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The field of 'explainable' artificial intelligence (XAI) has produced highlycited methods that seek to make the decisions of complex machine learning (ML)methods 'understandable' to humans, for example by attributing 'importance'scores to input features. Yet, a lack of formal underpinning leaves it unclearas to what conclusions can safely be drawn from the results of a given XAImethod and has also so far hindered the theoretical verification and empiricalvalidation of XAI methods. This means that challenging non-linear problems,typically solved by deep neural networks, presently lack appropriate remedies.Here, we craft benchmark datasets for three different non-linear classificationscenarios, in which the important class-conditional features are known bydesign, serving as ground truth explanations. Using novel quantitative metrics,we benchmark the explanation performance of a wide set of XAI methods acrossthree deep learning model architectures. We show that popular XAI methods areoften unable to significantly outperform random performance baselines and edgedetection methods. Moreover, we demonstrate that explanations derived fromdifferent model architectures can be vastly different; thus, prone tomisinterpretation even under controlled conditions.

XAI-TRIS: Non-linear image benchmarks to quantify false positive post-hoc attribution of feature importance