  Sharpness-Aware Minimization (SAM) is a recently proposed gradient-based
optimizer (Foret et al., ICLR 2021) that greatly improves the prediction
performance of deep neural networks. Consequently, there has been a surge of
interest in explaining its empirical success. We focus, in particular, on
understanding the role played by normalization, a key component of the SAM
updates. We theoretically and empirically study the effect of normalization in
SAM for both convex and non-convex functions, revealing two key roles played by
normalization: i) it helps in stabilizing the algorithm; and ii) it enables the
algorithm to drift along a continuum (manifold) of minima -- a property
identified by recent theoretical works that is the key to better performance.
We further argue that these two properties of normalization make SAM robust
against the choice of hyper-parameters, supporting the practicality of SAM. Our
conclusions are backed by various experiments.
