Coenen, Olivier
Coauthors(s): Olivier J.-M. D. Coenen *, Mike Arnold+, Terrence J. Sejnowski, Marwan A. Jabri- {olivier, terry}@salk.edu {mikea,marwan}@sedal.usyd.edu.au Computational Neurobiology Laboratory Howard Hughes Medical Institute Systems Neurobiology Laboratories The Salk Institute for Biological Studies 10010 North Torrey Pines Road La Jolla, CA 92037, USA *-+Computer Engineering Laboratory School of Electrical and Information Engineering Bldg. J03, University of Sydney Sydney, NSW 2006 Australia *Research on the Neuroscience of Autism Children's Hospital Research Center La Jolla, CA 92037, USA ^Department of Biology University of California, San Diego La Jolla, CA 92093, USA
San Diego Children's Hospital Research Center
Res. on the Neuroscience of Autism
Children's Hospital Research Center, Suite 201 8110 La Jolla Shores Dr., La Jolla, CA 92037
www.cnl.salk.edu/~olivier

A Hypothesis for Parallel Fiber Coding in a Cerebellar Model of Smooth Pursuit Eye Movement

Neural network models based on the anatomy and physiology of the cerebellum are presented. The models learn to generate predictive smooth pursuit eye movements to follow complex target trajectories, and respond to large tracking error by producing corrective saccades (Kettner et al., J. Neurophysiol. 1997). A novel and biologically motivated learning rule based on information theory controls the plasticity at the input layer of the cerebellum. The possibility that this unsupervised learning rule at the granule cell synapses of the cerebellum uncovers latent structures in their mossy fiber inputs is investigated. Using the unique convergence of the granule cells at the mossy fibers glomeruli, the learning rule approximates the emergence of a sparsely-distributed and statistically-independent code at the parallel fibers, in contrast with previous learning rules that only produce a decorrelated representation (Jonker et al., Network 1998; Foldiak, Biol. Cybern. 1990). Such a code is beneficial for learning downstream at the Purkinje cells: It simplifies the credit assignment problem between climbing and parallel fiber activities, while retaining the ability for generalization that binary codes or fixed synaptic weights used in many cerebellum models lack (Kettner et al., J. Neurophysiol. 1997; Spoelstra et al., Biol. Cybern. 2000). The credit assignment at the Purkinje cells is simplified in two ways: temporally due to the sparseness and spatially due to the statistical-independence of the parallel fibers firing. Simulations with two models of the cerebellum, a firing-rate model and a spiking model, are used to study the resulting representation at the parallel fibers and Purkinje cells. The performance and representations are compared to previous models (Kettner et al., 1997; Jonker et al., Network 1998) as well as to monkey data (Leung et al, J. Neurophysiol. 2000). The Purkinje cells, which receive on the order of 100 000 parallel fibers, axons of granule cells, face a difficult credit assignment problem in identifying which parallel fiber synapse must be modified in connection with climbing fiber activity. Cerebellum models often solve this problem by using thresholding together with a binary code to limit the number of active parallel fibers (Kettner et al., J. Neurophysiol. 1997). Often these models will have poorer generalization abilities than an analog code would. One way to keep the generalization benefits of an analog code and solve the credit assignment problem may be to use a sparsely-distributed (Field, Neural Comput. 1994) and statistically-independent representation in the parallel fibers. A sparsely-distributed code tends to minimize the time during which cells are active, and a statistically-independent representation minimizes the redundancy across active cells. Both properties reduce the complexity of the credit assignment between active parallel fibers and climbing fiber at a Purkinje cell. The emergence of these properties in the parallel fibers and their consequences on the emerging representation in Purkinje cells and performance in firing-rate based and spiking cerebellar models are investigated using predictive smooth pursuit of complex trajectories.