  We study how the degree of symmetry in the couplings influences the
performance of three mean field methods used for solving the direct and inverse
problems for generalized Sherrington-Kirkpatrick models. In this context, the
direct problem is predicting the potentially time-varying magnetizations. The
three theories include the first and second order Plefka expansions, referred
to as naive mean field (nMF) and TAP, respectively, and a mean field theory
which is exact for fully asymmetric couplings. We call the last of these simply
MF theory. We show that for the direct problem, nMF performs worse than the
other two approximations, TAP outperforms MF when the coupling matrix is nearly
symmetric, while MF works better when it is strongly asymmetric. For the
inverse problem, MF performs better than both TAP and nMF, although an ad hoc
adjustment of TAP can make it comparable to MF. For high temperatures the
performance of TAP and MF approach each other.
