Synfire chains in a balanced network of I

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Synfire chains in a balanced network of IF
neurons
Y. Aviel, E. Pavlov, M. Abeles and D. Horn
Corresponding author. Email
aviel_at_cc.huji.ac.il
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Balanced network
E
Excitatory population
Inhibitory population
I
External Input
Random sparse Connectivity.
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Synfire Chain
pool
Link


chain
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The Question

• A balanced network of integrate-and-fire neurons
  has a stable state of asynchronous activity.
  (Brunel 00)
• Will it keep this property if the E-E connections
  are constructed of synfire-chains?

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The Answer

• The answer depends on the ratio rw/K, where w is
  the pool width and K is the number of excitatory
  synapses on a single neuron.
• I will show both analytically and by simulation,
  that the transition between the synchronous and
  the asynchronous regimes is sensitive to the
  value of r.

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A Simplified Model
We have N binary neurons, each is represented by
a variable si, i1..N . si 1, if neuron i
fires or 0 otherwise. The si are correlated
stochastic variables that obey the following
characteristic
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Correlation of a Pair of Neurons.
I1 (K inputs)

X1 (K-w inputs)
Z (w inputs)

?h
?s

X2 (K-w inputs)
I2 (K inputs)
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Statistics of Sum of Three Uncorrelated Sub Fields
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Correlation of Two Fields With Partial
Correlation
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Correlation of a Pair of Neurons As a Function of
the Correlation in the Common Input
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(No Transcript)
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The correlations fixed point
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Steady State Correlations
Fixed-point correlation
w pool width K excitatory afferents r
w/K
r (w/K) in units of 1/sqrt(K)
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Steady state correlations, ?, as a function of
r,w.
Red curve is at wK1/2
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Simulation Result. Network Architecture
Superposition of synfire chains
Random connectivity
E
Excitatory population
Inhibitory population
I
External Input
NE10,000, NI2,500 Connectivity sparsness 10
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Simulation results
r94/2000
w pool width K excitatory afferents r
w/K
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Population rate.
Pool width 94 r 94/2000
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Dist. Of the Coefficient-of-Variance and the Rates
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A trace of Membrane potential.
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Distribution of Mem. Potential.
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Spectral density of the population rate.
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Simulation results
r95/2000
w pool width K excitatory afferents r
w/K
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Population rate in the epileptic regime
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Upper bound on the synaptic weights

• We have previously seen that in order to avoid
  epilepsy, we should take , or
• On the other hand, we want w inputs to a cell
  will drive it to fire a spike ,
  where ? O(1), is the threshold.
• We conclude that the synaptic weights are bounded

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Summary

• Using a model with binary neurons, we show that
  the ratio r between the size of a pool of neurons
  and the total excitatory input to a neuron,
  determines the correlation of any pair of neurons
  in a pool in a sigmoidal fashion.
• We show that the same effect exists in
  simulations of a network of IF neurons.
• Requiring the asynchronous state to be stable,
  implies an upper bound on the pool size
  .
• Requiring stable propagation of synfire implies
  scaling J, the synaptic weight, like .

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The Synfire Challenge

• We have shown that a network which is
  superpisition of chains, is capable of
  asynchronous activity.
• Can wave of SFC stably propagate along the
  chains?
• This necessitates a study of balanced networks of
  IF neurons in the strong coupling regime.

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Conclusions Capacity Bound
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Capacity Bound
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Steady state correlations, ro, as a function of
r,w. Red curve is at r1/w.
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Scaling synaptic weights
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More constraints on alpha
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ro as a function of K, alpha
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Scaling K

• If KepsN, there will always be significant
  correlations between any pair of neurons.
• If, however, Ksqrt(N), there will not.
• Qualitatively, our results holds true in either
  case.
• Biologically, the second case seems to be
  implausible.