Using a million cell simulation of the cerebellum: Network scaling and task generality

Several factors combine to make it feasible to build computer simulations of the cerebellum and to test them in biologically realistic ways. These simulations can be used to help understand the computational contributions of various cerebellar components, including the relevance of the enormous number of neurons in the granule cell layer. In previous work we have used a simulation containing 12000 granule cells to develop new predictions and to account for various aspects of eyelid conditioning, a form of motor learning mediated by the cerebellum. Here we demonstrate the feasibility of scaling up this simulation to over one million granule cells using parallel graphics processing unit (GPU) technology. We observe that this increase in number of granule cells requires only twice the execution time of the smaller simulation on the GPU. We demonstrate that this simulation, like its smaller predecessor, can emulate certain basic features of conditioned eyelid responses, with a slight improvement in performance in one measure. We also use this simulation to examine the generality of the computation properties that we have derived from studying eyelid conditioning. We demonstrate that this scaled up simulation can learn a high level of performance in a classic machine learning task, the cart-pole balancing task. These results suggest that this parallel GPU technology can be used to build very large-scale simulations whose connectivity ratios match those of the real cerebellum and that these simulations can be used guide future studies on cerebellar mediated tasks and on machine learning problems.

[1]  David Willshaw,et al.  The cerebellum as a neuronal machine , 1999 .

[2]  Stephen Grossberg,et al.  A neural model of timed response learning in the cerebellum , 1994, Neural Networks.

[3]  M. Mauk,et al.  Simulations of Cerebellar Motor Learning: Computational Analysis of Plasticity at the Mossy Fiber to Deep Nucleus Synapse , 1999, The Journal of Neuroscience.

[4]  Douglas R. Wylie,et al.  More on climbing fiber signals and their consequence(s) , 1996 .

[5]  M. Mauk,et al.  Pharmacological analysis of cerebellar contributions to the timing and expression of conditioned eyelid responses , 1998, Neuropharmacology.

[6]  E. J. Morris,et al.  Visual motion processing and sensory-motor integration for smooth pursuit eye movements. , 1987, Annual review of neuroscience.

[7]  R. F. Thompson,et al.  Cerebellum: essential involvement in the classically conditioned eyelid response. , 1984, Science.

[8]  J. W. Moore,et al.  Conditioned response timing and integration in the cerebellum. , 1997, Learning & memory.

[9]  S. Lisberger,et al.  The Cerebellum: A Neuronal Learning Machine? , 1996, Science.

[10]  J. Steinmetz,et al.  Dorsal accessory inferior olive activity diminishes during acquisition of the rabbit classically conditioned eyelid response , 1991, Brain Research.

[11]  J Szentágothai,et al.  Quantitative histological analysis of the cerebellar cortex in the cat. 3. Structural organization of the molecular layer. , 1971, Brain research.

[12]  J Szentágothai,et al.  Quantitative histological analysis of the cerebellar cortex in the cat. II. Cell numbers and densities in the granular layer. , 1971, Brain research.

[13]  T. Miles,et al.  Climbing fiber lesions disrupt conditioning of the nictitating membrane response in the rabbit , 1986, Brain Research.

[14]  D. Kleinfeld,et al.  Reversing cerebellar long-term depression , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Michael D Mauk,et al.  Cerebellar cortex contributions to the expression and timing of conditioned eyelid responses. , 2010, Journal of neurophysiology.

[16]  M. Mauk,et al.  Cerebellar cortex lesions disrupt learning-dependent timing of conditioned eyelid responses , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[17]  Dean V. Buonomano,et al.  Neural Network Model of the Cerebellum: Temporal Discrimination and the Timing of Motor Responses , 1999, Neural Computation.

[18]  Masao Ito,et al.  Long-lasting depression of parallel fiber-Purkinje cell transmission induced by conjunctive stimulation of parallel fibers and climbing fibers in the cerebellar cortex , 1982, Neuroscience Letters.

[19]  M. Mauk,et al.  Eyelid Conditioning to a Target Amplitude: Adding How Much to Whether and When , 2010, The Journal of Neuroscience.

[20]  S. Wang,et al.  Coincidence detection in single dendritic spines mediated by calcium release , 2000, Nature Neuroscience.

