Stability properties of labeling recursive auto-associative memory

Labeling recursive auto-associative memory (LRAAM) is an extension of the RAAM model by Pollack (1990) to obtain distributed reduced representations of labeled directed graphs. In this paper some mathematical properties of LRAAM are discussed. Specifically, sufficient conditions on the asymptotical stability of the decoding process along a cycle of the encoded structure are given. LRAAM can be transformed into an analog Hopfield network with hidden units and an asymmetric connections matrix by connecting the output units with the input units. In this architecture encoded data can be accessed by content and different access procedures can be defined depending on the access key. Each access procedure corresponds to a particular constrained version of the recurrent network. The authors give sufficient conditions under which the property of asymptotical stability of a fixed point in one particular constrained version of the recurrent network can be extended to related fixed points in different constrained versions of the network. An example of encoding of a labeled directed graph on which the theoretical results are applied is given and discussed