  We study dynamics for asymmetric spin glass models, proposed by Hertz et al.
and Sompolinsky et al. in the 1980's in the context of neural networks:
particles evolve via a modified Langevin dynamics for the
Sherrington--Kirkpatrick model with soft spins, whereby the disorder is i.i.d.
standard Gaussian rather than symmetric. Ben Arous and Guionnet (1995),
followed by Guionnet (1997), proved for Gaussian interactions that as the
number of particles grows, the short-term empirical law of this dynamics
converges a.s. to a non-random law $\mu_\star$ of a ``self-consistent single
spin dynamics,'' as predicted by physicists. Here we obtain universality of
this fact:
  For asymmetric disorder given by i.i.d. variables of zero mean, unit variance
and exponential or better tail decay, at every temperature, the empirical law
of sample paths of the
  Langevin-like dynamics in a fixed time interval has the same a.s. limit
$\mu_\star$.
