Rotor Associative Memory with a Periodic Activation Function

Complex-valued Associative Memory (CAM) can store multi-state patterns unlike Hopfield Associative Memory (HAM). CAM stores not only given training patterns but also many spurious patterns, such as their rotated patterns, at the same time. Rotor Associative Memory (RAM) can make the most of rotated patterns unstable but the reversed patterns remain stable. In the present work, we propose RAM with a Periodic Activation Function (PAF) to make the reversed patterns unstable. PAF is an activation function that Aizenberg introduced to CAM. We prove that RAM with a PAF has far fewer spurious patterns by using dynamic associative memories which can search the stored patterns.