  Direct searches for new particles at colliders have traditionally been
factorized into model proposals by theorists and model testing by
experimentalists. With the recent advent of machine learning methods that allow
for the simultaneous unfolding of all observables in a given phase space
region, there is a new opportunity to blur these traditional boundaries by
performing searches on unfolded data. This could facilitate a research program
where data are explored in their natural high dimensionality with as little
model bias as possible. We study how the information about physics beyond the
Standard Model is preserved by full phase space unfolding using an important
physics target at the Large Hadron Collider (LHC): exotic Higgs boson decays
involving hadronic final states. We find that if the signal cross section is
high enough, information about the new physics is visible in the unfolded data.
We will show that in some cases, quantifiably all of the information about the
new physics is encoded in the unfolded data. Finally, we show that there are
still many cases when the unfolding does not work fully or precisely, such as
when the signal cross section is small. This study will serve as an important
benchmark for enhancing unfolding methods for the LHC and beyond.
