Design and analysis of a nonequilibrium cross-coupled network with a detectable similarity measure

In this paper, a nonequilibrium network which works as a dynamical associative memory is designed. The design is based on a new similarity measure between any stored pattern and a state of the network. Although conventional similarity measures, such as Hamming distance, direction cosine, and so on, are not detectable in a cross-coupled network, the similarity measure proposed in this paper is. The new similarity measure is employed in our design. The network should include the following properties in its output pattern sequence, so that the dynamics of cross-coupled network may be designed: 1) Stored patterns are frequently associated in the dynamical association. 2) The dynamical association is very robust against variation of distributed parameters. Property 1) is achieved by introducing the next two operation modes with inverse N-shaped function into the dynamics of the proposed network, 1) When the state of the network is close enough to a stored pattern at a time step, the state is forced to evolve at the next time step, 2) The state of the network converges to a stored one while it is not close to any stored patterns. By considering these two operation modes, the frequency of associating stored patterns is increased. The authors emphasize the property 2) which is very important for a silicon implementation of the proposed network. In the silicon implementation, parameters of the network must be represented by transistors, resistors, capacitors, and other electric components which exhibit variation in their characteristics. Thus the second property guarantees the easy silicon implementation of the nonequilibrium network proposed in this paper.