Title: On Regularization for Explaining Graph Neural Networks: An Information Theory Perspective. Abstract: This work studies the explainability of graph neural networks (GNNs), which is important for the credibility of GNNs in practical usage. Existing work mostly follows the two-phase paradigm to interpret a prediction: feature attribution and selection. However, another important component --- regularization, which is crucial to facilitate the above paradigm --- has been seldom studied. In this work, we explore the role of regularization in GNNs explainability from the perspective of information theory. Our main findings are: 1) regularization is essentially pursuing the balance between two phases, 2) its optimal coefficient is proportional to the sparsity of explanations, 3) existing methods imply an implicit regularization effect of stochastic mechanism, and 4) its contradictory effects on two phases are responsible for the out-of-distribution (OOD) issue in post-hoc explainability. Based on these findings, we propose two common optimization methods, which can bolster the performance of the current explanation methods via sparsity-adaptive and OOD-resistant regularization schemes. Extensive empirical studies validate our findings and proposed methods. Code is available at  https://anonymous.4open.science/r/Rethink_Reg-07F0.
