# 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.

## Key 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.