Decision, Control and Optimization Seminar

Decision and Control Laboratory, Coordinated Science Laboratory

“Computing” in super-Turing function spaces reveals geometric relationships between structured systems

Professor Whitney Tabor

University of Connecticut, Psychology & Cognitive Science Dept.

Wednesday, April 11, 2012

3:00 PM to 4:00 PM

B02 CSL

Abstract
If learning is the gradual tuning of a system to its environment, then learning seems incompatible with complex mechanistic systems with mutually dependent parts. The system won’t function unless its pieces are all precisely in place, so how can it come into being gradually?   Human learning of recursive symbol systems (e.g., in natural and artificial languages) provides a case in point:  the mature systems are delicately balanced with mutual dependence among parts, but the evidence indicates that learning happens gradually.   Considering a class of iterated maps on complete metric spaces, I develop a formal framework for making sense of this situation.  Various loci in the parameter space are associated with familiar Turing Machine mechanisms (e.g., finite-state devices, stack machines) but many of the parameter settings are associated with noncomputable functions which fill in the continuum between the familiar structures.   The framework suggests a new way of thinking about the nature of a real system:  rather than viewing it as a noisy versions of an ideal device (that we typically want it to resemble), we can view it as being in metric and geometric relationships to multiple complex systems, which influence its behavior as a function of their proximity to it.  This approach shows promise of addressing challenging problems in the learning of complex structure from finite, noisy data.

Biography
Dr. Tabor has a BA in Mathematics from Middlebury College and a PhD in Linguistics from Stanford University.  He completed postdocs at the University of Rochester, MIT, and Cornell, before arriving at the University of Connecticut where he is now an Associate Professor of Psychology.  His initial work on the structural metamorphosis of grammar systems on a timescale of 10s to 100s of year segued into a focus on the flexibility of human language processing on timescales milliseconds to seconds.   He has employed a mixture text corpus analysis, human experimental work, computational modeling, and mathematical development, generally focused around the question of how new form comes into being.