Abstract by Benjamin Francis
Physics and Astronomy
Classification of sloppy models based on curvature
Some complex processes can be explained by relatively simple models (effective theories). This is possible due to a property known as sloppiness, that has recently been proposed using Information Geometry. In this approach, models, which map parameters to predictions, are naturally interpreted as manifolds. Sloppy models are characterized by a manifold that is bounded by many narrow widths. These correspond to irrelevant directions, while long dimensions correspond to the relevant components of the effective theory. We consider the curvature of several model manifolds. In many cases, the curvatures are small compared to the widths. In oscillatory systems, the curvatures are much larger. Large curvatures pose technical challenges, e. g. leading to local minima in the objective function when fitting to data. They are also a signature of high dimensionality in the effective theory. We propose a subclassification of sloppy models based on curvature and discuss broader implications for modeling complex systems.