Graphic illustration of the CNN models for the baseline method and our methods for correcting z_spec-dependent residuals and mode collapse. We use the network architecture adopted by Pasquet et al. (2019), in which multiscale inception modules (Szegedy et al. 2015) are used and the galactic reddening of galaxies is input in addition to images. The representation is obtained at the penultimate fully connected layer. The classification module is elaborated in the red rectangle: while the baseline method takes a final fully connected layer as a single-channel output for redshift prediction, our methods take parallel fully connected layers as multiple output channels to predict redshifts that also incorporate the magnitude information (discussed in Sect. 3.2.1). The labels n and m indicate the dimensions of the output layers, whose values are given in Table 1 for the SDSS data and the CFHTLS data. ≥ n means that additional bins are appended to the redshift outputs in step 3.