one to account for the fact that the signal events are unsmeared, resulting in a higher frequency of unsmeared events that the adversary is trained on.

4.  The adversary is trained on background events for one epoch using mini-batch gradient descent with a batch size of 500.

5.  Steps 3 and 4 are repeated until they have been performed a total of 1000 times, with the learning rate decaying every 100 epochs to a factor of 0.75 of its previous value, starting from an initial value of 0.01.

[0.475]{} ![Supervised neural network classifier output (a) and ROC curves (b) for an adversarial classifier trained to classify signal and background events. The three background distributions result from the three different directions of smearing.[]{data-label="fig:advcls"}](figures/CLSadv3response.pdf "fig:"){width="\textwidth"}

[0.49]{} ![Supervised neural network classifier output (a) and ROC curves (b) for an adversarial classifier trained to classify signal and background events. The three background distributions result from the three different directions of smearing.[]{data-label="fig:advcls"}](figures/CLSadv3ROC.pdf "fig:"){width="\textwidth"}

The weight factor $\alpha$ in Eq.  determines the relative importance of the two optimisation objectives. If it is set to zero, then the adversary has no effect on the training of the classifier. If it is too large, however, the performance of 