  Theoretical interpretations of particle physics data, such as the
determination of the Wilson coefficients of the Standard Model Effective Field
Theory (SMEFT), often involve the inference of multiple parameters from a
global dataset. Optimizing such interpretations requires the identification of
observables that exhibit the highest possible sensitivity to the underlying
theory parameters. In this work we develop a flexible open source framework,
ML4EFT, enabling the integration of unbinned multivariate observables into
global SMEFT fits. As compared to traditional measurements, such observables
enhance the sensitivity to the theory parameters by preventing the information
loss incurred when binning in a subset of final-state kinematic variables. Our
strategy combines machine learning regression and classification techniques to
parameterize high-dimensional likelihood ratios, using the Monte Carlo replica
method to estimate and propagate methodological uncertainties. As a proof of
concept we construct unbinned multivariate observables for top-quark pair and
Higgs+$Z$ production at the LHC, demonstrate their impact on the SMEFT
parameter space as compared to binned measurements, and study the improved
constraints associated to multivariate inputs. Since the number of neural
networks to be trained scales quadratically with the number of parameters and
can be fully parallelized, the ML4EFT framework is well-suited to construct
unbinned multivariate observables which depend on up to tens of EFT
coefficients, as required in global fits.
