  Fitting model parameters to experimental data is a common yet often
challenging task, especially if the model contains many parameters. Typically,
algorithms get lost in regions of parameter space in which the model is
unresponsive to changes in parameters, and one is left to make adjustments by
hand. We explain this difficulty by interpreting the fitting process as a
generalized interpretation procedure. By considering the manifold of all model
predictions in data space, we find that cross sections have a hierarchy of
widths and are typically very narrow. Algorithms become stuck as they move near
the boundaries. We observe that the model manifold, in addition to being
tightly bounded, has low extrinsic curvature, leading to the use of geodesics
in the fitting process. We improve the convergence of the Levenberg-Marquardt
algorithm by adding the geodesic acceleration to the usual Levenberg-Marquardt
step.
