  We consider dense, associative neural-networks trained with no supervision
and we investigate their computational capabilities analytically, via a
statistical-mechanics approach, and numerically, via Monte Carlo simulations.
In particular, we obtain a phase diagram summarizing their performance as a
function of the control parameters such as the quality and quantity of the
training dataset and the network storage, valid in the limit of large network
size and structureless datasets. Moreover, we establish a bridge between
macroscopic observables standardly used in statistical mechanics and loss
functions typically used in the machine learning. As technical remarks, from
the analytic side, we implement large deviations and stability analysis within
Guerra's interpolation to tackle the not-Gaussian distributions involved in the
post-synaptic potentials while, from the computational counterpart, we insert
Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of
the synaptic tensors, overall obtaining a novel and broad approach to
investigate neural networks in general.
