  In order to comprehend and enhance models that describes various brain
regions is important to study the dynamics of trained recurrent neural
networks. Including Dales law in such models usually presents several
challenges. However, this is an important aspect that allows computational
models to better capture the characteristics of the brain. Here we present a
framework to train networks using such constraint. Then we have used it to
train them in simple decision making tasks. We characterized the eigenvalue
distributions of the recurrent weight matrices of such networks. Interestingly,
we discovered that the non-dominant eigenvalues of the recurrent weight matrix
are distributed in a circle with a radius less than 1 for those whose initial
condition before training was random normal and in a ring for those whose
initial condition was random orthogonal. In both cases, the radius does not
depend on the fraction of excitatory and inhibitory units nor the size of the
network. Diminution of the radius, compared to networks trained without the
constraint, has implications on the activity and dynamics that we discussed
here.
