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In a variety of contexts, physicists study complex, nonlinear models withmany unknown or tunable parameters to explain experimental data. We explain whysuch systems so often are sloppy; the system behavior depends only on a few`stiff' combinations of the parameters and is unchanged as other `sloppy'parameter combinations vary by orders of magnitude. We contrast examples ofsloppy models (from systems biology, variational quantum Monte Carlo, andcommon data fitting) with systems which are not sloppy (multidimensional linearregression, random matrix ensembles). We observe that the eigenvalue spectrafor the sensitivity of sloppy models have a striking, characteristic form, witha density of logarithms of eigenvalues which is roughly constant over a largerange. We suggest that the common features of sloppy models indicate that theymay belong to a common universality class. In particular, we motivate focusingon a Vandermonde ensemble of multiparameter nonlinear models and show in onelimit that they exhibit the universal features of sloppy models.Comment: New content adde

Sloppy-Model Universality Class and the Vandermonde Matrix