STABILITY PROPERTIES OF LABELING RECURSIVE AUTOASSOCIATIVE MEMORY

Labeling recursive auto-associative memory (LRAAM) is an extension of the RAAM model by Pollack to obtain distributed reduced representation s of labeled directed graphs. In this paper some mathematical properti es of LRAAM are discussed, Specifically, sufficient conditions on the asymptotical stability of the decoding process along a cycle of the en coded structure are given, LRAAM can be transformed into an analog Hop field network with hidden units and an asymmetric connections matrix b y connecting the output units with the input units. In this architectu re encoded data can be accessed by content and different access proced ures can be defined depending on the access key, Each access procedure corresponds to a particular constrained version of the recurrent netw ork, We give sufficient conditions under which the property of asympto tical stability of a fixed point in one particular constrained version of the recurrent network can be extended to related fixed points in d ifferent constrained versions of the network. An example of encoding o f a labeled directed graph on which the theoretical results are applie d is given and discussed.