Message passing algorithms for the Hopfield network reconstruction: threshold behavior and limitation

TL;DR

This paper investigates message passing algorithms for reconstructing Hopfield networks, highlighting their improved performance over mean-field methods, the impact of data magnetization on their effectiveness, and the observed threshold behavior related to network size.

Contribution

It introduces an enhanced susceptibility propagation algorithm for Hopfield network reconstruction and analyzes its limitations and phase transition behavior.

Findings

Improved reconstruction performance over mean-field methods.

Algorithm performance declines with highly magnetized data.

Sharp transition in reconstruction quality as network size increases.

Abstract

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.