ABSTRACT
One of the barriers to integrating connectionist and symbolic computation is the difficulty of representing recursive structure in a distributed fashion. Hinton (1990) discusses this problem and proposes a framework in which “reduced descriptions” are used to represent parts and wholes in a part-whole hierarchy. Hinton’s framework requires that a number of vectors, each a part and together forming a whole, be compressed (reduced) into a single vector of the same dimension as the original vectors. This reduced vector can in turn be used as a part in the representation of some greater whole. The reduction must be reversible so that one can move in both directions in a part-whole hierarchy, i.e., reduce a set of vectors to a single vector (a whole to a part), and expand a single vector to a set of vectors (a part to a whole). In this way, compositional structure can be represented. For reduced descriptions to be truly useful they should be systematically related to their components, so that information about the components can be gleaned from the reduced description without requiring its expansion. It is this property that distinguishes reduced descriptions from pointer-based methods for representing recursive structure, in which the pointer is the “reduced description” but is arbitrary and is unrelated to the components of the object it points to.
