  Sloppy models are complex nonlinear models with outcomes that are
significantly affected by only a small subset of parameter combinations.
Despite forming an important universality class and arising frequently in
practice, formal and systematic explanations of sloppiness are lacking. By
unifying geometric interpretations of sloppiness with Chebyshev approximation
theory, we offer such an explanation, and show how sloppiness can be described
explicitly in terms of model smoothness. Our approach results in universal
bounds on model predictions for classes of smooth models, and our bounds
capture global geometric features that are intrinsic to their model manifolds.
We illustrate these ideas using three disparate models: exponential decay,
reaction rates from an enzyme-catalysed chemical reaction, and an epidemiology
model of an infected population.
