Evolving networks of integrate-and-fire neurons

This paper addresses the following question: ''What neural circuits can emulate the monosynaptic correlogram generated by a direct connection between two neurons?'' The search for answers to that question has been tackled in two steps: (1) we incorporated into an integrate-and-fire (IAF) neuron model those aspects of neuronal physiology that can influence cross-correlated activity; (2) we evolved networks of biologically realistic neurons towards circuits that are able to generate a monosynaptic correlogram between two neurons. Evolutionary strategies and genetic algorithms were used to explore a computationally intractable search space of physiological parameters and network connectivity. We found that evolutionary strategies perform well in refining good initial solutions, while the simple genetic algorithm achieves worse results even when using a higher computational load. The main obstacles in this challenging study of evolutionary neural networks are exposed and discussed, as well as the results obtained after intensive simulation.

[1]  D. Perkel,et al.  Cooperative firing activity in simultaneously recorded populations of neurons: detection and measurement , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[2]  R. Reid,et al.  Paired-spike interactions and synaptic efficacy of retinal inputs to the thalamus , 1998, Nature.

[3]  X. Yao Evolving Artificial Neural Networks , 1999 .

[4]  G. P. Moore,et al.  Neuronal spike trains and stochastic point processes. I. The single spike train. , 1967, Biophysical journal.

[5]  G L Gerstein,et al.  Mutual temporal relationships among neuronal spike trains. Statistical techniques for display and analysis. , 1972, Biophysical journal.

[6]  A. Hodgkin,et al.  The dual effect of membrane potential on sodium conductance in the giant axon of Loligo , 1952, The Journal of physiology.

[7]  R. Reid,et al.  Precisely correlated firing in cells of the lateral geniculate nucleus , 1996, Nature.

[8]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Henry C. Tuckwell,et al.  Introduction to theoretical neurobiology , 1988 .

[10]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[11]  P. Somogyi,et al.  Quantitative distribution of GABA-immunoreactive neurons in the visual cortex (area 17) of the cat , 2004, Experimental Brain Research.

[12]  R. Stein Some models of neuronal variability. , 1967, Biophysical journal.

[13]  Robert Shapley,et al.  Visual cortex: pushing the envelope , 1998, Nature Neuroscience.

[14]  J. Lambert Computational Methods in Ordinary Differential Equations , 1973 .

[15]  D N Mastronarde,et al.  Two classes of single-input X-cells in cat lateral geniculate nucleus. I. Receptive-field properties and classification of cells. , 1987, Journal of neurophysiology.

[16]  A. Hodgkin,et al.  The frequency of nerve action potentials generated by applied currents , 1967, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[17]  Dario Floreano,et al.  Evolving Spiking Neurons from Wheels to Wings , 2003 .

[18]  Prof. Dr. Valentino Braitenberg,et al.  Anatomy of the Cortex , 1991, Studies of Brain Function.

[19]  A. Hodgkin,et al.  Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo , 1952, The Journal of physiology.

[20]  T. M. Mayhew,et al.  Anatomy of the Cortex: Statistics and Geometry. , 1991 .

[21]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[22]  Bruce W. Knight,et al.  Dynamics of Encoding in a Population of Neurons , 1972, The Journal of general physiology.

[23]  D N Mastronarde,et al.  Two classes of single-input X-cells in cat lateral geniculate nucleus. II. Retinal inputs and the generation of receptive-field properties. , 1987, Journal of neurophysiology.

[24]  G. P. Moore,et al.  Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. , 1967, Biophysical journal.

[25]  Jose-Manuel Alonso,et al.  Factors determining the precision of the correlated firing generated by a monosynaptic connection in the cat visual pathway , 2005, The Journal of physiology.

[26]  Dario Floreano,et al.  Evolution of Spiking Neural Controllers for Autonomous Vision-Based Robots , 2001, EvoRobots.

[27]  A. Hodgkin,et al.  The components of membrane conductance in the giant axon of Loligo , 1952, The Journal of physiology.

[28]  A. Aertsen,et al.  Representation of cooperative firing activity among simultaneously recorded neurons. , 1985, Journal of neurophysiology.

[29]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[30]  C. Nicholson Electric current flow in excitable cells J. J. B. Jack, D. Noble &R. W. Tsien Clarendon Press, Oxford (1975). 502 pp., £18.00 , 1976, Neuroscience.

[31]  S. Hyakin,et al.  Neural Networks: A Comprehensive Foundation , 1994 .

[32]  Louis Édouard Lapicque,et al.  L'excitabilité en fonction du temps : la chronaxie, sa signification et sa mesure , 1926 .

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

[34]  J. Alonso,et al.  Functional connectivity between simple cells and complex cells in cat striate cortex , 1998, Nature Neuroscience.

[35]  G. P. Moore,et al.  Statistical signs of synaptic interaction in neurons. , 1970, Biophysical journal.