  Explainable machine learning attracts increasing attention as it improves
transparency of models, which is helpful for machine learning to be trusted in
real applications. However, explanation methods have recently been demonstrated
to be vulnerable to manipulation, where we can easily change a model's
explanation while keeping its prediction constant. To tackle this problem, some
efforts have been paid to use more stable explanation methods or to change
model configurations. In this work, we tackle the problem from the training
perspective, and propose a new training scheme called Adversarial Training on
EXplanations (ATEX) to improve the internal explanation stability of a model
regardless of the specific explanation method being applied. Instead of
directly specifying explanation values over data instances, ATEX only puts
requirement on model predictions which avoids involving second-order
derivatives in optimization. As a further discussion, we also find that
explanation stability is closely related to another property of the model,
i.e., the risk of being exposed to adversarial attack. Through experiments,
besides showing that ATEX improves model robustness against manipulation
targeting explanation, it also brings additional benefits including smoothing
explanations and improving the efficacy of adversarial training if applied to
the model.
