The adoption of machine learning for socially relevant tasks requires effective explainable artificial intelligence (XAI) methods to better understand the behavior of machine learning models. Attribution methods are a popular XAI approach in which input-output relationships are characterized by heat maps that reflect the relative importance of input features for a particular prediction. The quality of such maps is often assessed by measuring faithfulness based on the area under insertion and deletion curves, which measures changes in the model output as features are added and removed. In this study, we derive an objective function from this notion of faithfulness and a way to approximate its gradient. We establish the connection between insertion curves and top-$k$ feature selection, which leads to a loss function measuring the quality of attributions. Randomization of the loss allows us to efficiently approximate its gradient. To show the effectiveness of the general approach, we combine the loss function with the neural explanation mask framework. The resulting method, termed Ra-NEM, can be used with any differentiable model without affecting the model's performance. Experiments demonstrate that Ra-NEM provides accurate attributions robustly and efficiently. Compared to other algorithms, the attributions have not only higher faithfulness but also perform well in terms of other XAI metrics. The high inference speed of Ra-NEM makes the method suitable for online applications. The code is available online: https://github.com/baerminator/Ra_Nem

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