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Model-invariant features of correlations in recurrent networks

Moritz Helias1*, Dmytro Grytskyy1, Tom Tetzlaff1 and Markus Diesmann1, 2, 3
  • 1 Research Center Juelich, Computational and Systems Neuroscience, Germany
  • 2 RIKEN, Brain Science Institute, Japan
  • 3 RIKEN Brain Science Institute, Brain and Neural Systems Team, Japan

Depending on the scientific question to be investigated, different models of neural dynamics are commonly in use.
Many studies employ the leaky integrate-and-fire model [1], because it is able to predict spike sequences of real neurons to good accuracy [2], but the analysis of this model is complicated by the very nature of the non-linear threshold process involved. Some studies therefore resort to simplified neural dynamics, like linear stochastic point process models [3], in order to render the problem at hand tractable. An example is the interplay of spiking neural dynamics and synaptic plasticity in recurrent networks, where stochastic point process models have successfully been employed [4]. However, it often remains unclear how the different neuronal models relate to each other and if results from one model carry over to another.
In this work we aim to unify different approaches to recurrent neural networks with excitation and inhibition. We focus on the correlation structure of such networks in the irregular regime [5] and study four different models of neural activity: Linearly coupled rate units [6], linear stochastic point process models [3,4], binary stochastic neuron models with non-linear gain functions [7], and leaky integrate-and-fire models [1,5].
Recent advances in the theory of correlations in recurrent networks [8,9,6] showed that in the regime of asynchronous irregular activity, these models qualitatively yield similar results. Here we show that all four models map to the same self-consistency equation describing correlations in networks with irregular activity. Solving this equation once allows to obtain a self-consistent solution for the correlation structure in the presence of excitation, inhibition and conduction delays. This unification allows to convey results obtained from one model to the others. We exemplify this on the asymmetry of cross correlations [7] and the emergence of fast global oscillations [5].

Acknowledgements

Partially supported by the Helmholtz Alliance on Systems Biology, the Next-Generation Supercomputer Project of MEXT, EU Grant 15879 (FACETS), and EU Grant 269921 (BrainScaleS). All network simulations were carried out with NEST (http://www.nest-initiative.org).

References

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4 Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL, Biol. Cybern. (2009a) 101(2) : 81-102.
5 Brunel N (2000), Journal of Computational Neuroscience 8, 183–208
6 Tetzlaff T, Helias M, Einevoll GT, Diesmann M: CNS*2010, BMC Neuroscience (2010) 11(Suppl 1):O11, doi:10.1186/1471-2202-11-S1-O11
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8 Renart A, De la Rocha J, Bartho P, Hollander L, Parga N, Reyes A, Harris KD: Science (2010) 327: 587-590
9 Helias M, Tetzlaff T, Diesmann M: CNS*2010, BMC Neuroscience (2010) 11(Suppl 1):P47, doi:10.1186/1471-2202-11-S1-P47

Keywords: dynamical systems, networks, Neurons

Conference: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011, Freiburg, Germany, 4 Oct - 6 Oct, 2011.

Presentation Type: Poster

Topic: neurons, networks and dynamical systems (please use "neurons, networks and dynamical systems" as keywords)

Citation: Helias M, Grytskyy D, Tetzlaff T and Diesmann M (2011). Model-invariant features of correlations in recurrent networks. Front. Comput. Neurosci. Conference Abstract: BC11 : Computational Neuroscience & Neurotechnology Bernstein Conference & Neurex Annual Meeting 2011. doi: 10.3389/conf.fncom.2011.53.00219

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Received: 13 Aug 2011; Published Online: 04 Oct 2011.

* Correspondence: Dr. Moritz Helias, Research Center Juelich, Computational and Systems Neuroscience, Juelich, Germany, m.helias@fz-juelich.de