  The Hopfield network is reconstructed as an inverse Ising problem by passing
messages. The applied susceptibility propagation algorithm is shown to improve
significantly on other mean-field-type methods and extends well into the low
temperature region. However, this iterative algorithm is limited by the nature
of the supplied data. Its performance deteriorates as the data becomes highly
magnetized, and this method finally fails in the presence of the frozen type
data where at least two of its magnetizations are equal to one in absolute
value. On the other hand, a threshold behavior is observed for the
susceptibility propagation algorithm and the transition from good
reconstruction to poor one becomes sharper as the network size increases.
