Dynamical Encoding by Networks of Competing Neuron Groups : Winnerless Competition M. Rabinovich1, A

1
Dynamical Encoding by Networks of Competing
Neuron Groups Winnerless Competition M.
Rabinovich1, A. Volkovskii1, P. Lecanda2,3, R.
Huerta1,2, H.D.I. Abarbanel1,4, and G.
Laurent5presented byMichael Downes6

• 1Institute for Nonlinear Science, University of
  California, San Diego, La Jolla, California
  92093-0402
• 2GNB, E.T.S. de Ingenieria Informatica,
  Universidad Autonoma de Madrid, 28049 Madrid,
  Spain
• 3Instituto de Ciencia de Materiales de Madrid,
  CSIC Cantoblanco, 28049 Madrid, Spain
• 4Department of Physics and Marine Physical
  Laboratory, Scripps Institution of Oceanography,
  University of California, San Diego, La Jolla,
  California 93093-0402
• 5California Institute of Technology, Division of
  Biology, MC 139-74 Pasadena, California 91125
• 6Department of Physics, Drexel University,
  Philadelphia, PA 19104

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Introduction

• Competitive or Winnerless Competition Networks
• Identity or spatiotemporal coding
• Deterministic trajectories heteroclinic orbits
• Connect saddle fixed points or saddle limit
  cycles
• Saddle states correspond to neuron activity
• Separatrices correspond to sequential switching

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Introduction (cont.)

• Features of Neural Encoding Representation of
  Input Information
• Uses both space and time
• Sensitively depends on stimulus
• Deterministic and reproducible
• Robust against noise
• Observations Suggest
• Dissipative dynamical system gt forgetfulness
• Information represented as transient trajectories

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Model and Parameters

• Neuron Dynamics
• System of N neurons
• Fyi(t) nonlinear function describing ith
  neuron dynamics
• Gij(S) nonlinear operator describing
  inhibitory action of jth neuron on ith
• S(t) vector-represented stimuli
• Stimulus acts in 2 ways
• Excites subset of neurons through S(t)
• Modifies effective inhibitory connections through
  Gij(S)
• Instability in presence of stimulus leads to
• Sequence of heteroclinic trajectories
• Rapid action
• Robustness against noise
• Response independent of initial state

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Model and Parameters (cont.)

• Numerical Model
• 9 Fitzhugh-Nagumo Model neurons with constant
  stimulus
• x(t) membrane potential
• y(t) recovery variable
• z(t) synaptic current (included inhibition
  term)
• f(x) nonlinear Fitzhugh-Nagumo neuron dynamics
• G(x) inhibition function
• Asserted when membrane potential is greater than
  zero
• turns on inhibitory term gji 2 for neurons
  with inhibitory relationships

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Models and Parameters (cont.)
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Results

• Membrane Potential vs. time for 2 Stimuli
• S1 0.10,0.15,0.00,0.00,0.15,0.10,0.00,0.00,0.00
  
• S2 0.01,0.03,0.05,0.04,0.06,0.02,0.03,0.05,0.04
  
• Stimulus patterns distinguishable

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Model and Parameters

• Information Encoding
• Input information solely in inhibitory coupling
  strength between i and j
• Non-symmetric inhibitory connections lead to
  closed heteroclinic orbits
• Global attractors
• Change in stimulus gt new global attractor in
  orbit vicinity

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Model and Parameters (cont.)

• Capacity
• of different items the network can encode
• With N neurons
• N-1 cyclically equivalent permutation
  (1,2,3,4,5) ? (2,3,4,5,1)
• (N-1)! heteroclinic orbits
• More heteroclinic orbits associated with N-1,
  N-2, etc. subspaces
• For Large N,

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Conclusion

• Winnerless Competition model competent to
  describe data experimental data
• Unique trajectories sensitively dependent on
  stimulus
• Large Encoding Capability

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Questions?