tokens: 0.18, respectively, for the 80 per cent/20 per cent train/test split (right-hand panels in Figs 4 and 5 ). Given more training data for the final model, these hyperparameters should deliver an appropriate model complexity that does not overfit the data. As before, I train 100 models with different random states to avoid being biased by the random components in the fitting process. Henceforth, I will report the median value of the predictions from the 100 models. In Fig. 7 , I compare input T e metallicities with those predicted by the MLP model from strong lines. The error bars show the 1σ standard deviations of the 100 predictions. In general, the spread in metallicity due to the random components in the fitting process is much smaller than the dispersion of the calibration. Fig. 7 suggests that the best MLP model performs reasonably well over a wide range of metallicity. Figure 7. Comparison between oxygen abundances from the best MLP model (Section 2.3.4) and the T e method. The data points are the working sample described in Section 2.1 . The error bars are the standard deviations of the 100 predictions from the 100 model realizations. The dashed line is the one-to-one line. 2.3.5 Feature sensitivity Extracting physical interpretation from neuron weights and biases is known to be difficult. However, it is worth investigating how sensitive different features are to the output to understand their importance to the network. The sensitivity analysis can be achieved by computing the partial derivative of the output with respect to the input features. Using the best MLP model, I perturb one feature at a time while keeping the other features unchanged and compute the changes in the output metallicity. The small perturbation is set to 3 per cent of the standard deviation of the input feature of the working sample. The response of the model to the perturbations is calculated for the entire working sample. Fig. 8 presents histograms of the resulting changes in the output metallicities in the form of a ‘violin’ plot. The top three features that the network output is most sensitive to are [S ii ]/[N ii ], [N ii ]/[O ii ], and [N ii ] (deviate most from zero). Interestingly, photoionization models have demonstrated that the [N ii ]/[O ii ] ratio is a good metallicity diagnostic (at above 0.2 solar) due to its insensitivity to ionization parameter (Kewley Dopita 2002 ; Dopita et al. 2013 ). The combination of [N ii ]/[S ii ] and [N ii ]/H α is also suggested by Dopita et al. ( 2016 ) to be an excellent diagnostic that is insensitive to ISM pressure and ionization parameter. The neural network appears to rely more heavily on features that are also important in diagnostics developed from photoionization models, despite that this information is not given a priori. This demonstrates the ability of the neural network to directly ‘learn’ from the data. Figure 8. Feature sensitivity of the best MLP model, as measured by perturbing one feature at a time and
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