  In high energy physics, characterizing the response of a detector to
radiation is one of the most important and basic experimental tasks. In many
cases, this task is accomplished by parameterizing summary statistics of the
full detector response probability density. The parameterized detector response
can then be used for calibration as well as for directly improving physics
analysis sensitivity. This paper discusses how to parameterize summary
statistics of the detector response using neural networks. In particular,
neural networks are powerful tools for incorporating multidimensional data and
the loss function used during training determines which summary statistic is
learned. One common summary statistic that has not been combined with deep
learning (as far as the authors are aware) is the mode. A neural network-based
approach to mode learning is proposed and empirically demonstrated in the
context of high energy jet calibrations. Altogether, the neural network-based
toolkit for detector response parameterization can enhance the utility of data
collected at high energy physics experiments and beyond.
