A Trade-off between Memory Stability and Connection Sparsity in Simple Binary Associative Memories

Abstract

This letter studies a biobjective optimization problem in binary associative memories characterized by ternary connection parameters. First, we introduce a condition of parameters that guarantees storage of any desired memories and suppression of oscillatory behavior. Second, we define a biobjective problem based on two objectives that evaluate uniform stability of desired memories and sparsity of connection parameters. Performing precise numerical analysis for typical examples, we have clarified existence of a trade-off between the two objectives.