Auto Association And Traditional Application

When a known pattern p is entered, exactly this known pattern is returned. Thus,

a(p) = p,

With a being the associative this also works with inputs that are close to a pattern:

a(p ϵ) = p.

The auto associator is, in any case, in a stable state, namely in the state p. If the set of patterns P consists of, for example, letters or other characters in the form of pixels, the network will be able to correctly recognize deformed or noisy letters with high probability.

The primary fields of application of Hopfield networks are pattern recognition and pattern completion, such as the zip code recognition on letters in the eighties. But soon the Hopfield networks were replaced by other systems in most of their fields of application, for example by OCR systems in the field of letter recognition.

Today Hopfield networks are virtually no longer used, they have not become established in practice.