Learning Winner-take-all Competition Between Groups of Neurons in Lateral Inhibitory Networks

It has long been known that lateral inhibition in neural networks can lead to a winner-take-all competition, so that only a single neuron is active at a steady state. Here we show how to organize lateral inhibition so that groups of neurons compete to be active. Given a collection of poten(cid:173) tially overlapping groups, the inhibitory connectivity is set by a formula that can be interpreted as arising from a simple learning rule. Our analy(cid:173) sis demonstrates that such inhibition generally results in winner-take-all competition between the given groups, with the exception of some de(cid:173) generate cases. In a broader context, the network serves as a particular illustration of the general distinction between permitted and forbidden sets, which was introduced recently.