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Dimension reduction in heterogeneous neural networks: Generalized Polynomial Chaos (gPC) and ANalysis-Of-VAriance (ANOVA)

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Abstract

We propose, and illustrate via a neural network example, two different approaches to coarse-graining large heterogeneous networks. Both approaches are inspired from, and use tools developed in, methods for uncertainty quantification (UQ) in systems with multiple uncertain parameters – in our case, the parameters are heterogeneously distributed on the network nodes. The approach shows promise in accelerating large scale network simulations as well as coarse-grained fixed point, periodic solution computation and stability analysis. We also demonstrate that the approach can successfully deal with structural as well as intrinsic heterogeneities.

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Authors and Affiliations

  1. Department of Chemical and Biological Engineering, Princeton University, Princeton, USA

    M. Choi & T. Bertalan

  2. Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand

    C.R. Laing

  3. Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics, Princeton University, Princeton, USA

    I.G. Kevrekidis

Authors
  1. M. Choi
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  2. T. Bertalan
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  3. C.R. Laing
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  4. I.G. Kevrekidis
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Corresponding authors

Correspondence to M. Choi, T. Bertalan, C.R. Laing or I.G. Kevrekidis.

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Choi, M., Bertalan, T., Laing, C. et al. Dimension reduction in heterogeneous neural networks: Generalized Polynomial Chaos (gPC) and ANalysis-Of-VAriance (ANOVA). Eur. Phys. J. Spec. Top. 225, 1165–1180 (2016). https://doi.org/10.1140/epjst/e2016-02662-3

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  • DOI: https://doi.org/10.1140/epjst/e2016-02662-3

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