The dual of the space of interactions in neural network models

Daniele De Martino

Published 2015-05-12Version 1

In this work the problem of inferring interactions and fields for an Ising neural network from given patterns under a local stability hypothesis (Gardner problem) 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 space of interactions 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 pattern can be triggered in a non-linear discontinuous way.