  Toward achieving robust and defensive neural networks, the robustness against
the weight parameters perturbations, i.e., sharpness, attracts attention in
recent years (Sun et al., 2020). However, sharpness is known to remain a
critical issue, "scale-sensitivity." In this paper, we propose a novel
sharpness measure, Minimum Sharpness. It is known that NNs have a specific
scale transformation that constitutes equivalent classes where functional
properties are completely identical, and at the same time, their sharpness
could change unlimitedly. We define our sharpness through a minimization
problem over the equivalent NNs being invariant to the scale transformation. We
also develop an efficient and exact technique to make the sharpness tractable,
which reduces the heavy computational costs involved with Hessian. In the
experiment, we observed that our sharpness has a valid correlation with the
generalization of NNs and runs with less computational cost than existing
sharpness measures.
