Neural Control Variates at LO and NLO

We employ neural control variates to minimize the range of event weights and avoid negative weights for phase-space integration and event generation. A signed control variate, built from two normalizing flows, fulfills both tasks. Combined with neural importance sampling, it significantly reduces the computational cost of LO and NLO predictions. For the NLO case, our conditional neural control variate can be viewed as a trainable subtraction term, complementing the established physics subtraction schemes for enhanced sampling performance.