Uncertainties in Generative Deep Learning and Data Amplification for High Energy Physics

Abstract

The upcoming high-luminosity upgrade of the LHC requires an increase in simulated data. Due to the high computational cost of detector simulation, this demand threatens to surpass the computational resources. As a consequence, it is important to develop faster, less compute intensive alternatives to classical detector simulation with Markov chain Monte Carlo (MCMC). Generative Deep Learning surrogates are one possible candidate for speeding up the simulation and are already applied in ATLAS fast simulation tools. However, the quality of the surrogate data is intrinsically limited by the training statistics. We demonstrate that the amount of training data poses as an upper limit on the precision of global properties of observables constructed from the data. Such global properties include for example means or variances. Nevertheless, the inductive bias of the Neural Network fit allows to surpass the training statistics when analyzing smaller regions of the data space. We show that the relaxed limit, which still depends on the training data, can be estimated from uncertainties predicted by Bayesian Neural Networks. To achieve a truthful estimate, the uncertainty prediction needs to be well calibrated. We show one way to calibrate uncertainties for generative Bayesian Neural Networks and find that the common variational inference method is hard to calibrate. We therefore develop a new method based on stochastic gradient MCMC. This method is called AdamMCMC. It is easy to apply and replaces the stochastic optimization commonly employed in Deep Learning. In contrast to variational inference, the variance of the uncertainty prediction can be adapted e!ectively through variation of a single parameter. Diverse predictions indicate out-of-distribution application. Overall, we find that the stochastic gradient MCMC produces more reliable predictions than variational inference in multiple applications. Classifier Surrogates are one possible application of generative Machine Learning, where reliable uncertainties are crucial. This class of surrogates predicts the behavior of jet taggers working on detector data from more accessible data. Experimental analysis employing such taggers can be reinterpreted without the need for detector simulation. This cuts computational cost and enables sharing of the analysis outside the collaboration. However, the uncertainties introduced by the approximation need to be controlled and application to new data spaces needs to be prevented. We show that Continuous Normalizing Flows, in combination with AdamMCMC, can fulfill these requirements. Similar surrogates can be of high value for the community and could be implemented with every jet tagger employed at ATLAS or CMS.