This title appears in the Scientific Report :
2014
Please use the identifier:
http://hdl.handle.net/2128/10218 in citations.
Scalability of asynchronous networks is limited by one-to-one mapping between effective connectivity and correlations
Scalability of asynchronous networks is limited by one-to-one mapping between effective connectivity and correlations
Network models are routinely downscaled because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics is conserved, here we show that...
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Personal Name(s): | van Albada, Sacha |
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Helias, Moritz / Diesmann, Markus | |
Contributing Institute: |
Computational and Systems Neuroscience; IAS-6 Computational and Systems Neuroscience; INM-6 |
Published in: | S. 1411.4770 |
Imprint: |
2014
|
PubMed ID: |
26325661 |
Document Type: |
Preprint |
Research Program: |
The Human Brain Project Supercomputing and Modelling for the Human Brain Brain-inspired multiscale computation in neuromorphic hybrid systems Helmholtz Young Investigators Group (Helmholtz Young Investigators Group: Key Technologies) Signalling Pathways and Mechanisms in the Nervous System Theory, modelling and simulation |
Link: |
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Publikationsportal JuSER |
Network models are routinely downscaled because of a lack of computational resources, often without explicit mention of the limitations this entails. While reliable methods have long existed to adjust parameters such that the first-order statistics of network dynamics is conserved, here we show that this is generally impossible already for second-order statistics. We argue that studies in computational biology need to make the scaling applied explicit, and that results should be verified where possible by full-scale simulations. We consider neuronal networks, where the importance of correlations in network dynamics is obvious because they directly interact with synaptic plasticity, the neuronal basis of learning, but the conclusions are generic. We derive conditions for the preservation of both mean activities and correlations under a change in numbers of neurons or synapses in the asynchronous regime typical of cortical networks. Analytical and simulation results are obtained for networks of binary and networks of leaky integrate-and-fire model neurons, randomly connected with or without delays. The structure of average pairwise correlations in such networks is determined by the effective population-level connectivity. We show that in the absence of symmetries or zeros in the population-level connectivity or correlations, the converse is also true. This is in line with earlier work on inferring connectivity from correlations, but implies that such network reconstruction should be possible for a larger class of networks than hitherto considered. When changing in-degrees, effective connectivity and hence correlation structure can be maintained by an appropriate scaling of the synaptic weights, but only over a limited range of in-degrees determined by the extrinsic variance. Our results show that the reducibility of asynchronous networks is fundamentally limited. |