|Title:||Cognition: Discrete or continuous computation?|
|Comment:||Commentary for Turing Centenary collection of Turing papers|
|Abstract:||If cognition is computation, we must ask, what are the primitive computational elements, and how do they map onto cognitive entities? For the cognitive faculty of conscious rule interpretation, the computational primitives are the symbol-manipulating operations of discrete computation, with individual symbols mapping onto individual concepts. Mechanism operates on meaningful elements. For intuitive cognition, the same holds---according to the symbolic paradigm of cognitive science. In the subsymbolic paradigm, however, the computational primitives are the numerical operations of continuous computation, and a concept corresponds to an entire vector. Mechanism operates on individual numbers, activation values, beneath the level of meaning. Subsymbolic computational reduces complex mental processes to simple brain processes. Vector space theory provides tools now widely used for conceptual interpretation of recorded activation patterns in the brain. Dynamical systems theory provides tools for interpreting subsymbolic computation as optimization. Applied to language, this leads to a theory of grammar in which what is universal is the optimality-defining criteria for evaluating the products of language processing---as opposed to the process of producing these representations, previously the subject matter of mainstream grammatical theory.
The universe of computation opened up to us by Turing includes not just the discrete class of architectures, but also the continuous class; not just symbolic, but also vectorial representation of concepts; the means to formalize grammatical knowledge not just as procedures for computation, but also as criteria for evaluating products of computation.
|Area/Keywords:||computation, cognitive architecture, neural networks|