  The past few years have seen a rapid development of machine-learning
algorithms. While surely augmenting performance, these complex tools are often
treated as black-boxes and may impair our understanding of the physical
processes under study. The aim of this paper is to move a first step into the
direction of applying expert-knowledge in particle physics to calculate the
optimal decision function and test whether it is achieved by standard training,
thus making the aforementioned black-box more transparent. In particular, we
consider the binary classification problem of discriminating quark-initiated
jets from gluon-initiated ones. We construct a new version of the widely used
N-subjettiness, which features a simpler theoretical behaviour than the
original one, while maintaining, if not exceeding, the discrimination power. We
input these new observables to the simplest possible neural network, i.e. the
one made by a single neuron, or perceptron, and we analytically study the
network behaviour at leading logarithmic accuracy. We are able to determine
under which circumstances the perceptron achieves optimal performance. We also
compare our analytic findings to an actual implementation of a perceptron and
to a more realistic neural network and find very good agreement.
