  A key challenge in searches for resonant new physics is that classifiers
trained to enhance potential signals must not induce localized structures. Such
structures could result in a false signal when the background is estimated from
data using sideband methods. A variety of techniques have been developed to
construct classifiers which are independent from the resonant feature (often a
mass). Such strategies are sufficient to avoid localized structures, but are
not necessary. We develop a new set of tools using a novel moment loss function
(Moment Decomposition or MoDe) which relax the assumption of independence
without creating structures in the background. By allowing classifiers to be
more flexible, we enhance the sensitivity to new physics without compromising
the fidelity of the background estimation.
