On Some Stability Properties of the Lraam Model

In this report we discuss some mathematical properties of the LRAAM model. The LRAAM model is an extension of the RAAM model by Pollack. It allows one to obtain distributed reduced representations of labeled graphs. In particular, we give suucient conditions on the asymptotical stability of the decoding process along a cycle of the encoded structure. Data encoded in an LRAAM can also be accessed by content by transforming the LRAAM in an analog Hoppeld network with hidden units and asymmetric connection matrix (CA network.) Diierent access procedures can be deened according to the access key. Each access procedure corresponds to a particular constrained version of the CA network. We give suucient conditions under which the property of asymptotical stability of a xed point in one particular constrained version of the CA network can be extended to related xed points of diierent constrained versions of the CA network. An example of encoding of a labeled graph on which the theoretical results are applied is given as well.