Geometric Remove-and-Retrain (GOAR): Coordinate-Invariant eXplainable AI Assessment

Identifying the relevant input features that have a critical influence on the output results is indispensable for the development of explainable artificial intelligence (XAI). Remove-and-Retrain (ROAR) is a widely accepted approach for assessing the importance of individual pixels by measuring changes in accuracy following their removal and subsequent retraining of the modified dataset. However, we uncover notable limitations in pixel-perturbation strategies. When viewed from a geometric perspective, this method perturbs pixels by moving each sample in the pixel-basis direction. However, we have found that this approach is coordinate-dependent and fails to discriminate between differences among features, thereby compromising the reliability of the evaluation. To address this challenge, we introduce an alternative feature-perturbation approach named Geometric Remove-and-Retrain (GOAR). GOAR offers a perturbation strategy that takes into account the geometric structure of the dataset, providing a coordinate-independent metric for accurate feature comparison. Through a series of experiments with both synthetic and real datasets, we substantiate that GOAR's geometric metric transcends the limitations of pixel-centric metrics.