How can we trust opaque systems? Criteria for robust explanations in XAI

Deep learning (DL) algorithms are becoming ubiquitous in everyday life and in scientific research. However, the price we pay for their impressively accurate predictions is significant: their inner workings are notoriously opaque - it is unknown to laypeople and researchers alike what features of the data a DL system focuses on and how it ultimately succeeds in predicting correct outputs. A necessary criterion for trustworthy explanations is that they should reflect the relevant processes the algorithms' predictions are based on. The field of eXplainable Artificial Intelligence (XAI) presents promising methods to create such explanations. But recent reviews about their performance offer reasons for skepticism. As we will argue, a good criterion for trustworthiness is explanatory robustness: different XAI methods produce the same explanations in comparable contexts. However, in some instances, all methods may give the same, but still wrong, explanation. We therefore argue that in addition to explanatory robustness (ER), a prior requirement of explanation method robustness (EMR) has to be fulfilled by every XAI method. Conversely, the robustness of an individual method is in itself insufficient for trustworthiness. In what follows, we develop and formalize criteria for ER as well as EMR, providing a framework for explaining and establishing trust in DL algorithms. We also highlight interesting application cases and outline directions for future work.