Physical Modeling of Neural Networks

Publisher Summary This chapter presents studies on a general class of neural network models, that is, a randomly diluted network of McColluch–Pitts neurons that interact via Hebbian-type connections. It derives and solves exact dynamic equations that describe how the system evolves from its initial state under various conditions. The motivation for these studies is the incorporation of neurobiological features into theoretical models and studying their effects on the emergent network performance of associative memory. Specifically, it studies interactions of neural networks, a variable threshold, hysteresis at the level of a single neuron, and higher-order synaptic interactions in the presence of noise. The models discussed in the chapter simulate a wide variety of phenomena such as distraction, concentration, selective attention, (de)sensitization, anesthesia, noise resistance, oscillations, chaos, crisis, and multiplicity. The chapter presents a general discussion on noise in neurons and then gives a brief review on neural network models discussed by Little and Hopfield, together with a version studied by Derrida, Gardner, and Zippelius.

[1]  Roger W. Sperry,et al.  On the neural basis of the conditioned response , 1955 .

[2]  Sompolinsky,et al.  Spin-glass models of neural networks. , 1985, Physical review. A, General physics.

[3]  G. Engquist,et al.  Effects of preparatory information about sensations, threat of pain, and attention on cold pressor distress. , 1979, Journal of personality and social psychology.

[4]  D. B. Guralnik.  Webster's new world dictionary , 1967 .

[5]  G. J. Smith,et al.  Effects of the home environment on withholding behaviors and conditioning in infant and neonatal rats. , 1978, Science.

[6]  Haim Sompolinsky,et al.  STATISTICAL MECHANICS OF NEURAL NETWORKS , 1988 .

[7]  L. Wang,et al.  Oscillations and chaos in neural networks: an exactly solvable model. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[8]  J. Keeler,et al.  Noise in neural networks: thresholds, hysteresis, and neuromodulation of signal-to-noise. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[9]  W. Singer,et al.  Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Gordon L. Shaw,et al.  Persistent states of neural networks and the random nature of synaptic transmission , 1974 .

[11]  Robert P. Behringer,et al.  Rayleigh-Benard convection and turbulence in liquid helium , 1985 .

[12]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[13]  R. Quiroga,et al.  Chaos in Brain Function , 1990 .

[14]  M. Eigen.  Selforganization of matter and the evolution of biological macromolecules , 1971, Naturwissenschaften.

[15]  E. Gardner,et al.  An Exactly Solvable Asymmetric Neural Network Model , 1987 .

[16]  L. Wang,et al.  Synchronous neural networks of nonlinear threshold elements with hysteresis. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[17]  V. Mountcastle,et al.  Higher functions of the brain , 1987 .

[18]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[19]  B. Katz,et al.  A study of synaptic transmission in the absence of nerve impulses , 1967, The Journal of physiology.

[20]  B. Hess,et al.  Oscillatory phenomena in biochemistry. , 1971, Annual review of biochemistry.

[21]  G J Smith,et al.  Analysis of appetitive motivation in preweanling rats: application of bromocryptine mesylate. , 1985, Behavioral and neural biology.

[22]  Sompolinsky,et al.  Storing infinite numbers of patterns in a spin-glass model of neural networks. , 1985, Physical review letters.

[23]  G W Hoffmann,et al.  A neural network model based on the analogy with the immune system. , 1986, Journal of theoretical biology.

[24]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[25]  D Kleinfeld,et al.  Sequential state generation by model neural networks. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[26]  R. J. Field,et al.  Oscillations and Traveling Waves in Chemical Systems , 1985 .

[27]  R Dubner,et al.  Activity of trigeminothalamic neurons in medullary dorsal horn of awake monkeys trained in a thermal discrimination task. , 1984, Journal of neurophysiology.

[28]  Kanter,et al.  Temporal association in asymmetric neural networks. , 1986, Physical review letters.

[29]  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.

[30]  L. Wang,et al.  Interactions of neural networks: models for distraction and concentration. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

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

[32]  P. Peretto,et al.  Long term memory storage capacity of multiconnected neural networks , 2004, Biological Cybernetics.

[33]  I. Leuthäusser,et al.  An exact correspondence between Eigen’s evolution model and a two‐dimensional Ising system , 1986 .

[34]  D. O. Hebb,et al.  The organization of behavior , 1988 .