  In a previous report we have evaluated analytically the mutual information
between the firing rates of N independent units and a set of multi-dimensional
continuous+discrete stimuli, for a finite population size and in the limit of
large noise. Here, we extend the analysis to the case of two interconnected
populations, where input units activate output ones via gaussian weights and a
threshold linear transfer function. We evaluate the information carried by a
population of M output units, again about continuous+discrete correlates. The
mutual information is evaluated solving saddle point equations under the
assumption of replica symmetry, a method which, by taking into account only the
term linear in N of the input information, is equivalent to assuming the noise
to be large. Within this limitation, we analyze the dependence of the
information on the ratio M/N, on the selectivity of the input units and on the
level of the output noise. We show analytically, and confirm numerically, that
in the limit of a linear transfer function and of a small ratio between output
and input noise, the output information approaches asymptotically the
information carried in input. Finally, we show that the information loss in
output does not depend much on the structure of the stimulus, whether purely
continuous, purely discrete or mixed, but only on the position of the threshold
nonlinearity, and on the ratio between input and output noise.
