  In this paper we adapt the broken replica interpolation technique (developed
by Francesco Guerra to deal with the Sherrington-Kirkpatrick model, namely a
pairwise mean-field spin-glass whose couplings are i.i.d. standard Gaussian
variables) in order to work also with the Hopfield model (i.e., a pairwise
mean-field neural-network whose couplings are drawn according to Hebb's
learning rule): this is accomplished by grafting Guerra's telescopic averages
on the transport equation technique, recently developed by some of the Authors.
As an overture, we apply the technique to solve the Sherrington-Kirkpatrick
model with i.i.d. Gaussian couplings centered at $J_0$ and with finite variance
$J$; the mean $J_0$ plays the role of a signal to be detected in a noisy
environment tuned by $J$, hence making this model a natural test-case to be
investigated before addressing the Hopfield model. For both the models, an
explicit expression of their quenched free energy in terms of their natural
order parameters is obtained at the K-th step (K arbitrary, but finite) of
replica-symmetry-breaking. In particular, for the Hopfield model, by assuming
that the overlaps respect Parisi's decomposition (following the ziqqurat
ansatz) and that the Mattis magnetization is self-averaging, we recover
previous results obtained via replica-trick by Amit, Crisanti and Gutfreund
(1RSB) and by Steffan and K\"{u}hn (2RSB).
