  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
non-linear discontinuous way.
