Multiplicative Binding, Representation Operators & Analogy (Workshop Poster)
Abstract
Analogical inference depends on systematic substitution of the components of compositional structures. Simple systematic substitution has been achieved in a number of connectionist systems that support binding (the ability to create connectionist representations of the combination of component representations). These systems have used various implementations of two generic composition operators: bind() and bundle(). This paper introduces a novel implementation of the bind() operator that is simple, can be efficiently implemented, and highlights the relationship between retrieval queries and analogical mapping. A frame of role/filler bindings can easily be represented using bind() and bundle(). However, typical binding systems are unable to adequately represent multiple frames and arbitrary nested compositional structures. A novel family of representational operators (called braid()) is introduced to address these problems. Other binding systems make the strong assumption that the roles and fillers are disjoint in order to avoid ambiguities inherent in their representational idioms. The braid() operator can be used to avoid this assumption. The new representational idiom suggests how the cognitive processes of bottom-up and top-down object recognition might be implemented. These processes depend on analogical mapping to integrate disjoint representations and drive perceptual search.
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Multiplicative Binding, Representation Operators & Analogy (Workshop Poster)
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