Neural networks with fast time-variation of synapses

We study a kinetic neural network in which the intensity of synaptic couplings varies on a timescale of order p.1 p/ 1 compared with that for neuron variations. We describe some exact and mean-field results for p! 0. This includes, for example, the Hopfield model with random fluctuations of synapse intensities such that neurons couple each other, on average, according to the Hebbian learning rule. The consequences of such fluctuations on the performance of the network are analysed in detail for some specific choices of the rate and fluctuation distribution, including the case in which couplings are asymmetric.

[1]  Stationary distributions for systems with competing creation-annihilation dynamics , 1990 .

[2]  Garrido,et al.  Effective Hamiltonian description of nonequilibrium spin systems. , 1989, Physical review letters.

[3]  Y. Goda,et al.  Two components of transmitter release at a central synapse. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Joaquín Marro,et al.  Ising Systems with Conflicting Dynamics: Exact Results for Random Interactions and Fields , 1994 .

[5]  L. Pastur,et al.  The replica-symmetric solution without replica trick for the Hopfield model , 1994 .

[6]  S. Edwards,et al.  Theory of spin glasses , 1975 .

[7]  K. Martin,et al.  Excitatory synaptic inputs to spiny stellate cells in cat visual cortex , 1996, Nature.

[8]  P. Peretto.  An introduction to the modeling of neural networks , 1992 .

[9]  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.

[10]  Roberto Malinow,et al.  Measuring the impact of probabilistic transmission on neuronal output , 1993, Neuron.

[11]  Garrido,et al.  Nonequilibrium lattice models: A case with effective Hamiltonian in d dimensions. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  Anthony Zador,et al.  Synaptic transmission: Noisy synapses and noisy neurons , 1996, Current Biology.

[13]  C. Noback.  The Human Nervous System , 1967 .

[14]  K M Harris,et al.  Occurrence and three-dimensional structure of multiple synapses between individual radiatum axons and their target pyramidal cells in hippocampal area CA1 , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[15]  David Ferster,et al.  Is Neural Noise Just a Nuisance? , 1996, Science.

[16]  Pedro L. Garrido,et al.  Kinetic lattice models of disorder , 1994 .

[17]  D. Thouless,et al.  Stability of the Sherrington-Kirkpatrick solution of a spin glass model , 1978 .

[18]  D. Amit,et al.  Statistical mechanics of neural networks near saturation , 1987 .

[19]  Sompolinsky,et al.  Dynamics of spin systems with randomly asymmetric bonds: Ising spins and Glauber dynamics. , 1988, Physical review. A, General physics.

[20]  D. Mattis.  Solvable spin systems with random interactions , 1976 .

[21]  C. Stevens,et al.  An evaluation of causes for unreliability of synaptic transmission. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[22]  C. Noback,et al.  The human nervous system: basic principles of neurobiology , 1975 .