Email updates

Keep up to date with the latest news and content from BMC Neuroscience and BioMed Central.

This article is part of the supplement: Twenty First Annual Computational Neuroscience Meeting: CNS*2012

Open Access Poster presentation

Taming the model zoo: a unified view on correlations in recurrent networks

Dmytro Grytskyy1*, Moritz Helias13, Tom Tetzlaff1 and Markus Diesmann123

Author affiliations

1 Institute of Neuroscience and Medicine (INM-6), Computational and Systems Neuroscience, Research Center Jülich, Germany

2 Faculty of Medicine, RWTH Aachen University, Germany

3 RIKEN Brain Science Institute, Wako City, Japan

For all author emails, please log on.

Citation and License

BMC Neuroscience 2012, 13(Suppl 1):P147  doi:10.1186/1471-2202-13-S1-P147


The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/13/S1/P147


Published:16 July 2012

© 2012 Grytskyy et al; licensee BioMed Central Ltd.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Poster presentation

The meaning of correlated neural activity for the processing and representation of information in cortical networks is still not understood, but evidence for a pivotal role of correlations increases [1]. Recent theoretical work has shown [2-4] that balanced recurrent networks of binary model neurons [3] and spiking integrate-and-fire models [2-4] are able to produce weak correlations despite common input to pairs of cells. For binary model neurons, the theory of correlations in recurrent networks is well established [5]. Investigating learning in recurrent networks with spike-timing dependent plasticity requires spiking neuron models. Theoretical work often employs linear stochastic point process models [6] for their analytic tractability [7]. The diversity of neuron models used in contemporary theoretical neuroscience brings up the question, which features of correlations are generic properties of recurrent networks and which are peculiarities of the often abstracted neuronal dynamics. Moreover, the variety of different theories employed to describe pairwise correlations in neural networks is confusing at times, even for experts in the field. Currently it is unclear how different neuron models relate to each other and whether and how results obtained with one model carry over to another. In this work we present a unified theoretical view on pairwise correlations in recurrent random networks. We consider binary neuron models, leaky integrate-and-fire models, and linear point process models. For networks in the asynchronous irregular regime, we show that these models can be mapped to either of two definitions of an Ornstein-Uhlenbeck (OU) process [8]. The distinction between both classes is how the effective noise enters the model: Leaky integrate-and-fire models and spiking point process models belong to the class with noise on the output side, the binary neuron model is equivalent to an OU process with noise on the input side. The closed solution for the correlation structure of OU processes [8] holds for both classes. We extend this solution to the presence of synaptic conduction delays. The presented theory recovers and unifies the theories of correlations for binary neurons [5] and linear point processes [7] and generalizes both models to the case of finite conduction delays. Moreover we obtain a good approximation for the temporal structure of correlations for the spiking leaky integrate-and-fire model in the asynchronous regime [9]. Finally we show that the oscillatory instability known for networks of integrate-and-fire models [9] is a model-invariant feature of any of the studied dynamics and we explain the class dependent differences in the temporal shape of correlation functions.

Acknowledgements

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

References

  1. Cohen MR, Kohn A: Measuring and interpreting neuronal correlations.

    Nature Neuro 2011, 14(7):811-819. Publisher Full Text OpenURL

  2. Hertz J: Cross-Correlations in High-Conductance States of a Model Cortical Network.

    Neural Computation 2010, 22(2):427-447. PubMed Abstract | Publisher Full Text OpenURL

  3. Renart A, De la Rocha J, Bartho P, Hollander L, Parga N, Reyes A, Harris KD: The Asynchronous State in Cortical Circuits.

    Science 2010, 327:587-590. PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  4. Tetzlaff T, Helias M, Einevoll GT, Diesmann M: Decorrelation of neural-network activity by inhibitory feedback.

    PLoS Comp Biol 2012, in press.

    arXiv:1204.4393v1 [q-bio.NC]

    OpenURL

  5. Ginzburg I, Sompolinsky H: Theory of correlations in stochastic neural networks.

    Phys. Review E 1994, 50(4):3171-3191. Publisher Full Text OpenURL

  6. Gilson M, Burkitt AN, Grayden DB, Thomas DA, van Hemmen JL: Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks I: Input selectivity - strengthening correlated input pathways.

    Biol. Cybern 2009, 101(2):81-102. PubMed Abstract | Publisher Full Text OpenURL

  7. Hawkes A: Point spectra of some mutually exciting point processes.

    R. Statist. Soc. B 1971, 33(3):438-443. OpenURL

  8. Risken H: The Fokker-Planck-Equation. Methods of Solution and Applications. 2nd edition. Berlin: Springer; 1989.

  9. Brunel N: Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons.

    Journal of Computational Neuroscience 2000, 8:183-208. PubMed Abstract | Publisher Full Text OpenURL