\section{Conclusion}

In conclusion, through extensive empirical analysis, we showed that the proposed algorithm outperforms, in terms of speed and computational efficiency, state-of-the-art methods for Neural Network reliability assessment, for moderately high dimensional datasets such as MNIST and CIFAR10. However, as mentioned above, a crucial limitation of our approach, compared to the sequential Monte Carlo approach, is the inability to handle very high-dimensional data. Indeed, while their algorithm is slower, \cite{titaistats} show that it can efficiently estimate probabilities of failure on the ImageNet dataset. This limitation is directly linked to weight degeneracy, which becomes very difficult to handle when the problem dimension, $d$, is of the order of hundreds of thousands or more. Developing a hybrid approach between ours and splitting techniques, which has been done for another type of reliability problem \citep{combine}, is a promising avenue for future research.