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Real-world large-scale datasets usually contain noisy labels and areimbalanced. Therefore, we propose derivative manipulation (DM), a novel andgeneral example weighting approach for training robust deep models under theseadverse conditions.  DM has two main merits. First, loss function and example weighting are commontechniques in the literature. DM reveals their connection (a loss function doesexample weighting) and is a replacement of both. Second, despite that a lossdefines an example weighting scheme by its derivative, in the loss design, weneed to consider whether it is differentiable. Instead, DM is more flexible bydirectly modifying the derivative so that a loss can be a non-elementary formattoo. Technically, DM defines an emphasis density function by a derivativemagnitude function. DM is generic in that diverse weighting schemes can bederived.  Extensive experiments on both vision and language tasks prove DM'seffectiveness.

Derivative Manipulation for General Example Weighting