Fundamental Abilities of Rotor Associative Memory

Hopfield Associative Memory (HAM) is based on binary neurons, whereas Complex-valued Associative Memory (CAM) is based on the complex-valued neurons that can take multi-level states. Main models of the CAM are the continuous and discrete CAM. Rotor Associative Memory (RAM) is based on high-dimensional neurons. Especially 2-dimensional RAM includes the continuous CAM. It is known that the storage capacity of the 2-dimensional continuous RAM is approximately twice as large as that of the continuous CAM. The discrete RAM has been proposed by Kitahara et al. Moreover they proposed the chaotic RAM and showed that the RAM has far fewer spurious states than the CAM. But the fundamental abilities, such as storage capacity and noise robustness, have never been studied at all. In the present paper, they are investigated by computer simulations. The computer simulations will show that the storage capacity and noise robustness of the discrete RAM are better than those of the CAM. Moreover the ability to retrieve the phase changes is investigated. The CAM has an inherent property of rotation invariance so that it cannot retrieve the phase changes. The RAM does not have such property and can retrieve the phase changes.