Signal model parameter scan using Normalizing Flow

Abstract: This paper presents a parameter scan technique for BSM signal models based on normalizing flow. Normalizing flow is a type of deep learning model that transforms a simple probability distribution into a complex probability distribution as an invertible function. By learning an invertible transformation between a complex multidimensional distribution, such as experimental data observed in collider experiments, and a multidimensional normal distribution, the normalizing flow model gains the ability to sample (or generate) pseudo experimental data from random numbers and to evaluate a log-likelihood value from multidimensional observed events. The normalizing flow model can also be extended to take multidimensional conditional variables as arguments. Thus, the normalizing flow model can be used as a generator and evaluator of pseudo experimental data conditioned by the BSM model parameters. The log-likelihood value, the output of the normalizing flow model, is a function of the conditional variables. Therefore, the model can quickly calculate gradients of the log-likelihood to the conditional variables. Following this property, it is expected that the most likely set of conditional variables that reproduce the experimental data, i.e. the optimal set of parameters for the BSM model, can be efficiently searched. This paper demonstrates this on a simple dataset and discusses its limitations and future extensions.