A Finite Size Scaling Investigation for Q-State Hopfield Models - Storage Capacity and Basins of Attraction

The storage capacity of a Q-state Hopfield network is determined via finite size scaling for parallel dynamics and Q 8. The results are in good agreement with theoretical predictions by H. Rieger [4]. The basins of attraction and other associative memory properties are discussed for Q = 4; 6. A self controlling Q-state model with improved basins of attraction is proposed. 1 Introduction Recently binary Hopfield networks [1] have been generalized to models, where the neuron behaviour is more diversified [2-7]. One side of this development wants to get us closer to biology where neurons possess a richer stucture than the formal binary neurons of Hopfield. On the other side the associative memory properties of more evolved models are important to be investigated for possible applications. Especially grey-level neurons could in principle be an interesting representation for the distributed processing of grey-tone data [4-6]. In this paper we show that for applications grey-level neurons ..