Amplitude Uncertainties Everywhere All at Once

Abstract

Ultra-fast, precise, and controlled amplitude surrogates are essential for future LHC event generation. First, we investigate the noise reduction and biases of network ensembles and outline a new method to learn well-calibrated systematic uncertainties for them. We also establish evidential regression as a sampling-free method for uncertainty quantification. In a second part, we tackle localized disturbances for amplitude regression and demonstrate that learned uncertainties from Bayesian networks, ensembles, and evidential regression all identify numerical noise or gaps in the training data.

Figures (17)

• Figure 1: Comparison of MSE, heteroscedastic, and natural-heteroscedastic losses.
• Figure 2: Distribution of the squared amplitudes $A$ in the dataset used for training and evaluation.
• Figure 3: Relative uncertainty versus training dataset size for different kernel prefactors $\beta$. The plots show the relative systematic and statistical uncertainty, the mean accuracy $\langle \Delta \rangle$, and the mean systematic pull $\langle t_\text{syst} \rangle$. The error bars are calculated based on five independent runs.
• Figure 4: $\Delta$ distribution for a repulsive ensemble trained for 100 epochs with one hidden layer of dimension 32. The gray lines represent the individual ensemble members, while the red curve displays the mean over all members.
• Figure 5: Mean value for $\Delta$ calculated bin-wise for the true amplitudes $A_\text{true}$. Left: Comparing a full ensemble with its single member contribution. Right: Showing different network sizes and configurations in training length.