Identifying the relevant dependencies of the neural network response on characteristics of the input space

TL;DR

This paper introduces a Taylor expansion-based method to analyze neural network sensitivities, identifying key input characteristics influencing output, and evaluates its effectiveness in high-energy physics data analysis.

Contribution

It presents a novel metric derived from Taylor coefficients to determine input features that most affect neural network performance.

Findings

The metric effectively identifies influential input characteristics.

Application to physics data demonstrates practical utility.

Provides insights into neural network decision-making processes.

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.