Representing Part-Whole Relationships in Recurrent Neural….pdfVIP

Representing Part-Whole Relationships in Recurrent Neural Networks 2 1,2 1,2 Viren Jain , Valentin Zhigulin , and H. Sebastian Seung 1Howard Hughes Medical Institute and 2Brain Cog. Sci. Dept., MIT viren@mit.edu, valentin@mit.edu, seung@mit.edu Abstract There is little consensus about the computational function of top-down synaptic connections in the visual system. Here we explore the hypoth- esis 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 net- work 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 be- haviors 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]. In neural network models of visual object recognition [2, 6, 8], patterns of synaptic con- nectivity often reflect part-whole relationships between the features that are represented by neurons. For example, the connections of Figure 1 reflect the fact that feature B both contains simpler