  Flatness of the loss curve around a model at hand has been shown to
empirically correlate with its generalization ability. Optimizing for flatness
has been proposed as early as 1994 by Hochreiter and Schmidthuber, and was
followed by more recent successful sharpness-aware optimization techniques.
Their widespread adoption in practice, though, is dubious because of the lack
of theoretically grounded connection between flatness and generalization, in
particular in light of the reparameterization curse - certain
reparameterizations of a neural network change most flatness measures but do
not change generalization. Recent theoretical work suggests that a particular
relative flatness measure can be connected to generalization and solves the
reparameterization curse. In this paper, we derive a regularizer based on this
relative flatness that is easy to compute, fast, efficient, and works with
arbitrary loss functions. It requires computing the Hessian only of a single
layer of the network, which makes it applicable to large neural networks, and
with it avoids an expensive mapping of the loss surface in the vicinity of the
model. In an extensive empirical evaluation we show that this relative flatness
aware minimization (FAM) improves generalization in a multitude of applications
and models, both in finetuning and standard training. We make the code
available at github.
