  We explore the potential of Graph Neural Networks (GNNs) to improve the
performance of high-dimensional effective field theory parameter fits to
collider data beyond traditional rectangular cut-based differential
distribution analyses. In this study, we focus on a SMEFT analysis of $pp \to
t\bar t$ production, including top decays, where the linear effective field
deformation is parametrised by thirteen independent Wilson coefficients. The
application of GNNs allows us to condense the multidimensional phase space
information available for the discrimination of BSM effects from the SM
expectation by considering all available final state correlations directly. The
number of contributing new physics couplings very quickly leads to statistical
limitations when the GNN output is directly employed as an EFT discrimination
tool. However, a selection based on minimising the SM contribution enhances the
fit's sensitivity when reflected as a (non-rectangular) selection on the
inclusive data samples that are typically employed when looking for
non-resonant deviations from the SM by means of differential distributions.
