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The matrix element method is widely considered the ultimate LHC inferencetool for small event numbers. We show how a combination of two conditionalgenerative neural networks encodes the QCD radiation and detector effectswithout any simplifying assumptions, while keeping the computation oflikelihoods for individual events numerically efficient. We illustrate ourapproach for the CP-violating phase of the top Yukawa coupling in associatedHiggs and single-top production. Currently, the limiting factor for theprecision of our approach is jet combinatorics.

Two Invertible Networks for the Matrix Element Method