Several areas have been improved with Deep Learning during the past years.
Implementing Deep Neural Networks (DNN) for non-safety related applications
have shown remarkable achievements over the past years; however, for using DNNs
in safety critical applications, we are missing approaches for verifying the
robustness of such models. A common challenge for DNNs occurs when exposed to
out-of-distribution samples that are outside of the scope of a DNN, but which
result in high confidence outputs despite no prior knowledge of such input.
In this paper, we analyze three methods that separate between in- and
out-of-distribution data, called supervisors, on four well-known DNN
architectures. We find that the outlier detection performance improves with the
quality of the model. We also analyse the performance of the particular
supervisors during the training procedure by applying the supervisor at a
predefined interval to investigate its performance as the training proceeds. We
observe that understanding the relationship between training results and
supervisor performance is crucial to improve the model's robustness and to
indicate, what input samples require further measures to improve the robustness
of a DNN. In addition, our work paves the road towards an instrument for safety
argumentation for safety critical applications. This paper is an extended
version of our previous work presented at 2019 SEAA (cf. [1]); here, we
elaborate on the used metrics, add an additional supervisor and test them on
two additional datasets.

本文分析了三种 in - 和 out-of-distribution 数据的分离方法及其性能，包括超级监督的应用及其训练过程中的性能评估，研究表明理解训练结果与监督性能与提高模型强健性密切相关，为安全应用提供了论据，并应用于两个额外的数据集。

训练神经网络的异常检测性能分析

Performance Analysis of Out-of-Distribution Detection on Trained Neural Networks

It has recently been shown that ReLU networks produce arbitrarily
over-confident predictions far away from the training data. Thus, ReLU networks
do not know when they don't know. However, this is a highly important property
in safety critical applications. In the context of out-of-distribution
detection (OOD) there have been a number of proposals to mitigate this problem
but none of them are able to make any mathematical guarantees. In this paper we
propose a new approach to OOD which overcomes both problems. Our approach can
be used with ReLU networks and provides provably low confidence predictions far
away from the training data as well as the first certificates for low
confidence predictions in a neighborhood of an out-distribution point. In the
experiments we show that state-of-the-art methods fail in this worst-case
setting whereas our model can guarantee its performance while retaining
state-of-the-art OOD performance.

本文提出了一种新的方法以应对激活函数为 ReLU 的神经网络在数据训练远离时会过度自信并有可能失去安全性的问题，该方法可以提供数学上的低置信预测同时提供第一个在一个分布外点附近的低置信预测的证书。实验表明，该方法能够在保留 OOS 性能的同时，保证其性能。