  We study graded response attractor neural networks with asymmetrically
extremely dilute interactions and Langevin dynamics. We solve our model in the
thermodynamic limit using generating functional analysis, and find (in contrast
to the binary neurons case) that even in statics one cannot eliminate the
non-persistent order parameters. The macroscopic dynamics is driven by the
(non-trivial) joint distribution of neurons and fields, rather than just the
(Gaussian) field distribution. We calculate phase transition lines and present
simulation results in support of our theory.
