From Robustness to Explainability and Back Again

Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by poor scalability. At present, this limitation still holds true for some families of classifiers, the most significant being deep neural networks. This paper addresses the poor scalability of formal explainability and proposes novel efficient algorithms for computing formal explanations. The novel algorithm computes explanations by answering instead a number of robustness queries, and such that the number of such queries is at most linear on the number of features. Consequently, the proposed algorithm establishes a direct relationship between the practical complexity of formal explainability and that of robustness. To achieve the proposed goals, the paper generalizes the definition of formal explanations, thereby allowing the use of robustness tools that are based on different distance norms, and also by reasoning in terms of some target degree of robustness. Preliminary experiments validate the practical efficiency of the proposed approach.