Local Fit: The Compton form factors (CFFs) are extracted through a fit at fixed kinematics, usually across the independent variable $\phi$, the azimuthal angle between the lepton and hadron scattering planes. The fit independently determines the CFFs from measurements between different fixed kinematic bins. The analytical fit function (or loss function for ANNs) is defined by the helicity amplitudes so the results can be specific to a particular formalism. Without the necessary constraints using multiple observables in simultaneous fitting, there is a lack of uniqueness leading to large systematic errors in the extraction.
Global fits: An analytical parameterization depending on the GPDs is used to match to experimental data. Once parameterized interpolation and extrapolations are possible. The analytical expression used in the parameterization is generally a model proposed with a phenomenological interpretation but the range of possible models is vast so this approach suffers from initial biases built into the framework and so also contains large systematic errors that are difficult if not impossible to quantify. We do not use this approach but point it out only to make a clear distinction from the local fitting methods.
Local Multivariate Inference: A multivariate fit is performed in $Q^2$, $t$, and $x_B$ using a DNN at many fixed kinematics across the independent variable $\phi$. The analytical fit function (loss function) is defined by the helicity amplitudes so the results can be specific to a particular formalism, similar to the local fit. The DNN fit incorporates all of the information across the phase space of the experimental data resulting in a model that can interpolate and extrapolate. With this approach, there is no preconceived analytical expression defined, so there are no initial biases to contend with.