  The analysis of complex systems such as neural networks is made particularly
difficult by the overwhelming number of their interacting components. In the
absence of prior knowledge, identifying a small but informative subset of
network nodes on which the analysis should focus is a rather difficult task. In
this work, we address this problem in the context of a Hopfield model, for
which we seek representations given in terms of a subgroup of its neurons with
the aim of identifying those that can reveal the largest amount of information
about the system. Using a methodology based on concepts from information
theory, we reveal that such optimised low-resolution representations are not
only informative per se, but rather they also serve as probes of the neural
network properties; these results show a tight and potentially fruitful
relation between the level of detail at which the network is inspected and the
type and amount of information that can be extracted from it.
