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.

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 potentially overlappinggroups, the inhibitory connectivity is set by a formula that can be interpreted as arising from a simple learning rule. Our analysis demonstratesthat such inhibition generally results in winner-take-all competition between the given groups, with the exception of some degenerate 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. From this viewpoint, the computational functionof our network is to store and retrieve memories as permitted setsof coactive neurons.

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 potentially overlapping groups, the inhibitory connectivity is set by a formula that can be interpreted as arising from a simple learning rule. Our analysis demonstrates that such inhibition generally results in winner-take-all competition between the given groups, with the exception of some degenerate 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.

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 potentially overlapping groups, the inhibitory connectivity is set by a formula that can be interpreted as arising from a simple learning rule. Our analysis demonstrates that such inhibition generally results in winner-take-all competition between the given groups, with the exception of some degenerate 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.