Department of Computer Science Colloquium
Thursday February 7th, 2002 4:15pm
Upson Hall B17
Spaces as a General Framework for the Understanding of Cognition
Cornell Department of Psychology
Experimental Epistemology Project
It has been proposed that evolutionary pressure causes certain physical characteristics of the world to become internalized by the brain (R. N. Shepard 1984; 2001). The generality of this approach to the understanding of cognition stems from the possibility of describing cognitive task domains in terms of abstract spaces. In color vision, for example, the relevant space is the low-dimensional linear manifold related through principal component analysis to the characteristics of natural illumination and surface reflectances; in shape vision, it is the very high-dimensional measurement space spanned by the system's front end (the retina), in which the low-dimensional nonlinear manifold generated by the motion of the viewed object with respect to the observer is embedded. It is useful to think about the internalized structure of the world as embodied, quite literally, in a neural space, whose topology and, to some extent, metrics, reflect the layout of the represented abstract spaces. The utility of geometric formalisms in theorizing about neural representation stems from the straightforward interpretation of patterns of activities defined over ensembles of neurons as points in a multidimensional space. In this talk, I shall (1) describe some of the computational tools that can be used to address crucial issues, such as dimensionality reduction, stemming from the geometric approach to representation, (2) present experimental data, psychophysical and neurophysiological, that support the idea of neural spaces, (3) offer several operational conclusions from the adoption of this theoretical stance, and (4) mention the main theoretical and experimental challenges it faces.