Properties of Associative Memory Model with the β-th-order Synaptic Decay

概要

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Many associative memory models with synaptic decay such as the forgetting model and the zero-order decay model have been proposed and studied so far. The previous studies showed the relation between the storage capacity C and the synaptic decay coefficient α in each synaptic decay model. However, with the exceptions of a few studies, they did not compare the network retrieval performance between different synaptic decay models. We formulate the associative memory model with the β-th-order synaptic decay as an extension of the zero-order decay model. The parameter β denotes the synaptic decay order or the degree of the synaptic decay term, which enables us to compare the retrieval performance between different synaptic decay models. Using numerical simulations, we investigate the relation between the synaptic decay coefficient α and the storage capacity C of the network by varying the synaptic decay order β. The results show that the properties of the synaptic decay model are constant for a large decay order β. Moreover, we search the minimum β to avoid overloading and the optimal β to maximize the network retrieval performance. The minimum integer value of β to avoid overloading is -1. The optimal integer value of β to maximize the network retrieval performance is 1, i.e., the degree of the forgetting model, and the suboptimal integer β is 0, i.e., that of the zero-order synaptic decay model.