  Model update is a crucial process in the operation of ML/AI systems. While
updating a model generally enhances the average prediction performance, it also
significantly impacts the explanations of predictions. In real-world
applications, even minor changes in explanations can have detrimental
consequences. To tackle this issue, this paper introduces BCX, a quantitative
metric that evaluates the backward compatibility of feature attribution
explanations between pre- and post-update models. BCX utilizes practical
agreement metrics to calculate the average agreement between the explanations
of pre- and post-update models, specifically among samples on which both models
accurately predict. In addition, we propose BCXR, a BCX-aware model training
method by designing surrogate losses which theoretically lower bounds agreement
scores. Furthermore, we present a universal variant of BCXR that improves all
agreement metrics, utilizing L2 distance among the explanations of the models.
To validate our approach, we conducted experiments on eight real-world
datasets, demonstrating that BCXR achieves superior trade-offs between
predictive performances and BCX scores, showcasing the effectiveness of our
BCXR methods.
