Go with the flow. Normalizing flow applications for high energy physics

Deep Learning is becoming a standard tool across science and industry to optimally solve a variety of tasks. A challenge of great importance for the research program carried over at the Large Hadron Collider is realising a generative model to sample synthetic data from a desired probability density. While generative models such as Generative Adversarial Networks and Normalizing Flows have been originally designed to solve Machine Learning tasks such as classification and data generation, we illustrate how they can also be employed to statistically invert Monte Carlo simulations of detector effects. In particular, we show how conditional Generative Adversarial Networks and Normalizing Flows are capable of unfolding detector effects, using ZW production at the LHC as a benchmarking process. Two technical by-products of interest stemming from these studies are the introduction of a Bayesian Normalizing Flow and of the Latent Space Refinement (LaSeR) protocol. The former has been introduced in order to address the crucial question of explainability and uncertainty estimation of deep generative models, which is achieved by reformulating the training and prediction phases of Normalizing Flows as a Bayesian inference task. Finally, LaSeR is a method to refine a model's output using classifier weights. We show how LaSeR can critically improve the performances of a Normalizing Flow whenever the training data contains topological obstructions.