Stabilising the output frequency in multiplicative STDP

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Stabilising the output frequency in
multiplicative STDP

• Fleur Zeldenrust
• 7 November 2005

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Contents

• Recapitulation
• STDP
• Homeostatic scaling
• Model
• Aim of research
• Net
• 4 scenarios
• Conclusion and Discussion

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Bi Poo (1998)
Spike Timing Dependent Plasticity
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Spike Timing Dependent PlasticitySong et al.,
2000

• If the presynaptic cell fires first, the synapse
  is potentiated
• If the postsynaptic cell fires first, the synapse
  is depressed
• Important ratio between potentiation and
  depression a

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Homeostatic Scaling of Excitability

• keep the neuron within its working range
• adjust excitability
• e.g. van Welie et al. (2004)
• Ca CaT regulates gL to attain target firing
  rate (Golowasch et al. 99)

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Net

• 1000 inputs
• homeostatic scaling
• STDP
• Poisson

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Model

• Input-output relation
• Weight changes (STDP)
• Homeostatic scaling

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Aim of research

• Interactions of STDP with homeostatic scaling of
  excitability
• Can homeostatic scaling stabilise the output
  frequency?
• Would learning still be possible?

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4 scenarios

• Homogeneous inputs, uncorrelated
• Homogeneous inputs, homogeneously correlated
• Homogeneous inputs, inhomogeneously correlated
• Inhomogeneous inputs, uncorrelated

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Homogeneous inputs, uncorrelated

• all inputs have the same mean frequency
• only autocorrelations
• assumption all weights have the same value

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Homogeneous inputs, uncorrelated

• 2 steady state solutions of which one is stable
• output rate stabilisation
• dependence on potentiation/ depression ratio

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Homogeneous inputs, homogeneously correlated

• all inputs have the same mean frequency
• varying correlations between all the inputs
• assumption all weights have the same value

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Homogeneous inputs, homogeneously correlated

• 2 steady state solutions of which one is stable
• output rate stabilisation
• dependence on potentiation/ depression ratio and
  amount of correlation

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Homogeneous inputs, inhomogeneously correlated

• all inputs have the same mean frequency
• the group im1 iN is correlated
• assumption two groups of homogeneous weights

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Homogeneous inputs, inhomogeneously correlated

• 4 steady state solutions of which one is stable
• output rate stabilisation
• dependence on potentiation/ depression ratio,
  amount of correlation and group size m

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Homogeneous inputs, inhomogeneously correlated
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Inhomogeneous inputs, uncorrelated

• two groups of input frequencies
• only autocorrelations
• assumption two groups of homogeneous weights

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Inhomogeneous inputs, uncorrelated

• 4 steady state solutions of which one is stable
• w1 and w2 overlap
• output rate stabilisation
• dependence only on potentiation/ depression ratio
  

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Conclusion

• A net with STDP and homeostatic scaling of
  excitability can stabilise the output frequency
  while the weights remain sensitive to
  correlations (not to frequencies).

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Discussion

• What is the role of the timescale of homeostatic
  scaling?
• Stability of the homogeneous states?
• More groups than two?
• What happens without homeostatic scaling of
  excitability?
• Dependence on the target frequency?

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References

• 1 Bi, G. and Poo, M., Synaptic Modifications in
  Cultured Hippocampal Neurons Dependence on Spike
  Timing, Synaptic Strength, and Postsynaptic Cell
  Type, The Journal of Neuroscience, Vol.18, pp.
  10464-10472, 1998
• 2 Brunel, N., Dynamics of Sparsely Connected
  Networks of Excitatory and Inhibitory Spiking
  Neurons, Journal of Computational Neuroscience 8,
  pp. 183-208, 2000
• 3 Rossem, M.C.W. van, Bi, G.Q. and Turrigiano,
  G.G., Stable Hebbian learning from Spike
  Timing-Dependent Plasticity, The Journal of
  Neuroscience, Vol.20, pp. 8812-8821, 2000
• 4 Song, S., Miller, K.D. and Abbott, L.F.,
  Competitive Hebbian learning through
  spike-timing-dependent synaptic plasticity,
  Nature, Vol.3 no. 9, pp. 919-926, 2000
• 5 Welie, I. van, Hooft, J.A. van and Wadman,
  W.J., Homeostatic scaling of neuronal
  excitability by synaptic modulation of somatic
  hyperpolarization activated Ih channels, PNAS,
  Vol. 101, no. 14, pp. 5123-5128, 2004