Convergence property of topographic mapping formation from cell layer to cell layer through correlation learning rule
Convergence property of topographic mapping formation from cell layer to cell layer through correlation learning rule
复制标题
通过相关学习规则形成单元层到单元层地形图的收敛性
DOI：
10.1016/s0893-6080(00)00046-0
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Y. Kobuchi
中科院分区：
文献类型：
--
作者：
Shouji Sakamoto;Y. Kobuchi
为了阐明地形组织的机制，我们提出了一个简单的从一维细胞层到一维细胞层的地形制图形成模型。在我们的模型中，每个细胞都有一个二元状态值，我们考虑了几个学习原则，这些原则是Hebb规则的扩展。我们特别注意了一个相关学习规则，其中如果突触前和突触后细胞的状态值相同，则突触权重值会增加。首先，我们证明了在一定网络规模条件下，映射是稳定的，当且仅当它是地形的。其次，我们引入了一类特殊的权矩阵，称为带型权矩阵，并证明了带型权矩阵的集合是强闭的，这样的权矩阵不能产生地形映射。第三，我们证明了任何映射，如果它是由一个非带型权重矩阵定义的，收敛到一个地形映射。该证明方法在马尔可夫过程的框架内具有内在的组合性。
To elucidate the mechanism of topographic organization, we propose a simple topographic mapping formation model from one-dimensional cell layer to one-dimensional cell layer. In our model, each cell takes a binary state value and we consider several learning principles which are extensions of Hebb's rule. We pay special attention to a correlation learning rule where a synaptic weight value is increased if pre- and post-synaptic cells’ state values are the same. First, we show that under a certain network size condition, a mapping is stable with respect to the correlation learning if and only if it is topographic. 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 cannot yield a topographic mapping. Third, we show that any mapping, if it is defined by a non band type weight matrix, converges to a topographic mapping. The proof method is intrinsically of combinatorial nature in a framework of Markov process.