While enjoying the great achievements brought by deep learning (DL), people are also worried about the decision made by DL models, since the high degree of non-linearity of DL models makes the decision extremely difficult to understand. Consequently, attacks such as adversarial attacks are easy to carry out, but difficult to detect and explain, which has led to a boom in the research on local explanation methods for explaining model decisions. In this paper, we evaluate the faithfulness of explanation methods and find that traditional tests on faithfulness encounter the random dominance problem, \ie, the random selection performs the best, especially for complex data. To further solve this problem, we propose three trend-based faithfulness tests and empirically demonstrate that the new trend tests can better assess faithfulness than traditional tests on image, natural language and security tasks. We implement the assessment system and evaluate ten popular explanation methods. Benefiting from the trend tests, we successfully assess the explanation methods on complex data for the first time, bringing unprecedented discoveries and inspiring future research. Downstream tasks also greatly benefit from the tests. For example, model debugging equipped with faithful explanation methods performs much better for detecting and correcting accuracy and security problems.

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