[21]  Paul R. Solomon,et al.  Lesions of the middle cerebellar peduncle disrupt acquisition and retention of the rabbit's classically conditioned nictitating membrane response. , 1987, Behavioral neuroscience.

[22]  M. Fujita,et al.  Adaptive filter model of the cerebellum , 1982, Biological Cybernetics.

[23]  C.W. Anderson,et al.  Learning to control an inverted pendulum using neural networks , 1989, IEEE Control Systems Magazine.

[24]  D. Signorini,et al.  Neural networks , 1995, The Lancet.

[25]  M. Mauk,et al.  A Mechanism for Savings in the Cerebellum , 2001, The Journal of Neuroscience.

[26]  T. Sejnowski,et al.  Learning and memory in the vestibulo-ocular reflex. , 1995, Annual review of neuroscience.

[27]  Stephen G Lisberger,et al.  Visual Guidance of Smooth-Pursuit Eye Movements: Sensation, Action, and What Happens in Between , 2010, Neuron.

[28]  Javier F. Medina,et al.  Timing Mechanisms in the Cerebellum: Testing Predictions of a Large-Scale Computer Simulation , 2000, The Journal of Neuroscience.

[29]  Richard F. Thompson,et al.  Retention of classically conditioned eyelid responses following acute decerebration , 1987, Brain Research.

[30]  S G Lisberger,et al.  Vestibular signals carried by pathways subserving plasticity of the vestibulo-ocular reflex in monkeys , 1986, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[31]  D. Marr A theory of cerebellar cortex , 1969, The Journal of physiology.

[32]  R. F. Thompson,et al.  Classical conditioning in rabbits using pontine nucleus stimulation as a conditioned stimulus and inferior olive stimulation as an unconditioned stimulus , 1989, Synapse.

[33]  Javier F. Medina,et al.  Computer simulation of cerebellar information processing , 2000, Nature Neuroscience.

[34]  W. T. Thach,et al.  Purkinje cell activity during motor learning , 1977, Brain Research.

[35]  S. M. Morton,et al.  Cerebellar Control of Balance and Locomotion , 2004, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[36]  S G Lisberger,et al.  The neural basis for learning of simple motor skills. , 1988, Science.

[37]  Michael D Mauk,et al.  A Subtraction Mechanism of Temporal Coding in Cerebellar Cortex , 2011, The Journal of Neuroscience.

[38]  I. Raman,et al.  Potentiation of Mossy Fiber EPSCs in the Cerebellar Nuclei by NMDA Receptor Activation followed by Postinhibitory Rebound Current , 2006, Neuron.

[39]  M. Mauk,et al.  Inhibition of climbing fibres is a signal for the extinction of conditioned eyelid responses , 2002, Nature.

[40]  I. Raman,et al.  Mechanisms of Potentiation of Mossy Fiber EPSCs in the Cerebellar Nuclei by Coincident Synaptic Excitation and Inhibition , 2008, The Journal of Neuroscience.

[41]  M. Mauk,et al.  Cerebellar Cortex Lesions Prevent Acquisition of Conditioned Eyelid Responses , 1999, The Journal of Neuroscience.

[42]  R. F. Thompson,et al.  Classical conditioning using stimulation of the inferior olive as the unconditioned stimulus. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[43]  L. Aitkin,et al.  Acoustic input to the lateral pontine nuclei , 1978, Hearing Research.

[44]  M. Mauk,et al.  Extinction of conditioned eyelid responses requires the anterior lobe of cerebellar cortex , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[45]  E. De Schutter,et al.  Synchronization of golgi and granule cell firing in a detailed network model of the cerebellar granule cell layer. , 1998, Journal of neurophysiology.

[46]  M. Mauk,et al.  Learning-Induced Plasticity in Deep Cerebellar Nucleus , 2006, The Journal of Neuroscience.

[47]  Stephen G. Lisberger,et al.  Learned Timing of Motor Behavior in the Smooth Eye Movement Region of the Frontal Eye Fields , 2011, Neuron.

[48]  Masao Ito The Cerebellum And Neural Control , 1984 .

[49]  M. Ito,et al.  Long-term depression. , 1989, Annual review of neuroscience.