Models of Spiking Neurons and Spiking Neural Networks

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Models of Spiking Neurons and Spiking Neural
Networks
Peter Stratton Janet WilesThinking Systems
ProjectQueensland Brain InstituteUniversity of
Queensland 21 June 2007
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• Izhikevich Spiking Neuron Model (2003)
• Claimed to be as realistic as Hodgkin-Huxley
  neurons.
• As computationally efficient as simple
  integrate-and-fire.

Izhikevich, E. M. (2003). "Simple model of
spiking neurons." IEEE Transactions on Neural
Networks 14(6) 1569-1572.
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Electronic version of the figure and reproduction
permissions are freely available at
www.izhikevich.com
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2 Variables v Membrane potential. u Membrane
Recovery variable, giving -ve feedback to v
(higher value means neuron less likely to fire),
representing Na and K ionic currents. 4
Parameters c Reset value for v higher value
means easier / more likely to fire again. a
Speed of recovery of u higher value means faster
recovery. b Sensitivity of u to v higher values
tightly couple the 2 variables resulting in
possible sub-threshold oscillations and low
threshold spiking. d Additive reset value for u
higher value means harder / less likely for
neuron to fire again.
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Izhikevich, E. M. (2004). "Which model to use for
cortical spiking neurons? IEEE Transactions on
Neural Networks 15(5) 1063-1070.
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Small Spiking Network Simulation
Input Current (I)
Interneuron
Pyramidal cell (uninhibited)
Pyramidal cell (inhibited)
(10 ms)
Pyramidal cell (conjunction)
Pyramidal cell (delayed conjunction)
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Small Spiking Network Simulation no input
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Small Spiking Network Simulation
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Small Spiking Network Simulation
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Small Spiking Network Simulation
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Large Spiking Network Simulation

• 1000 fully connected neurons.
• Exhibits alpha (8-10 Hz) and occasionally gamma
  (40 Hz) oscillations.
• Simulates 106 connections in real-time using
  Matlab (3 GHz CPU).

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Spiking Network Simulation

• Network behaviour on one trial for slightly
  increased mean synaptic strength and slightly
  decreased mean thalamic input.

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Heat Map Metrics
Total Number of Spikes in 1000ms in this case
874 total spikes.
Dominant Oscillation Frequency highest peak in
the Discreet Fourier Analysis of the Spikes /
millisecond graph in this case 8Hz.

Structure Score (kurtosis skewness) of the
Spikes / millisecond histogram in this case
28.4.
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Structure Score examples
A 2.5
B 36.5
C 7.1
D 52.3
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Phase Space Visualisations
Structure Score
D
C
B
A
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Phase Space Visualisations
Total Number of Spikes in 1000ms
Dominant Oscillation Frequency
Structure Score
Average value over 500 trials
D
D
D
C
B
C
B
C
B
A
A
A
Coefficient of Variation
D
D
D
C
B
C
B
C
B
A
A
A
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Phase Space Visualisations
Total Number of Spikes in 1000ms
Dominant Oscillation Frequency
Structure Score
Average value over 500 trials
C
B
C
B
C
B
A
A
A
Coefficient of Variation
C
B
C
B
C
B
A
A
A
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What Happens in a Phase Change

• Number of Spikes distribution over 1000 trials
  for
• left - Izhikevichs parameters (synaptic weight
  0.5, thalamic input 5)
• right average synaptic weight increased to 0.6

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STDP leading to nested Delta (2-4 Hz) and Gamma
(30-100 Hz) oscillations
Izhikevich, E. M. (2005). "Polychronization
Computation with Spikes." Neural Computation
18(2) 245-282.