Mutual information decomposition for analyzing the contributions of different photometric bands to the stellar mass estimation (defined in Table 4). The redundant, unique, and synergistic components are all illustrated. I (M) refers to the datasets that contain images (photometry). The label X refers to a single band that is separated out, and \X refers to the remaining bands, distinguished for the unique information (shown in red and blue, respectively). First row: average information level of each component (in units of nats) for the image-based cases in which X runs over all the optical bands, separately shown for star-formin𝑔, passive, and other galaxies from the test sample. The black dotted lines indicate zero mutual information. Second row: same as the first row, but for the photometry-only cases in which X runs over all the optical and infrared bands. No sharp contrast can be seen between different bands, except that the 𝑔 band has the largest incremental contribution in the presence of the other bands. The single-band images typically have larger contributions than the single-band photometry. Remaining rows: stack plots of different information components (in units of nats) as a function of stellar mass or r-band magnitude for the cases in which the 𝑔 band or the W1 band is separated out, shown for star-forming, passive, and other galaxies from the test sample. Similar to Fig. 6, the stack plots reveal the behaviors of data imbalance, which are not the same for optical and infrared bands.