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Noise decouples covariances from interaction strength
BMC Neuroscience volume 14, Article number: P164 (2013)
Correlated neural activity is a known feature of the brain  and evidence increases that it is closely linked to information processing . In our recent work we have shown how to map different network models, including binary networks, onto linear dynamics . For binary neurons the mean-field approach takes random fluctuations into account to accurately predict the average activity in such networks . Expressions for covariances follow from a master equation . Binary neurons with a Heaviside gain function are inaccessible to the classical treatment . Based on our earlier preliminary results  here we show how random fluctuations generated by the network effectively linearize the system of binary neurons, including the case of the Heaviside gain function, and how they implement a self-regulating mechanism which renders population-averaged covariances independent of the synaptic coupling strength. Figure 1A, B illustrate this invariance.
The mechanism is based on the increase of fluctuations in the input signal in proportion to the synaptic weight. The fluctuations cause portions of the gain function with smaller slope to be visited more frequently, effectively reducing the transmission gain. This keeps the linearized system away from instability, with the eigenvalues of its effective connectivity matrix bounded by a constant less than unity (see Figure 1C). Although of local origin the mechanism controls global features of the network dynamics.
Cohen MR, Kohn A: Measuring and interpreting neuronal correlations. Nat Rev Neurosci. 2011, 14 (7): 811-819. 10.1038/nn.2842.
Gerstein GL, Perkel DH: Simultaneously recorded trains of action potentials: analysis and functional interpretation. Science. 1969, 881 (164): 828-830.
Sompolinsky H: Theory of correlations in stochastic neural networks. Phys Rev E. 1994, 50 (4): 3171-3191. 10.1103/PhysRevE.50.3171.
Grytskyy D, Tetzlaff T, Diesmann M, Helias M: Taming the model zoo: A unified view on correlations in recurrent networks. BMC Neurosci. 2012, 13 (1): 147-10.1186/1471-2202-13-147.
van Vreeswijk CA, Sompolinsky H: Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science. 1996, 274: 1724-1726. 10.1126/science.274.5293.1724.
Grytskyy D, Tetzlaff T, Helias M: Invariance of covariances arises out of noise. AIP Conf Proc. 2013, 258-262. 1510
We gratefully acknowledge funding by the Helmholtz Association: HASB and portfolio theme SMHB, the Next-Generation Supercomputer Project of MEXT, EU Grant 269921 (BrainScaleS). All network simulations were carried out with NEST (http://www.nest-initiative.org).
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Grytskyy, D., Tetzlaff, T., Diesmann, M. et al. Noise decouples covariances from interaction strength. BMC Neurosci 14, P164 (2013). https://doi.org/10.1186/1471-2202-14-S1-P164
- Coupling Strength
- Master Equation
- Network Dynamic
- Interaction Strength
- Synaptic Weight