  Recently, sharpness-aware minimization (SAM) has attracted a lot of attention
because of its surprising effectiveness in improving generalization
performance.However, training neural networks with SAM can be highly unstable
since the loss does not decrease along the direction of the exact gradient at
the current point, but instead follows the direction of a surrogate gradient
evaluated at another point nearby. To address this issue, we propose a simple
renormalization strategy, dubbed StableSAM, so that the norm of the surrogate
gradient maintains the same as that of the exact gradient. Our strategy is easy
to implement and flexible enough to integrate with SAM and its variants, almost
at no computational cost. With elementary tools from convex optimization and
learning theory, we also conduct a theoretical analysis of sharpness-aware
training, revealing that compared to stochastic gradient descent (SGD), the
effectiveness of SAM is only assured in a limited regime of learning rate. In
contrast, we show how StableSAM extends this regime of learning rate and when
it can consistently perform better than SAM with minor modification. Finally,
we demonstrate the improved performance of StableSAM on several representative
data sets and tasks.
