Robustness is a fundamental property of machine learning classifiers to achieve safety and reliability. In the fields of adversarial robustness and formal robustness verification of image classification models, robustness is commonly defined as the stability to all input variations within an Lp-norm distance. However, robustness to random corruptions is usually improved and evaluated using variations observed in the real-world, while mathematically defined Lp-norm corruptions are rarely considered. This study investigates the use of random Lp-norm corruptions to augment the training and test data of image classifiers. We adapt an approach from the field of adversarial robustness to assess the model robustness to imperceptible random corruptions. We empirically and theoretically investigate whether robustness is transferable across different Lp-norms and derive conclusions on which Lp-norm corruptions a model should be trained and evaluated on. We find that training data augmentation with L0-norm corruptions improves corruption robustness while maintaining accuracy compared to standard training and when applied on top of selected state-of-the-art data augmentation techniques.

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