On the thermodynamics of associative recall of structured patterns within a given context

Abstract

Within a thermodynamic approach we study the associative recall of structured patterns, e.g. complex impressions composed of auditory and visual components, or words consisting of various letters. These words can be recognized either without context, i.e. letter by letter in an independent way, or they can be put into context by favouring a certain percentage of preferred letter combinations (“meaningful” words) in the Hamiltonian. Particular emphasis is put on the question, under which conditions the system can recognize the preferred words in an improved way without loosing the quality of retrieval of the remaining arbitrary letter combinations. For two-letter words we find a phase diagram depending on three parameters, i.e. the temperatureT, the ratio α between the number of letters within the alphabet and the number of neurons, and the enhancement parameter λ for the preferred combinations. This phase diagram is very rich, e.g. for a given α and 0<λ<1, below a critical temperatureT ₂(λ) one can recognize both the preferred words and-with somewhat reduced error tolerance-also any arbitrary letter combination, whereas forT ₂(λ)<T<T ₁(λ) only the preferred words can be recognized. For λ<0 the role of preferred and non-preferred combinations is interchanged.