Design of GBSB neural associative memories using semidefinite programming

This paper concerns reliable search for the optimally performing GBSB (generalized brain-state-in-a-box) neural associative memory given a set of prototype patterns to be stored as stable equilibrium points. First, we observe some new qualitative properties of the GBSB model. Next, we formulate the synthesis of GBSB neural associative memories as a constrained optimization problem. Finally, we convert the optimization problem into a semidefinite program (SDP), which can be solved efficiently by recently developed interior point methods. The validity of this approach is illustrated by a design example.