![Autoencoder loss (a) and ROC curves (b) for an adversarial autoencoder trained only on background events. The three background distributions result from the three different directions of smearing.[]{data-label="fig:AEadv"}](figures/AEadv3ROC.pdf "fig:"){width="\textwidth"}

In addition, we note that our setup also has the ability to interpolate to smaller amounts of smearing—although we have trained using background data which has been systematically smeared by a very large amount, we find that if it is tested on samples which have been smeared by a much smaller amount (without the increase by a factor of three), then the output of the adversarially-trained autoencoder (and also for the classifier in the previous section) is still insensitive to the smearing. Furthermore, we find that the AUC score increases when it is tested on a smaller amount of smearing, and is similar to the result of having both trained and tested it on this smaller amount. Therefore, the fact that the adversary is trained on a larger amount of smearing than is realistic does not adversely affect its performance.

We will now briefly recap what we have achieved by combining an autoencoder with an adversarial neural network. We started with three sets of background events—one which had been smeared upwards, 