A geometrical analysis of the dynamics of associative memory

This paper proposes a geometrical method of analyzing associative memory models. The geometrical method has the following two features: first, the state transitions of the associative memory model are subdivided into a linear transformation part based on the connection weight matrix and a nonlinear transformation part based on the sign function ; second, a flow defined on the spherical surface is introduced. The flow consists of the dynamics on the spherical surface generated by the connection weight matrix and represents the dynamics of the model. The properties of the flow change suddenly when the memory exceeds a certain limit. This paper analyzes the relation of this change of flow and of the stability of the memorized vector itself. This paper shows that the geometrical method not only is effective in the analysis of the associative memory models, but also gives a good insight into ways of improving associative memory models and facilitates the understanding of the concept formation.

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