Flatness is a False Friend

Hessian based measures of flatness, such as the trace, Frobenius and spectral norms, have been argued, used and shown to relate to generalisation. In this paper we demonstrate that, for feed-forward neural networks under the cross-entropy loss, low-loss solutions with large neural network weights have small Hessian based measures of flatness. This implies that solutions obtained without L2 regularisation should be less sharp than those with...