  The notion of flat minima has played a key role in the generalization studies
of deep learning models. However, existing definitions of the flatness are
known to be sensitive to the rescaling of parameters. The issue suggests that
the previous definitions of the flatness might not be a good measure of
generalization, because generalization is invariant to such rescalings. In this
paper, from the PAC-Bayesian perspective, we scrutinize the discussion
concerning the flat minima and introduce the notion of normalized flat minima,
which is free from the known scale dependence issues. Additionally, we
highlight the scale dependence of existing matrix-norm based generalization
error bounds similar to the existing flat minima definitions. Our modified
notion of the flatness does not suffer from the insufficiency, either,
suggesting it might provide better hierarchy in the hypothesis class.
