Wing Sheung Chan

Event selection and classification 81 Table 4.7.: Configurations and hyperparameters of the NN architecture and optimiser. Defini- tions of β 1 , β 2 and the learning rate can be found in Reference [96] . Configuration/hyperparmeter Value Architecture Number of hidden layer 2 Number of neurons per hidden layer 20 Connection between layers Fully connected (Dense) Hidden-layer activation Rectified linear unit (ReLU) Output-layer activation Standard logistic sigmoid Optimiser Loss function Binary cross-entropy Training epochs 200 Batch size 256 Algorithm Adam (non-AMSGrad variant) Learning rate (NN Z ττ , 1P) 5 × 10 − 5 Learning rate (NN Z `` , 1P) 2 . 5 × 10 − 4 Learning rate (others) 1 × 10 − 4 β 1 0.9 β 2 0.999 Regularisation None Dropout None where the summation is over b = Z τ τ , Wjets , Z `` ( b = Z τ τ , Wjets) for events with 1-prong (3-prong) τ had - vis candidates, and { w b } are constant weights assigned to the corresponding individual classifiers and are free parameters of the combination formula. By construction, the combined NN output also ranges from zero to one, with one again representing the most signal-like event and zero representing the most generally background-like event. With Equation (4.8) , we have the freedom to choose the values of { w b } . If w Z ττ = w Wjets = w Z `` , for events in the 1P region, the combined NN output simply represents one minus the normalised distance in a three-dimensional space between the point (NN Z ττ output, NN Wjets output, NN Z `` output) for the considered event and the point (1 , 1 , 1) that corresponds to the theoretically most signal-like event possible (or similarly in a two-dimensional space for events in the 3P region). If different values for { w b } are chosen, the distance along certain directions in the NN Z ττ -output–NN Wjets -output–NN Z `` -output space would be amplified, thus giving the output of certain individual classifiers more im- portance. The choice of the values of { w b } has an impact on the sensitivity of the analysis,