurons and neuron groups for the association of signal vectors are considered.

### 3.1.2 Basic neuron models

The McCulloch–Pitts neuron (McCulloch and Pitts, 1943) is generally considered as the historical starting point for artificial neural networks. The McCulloch–Pitts neuron is a computational unit that accepts a number of signals *x*(*i*) as inputs, multiplies each of these with a corresponding weight value *w*(*i*) and sums these products together. This sum value is then compared to a threshold value and an output signal *y* is generated if the sum value exceeds the threshold value. The McCulloch–Pitts ...