Supervised contrastive learning (SCL) framework. It contains an encoder, an estimator, and a decoder. The encoder, the same as that shown in Fig. 2, takes multi-band galaxy images and additional data as inputs, and produces two vectors v_A and v_B. The vector v_A is used to encode redshift information and is referred to as the ‘latent vector’ throughout this work. It is inputted to the estimator that produces a redshift output supervised by the spectroscopic redshift label for extracting redshift information. The concatenation of v_A and v_B is inputted to the decoder to reconstruct images that resemble the input images. With the reconstructed images as inputs, this process is conducted again using the three networks with shared weights, producing the vector v_A. Furthermore, the images reshaped with random flipping and rotation by 90 deg steps are exploited as inputs, producing the vector v_A. For contrastive learning, the contrast between v_A and v_A and the contrast between v_A and v_A for the same galaxy are minimised (i.e. positive pairs), which are characterised by the Euclidean distance. The contrast between the latent vectors for any two different galaxies is maximised (i.e. a negative pair).