Cogprints

Multiplicative Binding, Representation Operators & Analogy (Workshop Poster)

Gayler, Ross W. (1998) Multiplicative Binding, Representation Operators & Analogy (Workshop Poster). [Preprint]

Full text available as:

[img]
Preview
 Postscript
240Kb
[img] Postscript
240Kb

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.

Item Type:Preprint
Keywords:analogy, analogical mapping, systematic substitution, connectionist, binding, role filler binding, vector representation, tensor representation, holographic reduced representation, spatter coding, reduced representation
Subjects:Psychology > Cognitive Psychology
Computer Science > Neural Nets
ID Code:502
Deposited By: Gayler, Dr Ross
Deposited On:30 Jul 1998
Last Modified:11 Mar 2011 08:54

References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

Blank, D., & Gasser, M. (1992). Grounding via scanning: cooking up roles from scratch. In Proceedings of the 1992 Midwest Artificial Intelligence and Cognitive Science Society Conference.

Cohen, P. R. (1998). Growing ontologies (Computer Science Technical Report 98-20). Amherst: University of Massachusetts, Computer Science Department.

Gentner, D. (1983). Structure-mapping: a theoretical framework for analogy. Cognitive Science, 7, 155-170.

Halford, G. S., Wilson, W. H., Guo, J., Gayler, R. W., Wiles, J., & Stewart, J. E. M. (1994). Connectionist Implications for Processing Capacity Limitations in Analogies. In K. J. Holyoak & J. A. Barnden (Eds.), Advances in connectionist and neural computation theory, Vol. 2: Analogical connections. Norwood, NJ: Ablex.

Hinton, G. E. (1990). Mapping part-whole hierarchies into connectionist networks. Artificial Intelligence, 46, 47-76.

Holyoak, K. J. & Thagard, P. (1989). Analogical mapping by constraint satisfaction. Cognitive Science, 13, 295-355.

Kanerva, P. (1997). Fully distributed representation. In Proceedings RWC Symposium 1997 (Tokyo, Japan), 358-365.

Plate, T. A. (1994). Distributed representations and nested compositional structure. Ph.D. thesis, Department of Computer Science, University of Toronto.

Smolensky, P. (1990). Tensor product variable binding and the representation of symbolic structures in connectionist systems. Artificial Intelligence, 46, 159-216.

Metadata

Repository Staff Only: item control page

Cogprints is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton. More information and software credits.