  Signal-background classification is a central problem in High-Energy Physics
(HEP), that plays a major role for the discovery of new fundamental particles.
A recent method -- the Parametric Neural Network (pNN) -- leverages multiple
signal mass hypotheses as an additional input feature to effectively replace a
whole set of individual classifiers, each providing (in principle) the best
response for the corresponding mass hypothesis. In this work we aim at
deepening the understanding of pNNs in light of real-world usage. We discovered
several peculiarities of parametric networks, providing intuition, metrics, and
guidelines to them. We further propose an alternative parametrization scheme,
resulting in a new parametrized neural network architecture: the AffinePNN;
along with many other generally applicable improvements, like the balanced
training procedure. Finally, we extensively and empirically evaluate our models
on the HEPMASS dataset, along its imbalanced version (called HEPMASS-IMB) we
provide here for the first time, to further validate our approach. Provided
results are in terms of the impact of the proposed design decisions,
classification performance, and interpolation capability, as well.
