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. 2005 Apr;17(4):881-902.
doi: 10.1162/0899766053429408.

Rate and synchrony in feedforward networks of coincidence detectors: analytical solution

Shawn Mikula  1 , Ernst Niebur
Affiliations

Rate and synchrony in feedforward networks of coincidence detectors: analytical solution

Shawn Mikula et al. Neural Comput. 2005 Apr.

Abstract

We provide an analytical recurrent solution for the firing rates and cross-correlations of feedforward networks with arbitrary connectivity, excitatory or inhibitory, in response to steady-state spiking input to all neurons in the first network layer. Connections can go between any two layers as long as no loops are produced. Mean firing rates and pairwise cross-correlations of all input neurons can be chosen individually. We apply this method to study the propagation of rate and synchrony information through sample networks to address the current debate regarding the efficacy of rate codes versus temporal codes. Our results from applying the network solution to several examples support the following conclusions: (1) differential propagation efficacy of rate and synchrony to higher layers of a feedforward network is dependent on both network and input parameters, and (2) previous modeling and simulation studies exclusively supporting either rate or temporal coding must be reconsidered within the limited range of network and input parameters used. Our exact, analytical solution for feedforward networks of coincidence detectors should prove useful for further elucidating the efficacy and differential roles of rate and temporal codes in terms of different network and input parameter ranges.

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Figures

Figure 1
Figure 1
A simple n+1-layer feedforward network with cyclical boundary conditions, period 4. Coincidence detectors are represented by a circle with a Θ(Σ) symbol in them, and connections are shown as directed arrows between coincidence detectors. Input is shown as stylized spike trains at the very bottom. Comma-separated pairs of numbers indicate layer (second number) and neuron in this layer (first number).
Figure 2
Figure 2
Effect of uniform, uncorrelated input firing rate. (A) Mean firing rates for the network. (B) Nearest-neighbor cross-correlations for the network. (C) Cross-correlation matrices for each layer.
Figure 3
Figure 3
(A) Higher-layer output rate versus input rate curve. (B) higher-layer cross-correlation versus input rate curve for the case of uncorrelated inputs of uniform rate.
Figure 4
Figure 4
Effect of spatially localized high input rates. (A) Mean firing rates for the network. (B) nearest-neighbor cross-correlations for the network. (C) Cross-correlation matrices for each layer.
Figure 5
Figure 5
Effect of halving input rates of Figure 4. (A) Mean firing rates for the network. (B) Nearest-neighbor cross-correlations for the network. (C) Cross-correlation matrices for each layer.
Figure 6
Figure 6
Effect of spatially localized high cross-correlation (q = .4) between inputs 2 and 3. (A) Mean firing rates for the network. (B) Nearest-neighbor cross-correlations for the network. (C) Cross-correlation matrices for each layer.
Figure 7
Figure 7
Effect of spatially localized high cross-correlation (q = .8) between inputs 2 and 3. (A) Mean firing rates for the network. (B) Nearest-neighbor cross-correlations for the network. (C) Cross-correlation matrices for each layer.
Figure 8
Figure 8
Effect of spatially localized high cross-correlation (q = .6) and high firing ratebetween inputs 2 and 3. (A) Mean firing rates for the network. (B) Nearest-neighbor cross-correlations for the network. (C) Cross-correlation matrices for each layer.
Figure 9
Figure 9
Mean layer output rates as a function of network layer. (A) Mean input rate of 0.2. (B) mean input rate of 0.4.
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References

    1. Diesmann M, Gewaltig MO, Aertsen A. Stable propagation of synchronous spiking in cortical neural networks. Nature. 1999;402:529–533. - PubMed
    1. Fries P, Reynolds JH, Rorie AE, Desimone R. Modulation of oscillatory neuronal synchronization by selective visual attention. Science. 2001;291:1560–11563. - PubMed
    1. Litvak V, Sompolinsky H, Segev I, Abeles M. On the transmission of rate code in long feedforward networks with excitatory-inhibitory balance. J. Neurosci. 2003;23:3006–3015. - PMC - PubMed
    1. Mikula S, Niebur E. The effects of input rate and synchrony on a coincidence detector: Analytical solution. Neural Computation. 2003a;15:539–547. - PubMed
    1. Mikula S, Niebur E. Synaptic depression leads to nonmonotonic frequency dependence in the coincidence detector. Neural Computation. 2003b;15(10):2339–2358. - PubMed

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