nips nips2008 nips2008-204 nips2008-204-reference knowledge-graph by maker-knowledge-mining
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Author: Vicençc Gómez, Andreas Kaltenbrunner, Vicente López, Hilbert J. Kappen
Abstract: Large networks of spiking neurons show abrupt changes in their collective dynamics resembling phase transitions studied in statistical physics. An example of this phenomenon is the transition from irregular, noise-driven dynamics to regular, self-sustained behavior observed in networks of integrate-and-fire neurons as the interaction strength between the neurons increases. In this work we show how a network of spiking neurons is able to self-organize towards a critical state for which the range of possible inter-spike-intervals (dynamic range) is maximized. Self-organization occurs via synaptic dynamics that we analytically derive. The resulting plasticity rule is defined locally so that global homeostasis near the critical state is achieved by local regulation of individual synapses. 1
[1] P. Bak. How nature works: The Science of Self-Organized Criticality. Springer, 1996.
[2] J. M. Beggs and D. Plenz. Neuronal avalanches in neocortical circuits. Journal of Neuroscience, 23(35):11167–11177, December 2003.
[3] N. Bertschinger, T. Natschl¨ ger, and R. A. Legenstein. At the edge of chaos: Real-time computations a and self-organized criticality in recurrent neural networks. In Advances in Neural Information Processing Systems 17, pages 145–152. MIT Press, Cambridge, MA, 2005.
[4] G. Q. Bi and M. M. Poo. Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type. Journal Of Neuroscience, 18:10464–10472, 1998.
[5] G. L. Gerstein and B. Mandelbrot. Random walk models for the spike activity of a single neuron. Biophys J., 4:41–68, 1964.
[6] V. G´ mez, A. Kaltenbrunner, and V. L´ pez. Event modeling of message interchange in stochastic neural o o ensembles. In IJCNN’06, Vancouver, BC, Canada, pages 81–88, 2006.
[7] A. Kaltenbrunner, V. G´ mez, and V. L´ pez. Phase transition and hysteresis in an ensemble of stochastic o o spiking neurons. Neural Computation, 19(11):3011–3050, 2007.
[8] O. Kinouchi and M. Copelli. Optimal dynamical range of excitable networks at criticality. Nature Physics, 2:348, 2006.
[9] C. G. Langton. Computation at the edge of chaos: Phase transitions and emergent computation. Physica D Nonlinear Phenomena, 42:12–37, jun 1990.
[10] A. Levina, J. M. Herrmann, and T. Geisel. Dynamical synapses causing self-organized criticality in neural networks. Nature Physics, 3(12):857–860, 2007.
[11] N. H. Packard. Adaptation toward the edge of chaos. In: Dynamics Patterns in Complex Systems, pages 293–301. World Scientific: Singapore, 1988. A. J. Mandell, J. A. S. Kelso, and M. F. Shlesinger, editors.
[12] F. Rodr´guez, A. Su´ rez, and V. L´ pez. Period focusing induced by network feedback in populations of ı a o noisy integrate-and-fire neurons. Neural Computation, 13(11):2495–2516, 2001.
[13] S. Song, K. D. Miller, and L. F. Abbott. Competitive hebbian learning through spike-timing-dependent synaptic plasticity. Nature Neuroscience, 3(9):919–926, 2000.
[14] G. G. Turrigiano and S. B. Nelson. Homeostatic plasticity in the developing nervous system. Nature Reviews Neuroscience, 5(2):97–107, 2004.
[15] C. Van Vreeswijk and L. F. Abbott. Self-sustained firing in populations of integrate-and-fire neurons. SIAM J. Appl. Math., 53(1):253–264, 1993. 8