Capacity analysis of the asymptotically stable multi-valued exponential bidirectional associative memory

The exponential bidirectional associative memory (eBAM) has been proposed and proved to be a stable and high capacity associative neural network. However, the intrinsic structure and the evolution functions of this network restrict the representation of patterns to be either bipolar or binary vectors. We consider the promising development of multi-valued systems and then design a multi-valued discrete eBAM (MV-eBAM). The multi-valued eBAM has been proved to be asymptotically stable under certain constraints. Although MV-eBAM is also verified to possess high capacity by thorough simulations, there are important characteristics to be explored, including the absolute lower bound of the radix, and the approximate capacity. In order to estimate the capacity of the MV-eBAM, a modified evolution equation is also proposed. Hence, an analytic solution is derived. Besides, a radix searching algorithm is presented such that the absolute lower bound of the radix for this MV-eBAM can be found.