Stuart Geman
Professor:
Applied Mathematics
Phone: +1 401 863 3088
Stuart_Geman
Brown.edu
Ph.D., Massachusetts Institute of Technology, 1977
What are the basic principles of representation and computation in the nervous system? Cognitive scientists have argued for a theory based upon compositionality, which refers to the evident ability of brains to represent objects, scenes, thoughts and actions in a hierarchical structure. I am studying a mathematical formulation for compositionality, and the implications of this formulation for interpreting neural activity patterns and for building computer vision systems.
Interests
Compositional Vision.
Compositionality refers to the ability of humans to represent entities as hierarchies of reusable parts. The parts themselves are meaningful entities and are reusable in a near-infinite assortment of meaningful combinations. Compositional hierarchies can be fitted with a probability distribution and used as prior models in a scene interpretation system.
Neural Representation.
Certain predictions about the nature of the neural code follow from the principle of compositionality. In particular, there must be a mechanism for rapidly and reversibly binding otherwise uncorrelated spatio-temporal patterns of neural activities. Evidence of binding may be present in the fine-temporal structure of neural discharges. Statistical methods are being devised for a systematic search for fine-temporal structure in stable multi-unit recordings.
Neural Modeling.
Common inputs to multiple neurons promote synchronous firing. And synchronous firing among presynaptic neurons promotes postsynaptic activity. Therefore, a neuron's activity reflects in part the extent of common active input to its active presynaptic neurons. Common active input is circumstantial and therefore carries information. I am exploring the hypothesis that the nervous system represents binding by commonality of inputs. The assumption is that all predicates can be reduced to the overlapping of representations of constituent parts. Overlapping generates common inputs, common inputs generate synchrony, and synchrony generates activity in selected postsynaptic neurons. Activity in these postsynaptic neurons thereby signals a composition of parts.
