Causal analysis and mutual information decomposition methods adopted in this work. Upper panel: causal graph that represents the stellar mass-predicting process of an end-to-end deep learning model. Each node refers to a variable or a set of variables. Each arrow represents a causal link. Xⁱⁿ refers to the set of input data to the model. Y refers to the target variable (i.e., stellar mass in this work). X^ex refers to the set of external variables that contain the information on stellar mass but missing in the input data. S refers to the low-dimensional latent vector that encodes the information on stellar mass extracted from the input data, the intermediary variable between Xⁱⁿ and Y. The line between X^ex and Xⁱⁿ that has no direction specified refers to their possible dependence, which is not necessarily a direct causal link. There may be inner structures between the individual variables in the set X^ex and Y, shown by the exemplar variables $X_1^{ex}$, $X_2^{ex}$, and $X_3^{ex}$. The undirected lines between $X_1^{ex}$ and $X_2^{ex}$ and between $X_1^{ex}$ and $X_3^{ex}$ refer to their possible undirected dependences. Lower panel: diagram of the decomposition of mutual information between the target Y and two sets of input data X₁, X₂. Redundant(Y; X₁, X₂) refers to the redundant information on Y that both X₁ and X₂ can provide. Unique(Y; X₁) and Unique(Y; X₂) refer to the unique information that only X₁ or X₂ can provide. S ynergistic(Y; X₁, X₂) refers to the synergistic information that exists only when both X₁ and X₂ are available.