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The dual of the space of interactions in neural network models

Author

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  • D. De Martino

    (Center for Life Nanoscience CLNS-IIT, P. le A. Moro 2, 00815 Rome, Italy)

Abstract

In this work, the Gardner problem of inferring interactions and fields for an Ising neural network from given patterns under a local stability hypothesis is addressed under a dual perspective. By means of duality arguments, an integer linear system is defined whose solution space is the dual of the Gardner space and whose solutions represent mutually unstable patterns. We propose and discuss Monte Carlo methods in order to find and remove unstable patterns and uniformly sample the space of interactions thereafter. We illustrate the problem on a set of real data and perform ensemble calculation that shows how the emergence of phase dominated by unstable patterns can be triggered in a nonlinear discontinuous way.

Suggested Citation

  • D. De Martino, 2016. "The dual of the space of interactions in neural network models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(06), pages 1-13, June.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:06:n:s0129183116500674
    DOI: 10.1142/S0129183116500674
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