  The retrieval capabilities of associative neural networks can be impaired by
different kinds of noise: the fast noise (which makes neurons more prone to
failure), the slow noise (stemming from interference among stored memories),
and synaptic noise (due to possible flaws during the learning or the storing
stage). In this work we consider dense associative neural networks, where
neurons can interact in $p$-plets, in the absence of fast noise, and we
investigate the interplay of slow and synaptic noise. In particular, leveraging
on the duality between associative neural networks and restricted Boltzmann
machines, we analyze the effect of corrupted information, imperfect learning
and storing errors. For $p=2$ (corresponding to the Hopfield model) any source
of synaptic noise breaks-down retrieval if the number of memories $K$ scales as
the network size. For $p>2$, in the relatively low-load regime $K \sim N$,
synaptic noise is tolerated up to a certain bound, depending on the density of
the structure.
