  The generation of unit-weight events for complex scattering processes
presents a severe challenge to modern Monte Carlo event generators. Even when
using sophisticated phase-space sampling techniques adapted to the underlying
transition matrix elements, the efficiency for generating unit-weight events
from weighted samples can become a limiting factor in practical applications.
Here we present a novel two-staged unweighting procedure that makes use of a
neural-network surrogate for the full event weight. The algorithm can
significantly accelerate the unweighting process, while it still guarantees
unbiased sampling from the correct target distribution. We apply, validate and
benchmark the new approach in high-multiplicity LHC production processes,
including $Z/W$+4 jets and $t\bar{t}$+3 jets, where we find speed-up factors up
to ten.
