  The relation between the input and output spaces of neural networks (NNs) is
investigated to identify those characteristics of the input space that have a
large influence on the output for a given task. For this purpose, the NN
function is decomposed into a Taylor expansion in each element of the input
space. The Taylor coefficients contain information about the sensitivity of the
NN response to the inputs. A metric is introduced that allows for the
identification of the characteristics that mostly determine the performance of
the NN in solving a given task. Finally, the capability of this metric to
analyze the performance of the NN is evaluated based on a task common to data
analyses in high-energy particle physics experiments.
