Stability of Topographic Mappings between Generalized Cell Layers

概要

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To elucidate the mechanism of topographic organization, we propose a simple topographic mapping formation model from generalized cell layer to generalized cell layer. Here generalized cell layer means that we consider arbitrary cell neigh-borhood relations. In our previous work we investigated a topographic mapping formation model between one dimensional cell layers. In this paper we extend the cell layer structure to any dimension. In our model, each cell takes a binary state value and we consider a class of learning principles which are extensions of Hebb's rule and Anti-Hebb's rule. We pay special attention to correlation type learning rules where a synaptic weight value is increased if pre and post synaptic cell states have the same value. We first show that a mapping is stable with respect to the correlational learning if and only if it is semi-embedding. Second, we introduce a special class of weight matrices called band type and show that the set of band type weight matrices is strongly closed and such a weight matrix can not yield a topographic mapping. Third, we show by computer simulations that a mapping, if it is defined by a non band type weight matrix, converges to a topographic mapping under the correlational learning rules.
一般社団法人電子情報通信学会の論文
2002-07-01