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Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks

Muir, Dylan R. and Mrsic-Flogel, Thomas. (2015) Eigenspectrum bounds for semirandom matrices with modular and spatial structure for neural networks. Physical review. E, Statistical, nonlinear, and soft matter physics, 91 (4). 042808.

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Official URL: http://edoc.unibas.ch/41441/

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Abstract

The eigenvalue spectrum of the matrix of directed weights defining a neural network model is informative of several stability and dynamical properties of network activity. Existing results for eigenspectra of sparse asymmetric random matrices neglect spatial or other constraints in determining entries in these matrices, and so are of partial applicability to cortical-like architectures. Here we examine a parameterized class of networks that are defined by sparse connectivity, with connection weighting modulated by physical proximity (i.e., asymmetric Euclidean random matrices), modular network partitioning, and functional specificity within the excitatory population. We present a set of analytical constraints that apply to the eigenvalue spectra of associated weight matrices, highlighting the relationship between connectivity rules and classes of network dynamics.
Faculties and Departments:05 Faculty of Science > Departement Biozentrum > Former Organization Units Biozentrum > Neural Networks (Mrsic-Flogel)
UniBasel Contributors:Mrsic-Flogel, Thomas and Muir, Dylan R
Item Type:Article, refereed
Article Subtype:Research Article
ISSN:1550-2376
e-ISSN:1550-2376
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:16 Aug 2016 13:58
Deposited On:16 Aug 2016 13:58

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