Papers
Vector Symbolic Architectures answer Jackendoff's challenges for cognitive neuroscience
Gayler, R.W. (2003). Vector Symbolic Architectures answer Jackendoff’s challenges for cognitive neuroscience. In Peter Slezak (Ed.), ICCS/ASCS International Conference on Cognitive Science (pp. 133-138). Sydney, Australia: University of New South Wales.
Jackendoff (2002) posed four challenges that linguistic combinatoriality and rules of language present to theories of brain function. The essence of these problems is the question of how to neurally instantiate the rapid construction and transformation of the compositional structures that are typically taken to be the domain of symbolic processing. He contended that typical connectionist approaches fail to meet these challenges and that the dialogue between linguistic theory and cognitive neuroscience will be relatively unproductive until the importance of these problems is widely recognised and the challenges answered by some technical innovation in connectionist modelling. This paper claims that a little-known family of connectionist models (Vector Symbolic Architectures) are able to meet Jackendoff's challenges.
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Comment: Classifier technology and the illusion of progress - Credit scoring
Gayler, R.W. (2006). Comment: Classifier technology and the illusion of progress - Credit scoring. Statistical Science, 21(1), 19-23. Commentary on: Hand, D.J. (2006) "Classifier technology and the illusion of progress", Statistical Science, 21(1), 1-15.
These comments support Hand’s argument for the lack of practical progress in classifier technology by pursuing them a little deeper in the specific context of credit scoring. Academic development of modeling techniques tends to ignore the role of the practitioner and the impact of business objectives. In credit scoring it can be seen that the nature of the task forces practitioners to adopt modeling strategies that positively favor simple techniques or, at least, limit the possible advantage of sophisticated techniques. The strategies adopted by credit scorers can be viewed as a heuristic approach to inference of the unobserved (and unobservable) distribution of possible data sets. The technical progress examined by Hand has been aimed toward better goodness of fit. However, technical progress toward a more principled basis for inferring the distribution of future problem data would be more likely to be adopted in practice.
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“Lateral Inhibition” in a Fully Distributed Connectionist Architecture
Levy, S.D., & Gayler, R.W. (in press). "Lateral inhibition" in a fully distributed connectionist architecture. Proceedings of the Ninth International Conference on Cognitive Modeling (ICCM 2009).
We present a fully distributed connectionist architecture supporting lateral inhibition / winner-takes all competition. All items (individuals, relations, and structures) are represented by high-dimensional distributed vectors, and (multi)sets of items as the sum of such vectors. The architecture uses a neurally plausible permutation circuit to support a multiset intersection operation without decomposing the summed vector into its constituent items or requiring more hardware for more complex representations. Iterating this operation produces a vector in which an initially slightly favored item comes to dominate the others. This result (1) challenges the view that lateral inhibition calls for localist representation; and (2) points toward a neural implementation where more complex representations do not require more complex hardware.
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A distributed basis for analogical mapping
Levy, S.D., & Gayler, R.W. (in press). A distributed basis for analogical mapping. Proceedings of the Second International Analogy Conference (Analogy 09).
We are concerned with the practical feasibility of the neural basis of analogical mapping. All existing connectionist models of analogical mapping rely to some degree on localist representation (each concept or relation is represented by a dedicated unit/neuron). These localist solutions are implausible because they need too many units for human-level competence or require the dynamic re-wiring of networks on a sub-second time-scale.
Analogical mapping can be formalised as finding an approximate isomorphism between graphs representing the source and target conceptual structures. Connectionist models of analogical mapping implement continuous heuristic processes for finding graph isomorphisms. We present a novel connectionist mechanism for finding graph isomorphisms that relies on distributed, high-dimensional representations of structure and mappings. Consequently, it does not suffer from the problems of the number of units scaling combinatorially with the number of concepts or requiring dynamic network re-wiring.
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