Representing part-whole relationships in recurrent neural networks

There is little consensus about the computational function of top-down synaptic connections in the visual system. Here we explore the hypothesis that top-down connections, like bottom-up connections, reflect part whole relationships. We analyze a recurrent network with bidirectional synaptic interactions between a layer of neurons representing parts and a layer of neurons representing wholes. Within each layer, there is lateral inhibition. When the network detects a whole, it can rigorously enforce part-whole relationships by ignoring parts that do not belong. The network can complete the whole by filling in missing parts. The network can refuse to recognize a whole, if the activated parts do not conform to a stored part-whole relationship. Parameter regimes in which these behaviors happen are identified using the theory of permitted and forbidden sets [3, 4]. The network behaviors are illustrated by recreating Rumelhart and McClelland's "interactive activation" model [7].