  We present powerful new analysis techniques to constrain effective field
theories at the LHC. By leveraging the structure of particle physics processes,
we extract extra information from Monte-Carlo simulations, which can be used to
train neural network models that estimate the likelihood ratio. These methods
scale well to processes with many observables and theory parameters, do not
require any approximations of the parton shower or detector response, and can
be evaluated in microseconds. We show that they allow us to put significantly
stronger bounds on dimension-six operators than existing methods, demonstrating
their potential to improve the precision of the LHC legacy constraints.
