A common problem arises when the hypersurface is flat (plateaus) the gradients become close to zero. A very simple way to mitigate this problem is based on adding a small homoscedastic noise component to the gradients:

The covariance matrix is normally diagonal with all elements set to σ²(t), and this value is decayed during the training process to avoid perturbations when the corrections are very small. This method is conceptually reasonable, but its implicit randomness can yield undesired effects when the noise component is dominant. As it's very difficult to tune up the variances in deep models, other (more deterministic) strategies have been proposed.