# Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem

## TL;DR

This paper investigates why ReLU neural networks tend to produce high-confidence predictions far from training data and introduces a robust training method to mitigate this issue, improving reliability in safety-critical applications.

## Contribution

The paper identifies the failure mode of ReLU networks in producing high-confidence predictions far from data and proposes a new adversarial training-inspired technique to address this problem.

## Key findings

- The method effectively reduces confidence far from training data.
- It maintains high accuracy on the original classification task.
- The approach improves reliability in safety-critical systems.

## Abstract

Classifiers used in the wild, in particular for safety-critical systems, should not only have good generalization properties but also should know when they don't know, in particular make low confidence predictions far away from the training data. We show that ReLU type neural networks which yield a piecewise linear classifier function fail in this regard as they produce almost always high confidence predictions far away from the training data. For bounded domains like images we propose a new robust optimization technique similar to adversarial training which enforces low confidence predictions far away from the training data. We show that this technique is surprisingly effective in reducing the confidence of predictions far away from the training data while maintaining high confidence predictions and test error on the original classification task compared to standard training.