  Flatness of the loss curve is conjectured to be connected to the
generalization ability of machine learning models, in particular neural
networks. While it has been empirically observed that flatness measures
consistently correlate strongly with generalization, it is still an open
theoretical problem why and under which circumstances flatness is connected to
generalization, in particular in light of reparameterizations that change
certain flatness measures but leave generalization unchanged. We investigate
the connection between flatness and generalization by relating it to the
interpolation from representative data, deriving notions of representativeness,
and feature robustness. The notions allow us to rigorously connect flatness and
generalization and to identify conditions under which the connection holds.
Moreover, they give rise to a novel, but natural relative flatness measure that
correlates strongly with generalization, simplifies to ridge regression for
ordinary least squares, and solves the reparameterization issue.
