Interpreting deep learning-based stellar mass estimation via causal analysis and mutual information decomposition

End-to-end deep learning models fed with multi-band galaxy images are powerful data-driven tools used to estimate galaxy physical properties in the absence of spectroscopy. However, due to a lack of interpretability and the associational nature of such models, it is difficult to understand how the information that is included in addition to integrated photometry (e.g., morphology) contributes to the estimation task. Improving our understanding in this field would enable further advances into unraveling the physical connections among galaxy properties and optimizing data exploitation. Therefore, our work is aimed at interpreting the deep learning-based estimation of stellar mass via two interpretability techniques: causal analysis and mutual information decomposition. The former reveals the causal paths between multiple variables beyond nondirectional statistical associations, while the latter quantifies the multicomponent contributions (i.e., redundant, unique, and synergistic) of different input data to the stellar mass estimation. Using data from the Sloan Digital Sky Survey (SDSS) and the Wide-field Infrared Survey Explorer (WISE), we obtained meaningful results that provide physical interpretations for image-based models. Our work demonstrates the gains from combining deep learning with interpretability techniques, and holds promise in promoting more data-driven astrophysical research (e.g., astrophysical parameter estimations and investigations on complex multivariate physical processes).