  In the context of the Standard Model effective field theory (SMEFT), we study
the LHC sensitivity to four fermion operators involving heavy quarks by
employing cross section measurements in the $t\bar{t}b\bar{b}$ final state.
Starting from the measurement of total rates, we progressively exploit
kinematical information and machine learning techniques to optimize the
projected sensitivity at the end of Run III. Indeed, in final states with high
multiplicity containing inter-correlated kinematical information, multi-variate
methods provide a robust way of isolating the regions of phase space where the
SMEFT contribution is enhanced. We also show that training for multiple output
classes allows for the discrimination between operators mediating the
production of tops in different helicity states. Our projected sensitivities
not only constrain a host of new directions in the SMEFT parameter space but
also improve on existing limits demonstrating that, on one hand,
$t\bar{t}b\bar{b}$ production is an indispensable component in a future global
fit for top quark interactions in the SMEFT, and on the other, multi-class
machine learning algorithms can be a valuable tool for interpreting LHC data in
this framework.
