them more robust with respect to such manipulations. This is achieved by projecting explanations on the tangent space of the data manifold. This is exciting because it connects explainability to the field of manifold learning. For applying these methods, it is however necessary to estimate the tangent space of the data manifold. For high-dimensional datasets, such as ImageNet, this is an expensive and challenging task. Future work will try to overcome this hurdle. Another promising direction for further research is to apply the methods developed in this work to other application domains such as natural language processing.
Acknowledgements
We thank the reviewers for their valuable feedback. P.K. is greatly indebted to his mother-in-law as she took care of his sick son and wife during the final week before submission. We acknowledge Shinichi Nakajima for stimulating discussion. K-R.M. was supported in part by the German Ministry for Education and Research (BMBF) under Grants 01IS14013A-E, 01GQ1115, 01GQ0850, 01IS18025A and 01IS18037A. This work is also supported by the Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (No. 2017-001779), as well as by the Research Training Group "Differential Equation- and Data-driven Models in Life Sciences and Fluid Dynamics (DAEDALUS)" (GRK 2433) and Grant Math+, EXC 2046/1, Project ID 390685689 both funded by the German Research Foundation (DFG).
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