Identifying the Relevant Dependencies of the Neural Network Response on Characteristics of the Input Space

Abstract

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.