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Fig. 3

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Correspondence of the input parameter space and the target output space represented by the multichannel output unit. The input space is divided into a grid with 2m − 1 rows covering different magnitudes and n columns covering different redshifts. The output unit is comprised of one magnitude output with m bins and m corresponding redshift outputs. Each redshift output has n bins corresponding to the input space before being extended in step 3. The values of n and m for the SDSS data and the CFHTLS data are given in Table 1. The shaded green boxes indicate the extended redshift intervals. Each of the rows in the input space is connected to one or two redshift outputs alternately. Equivalently, each redshift output responds to three adjacent input rows (or two rows at the edges). As an example, in response to a data instance drawn from the input space indicated by the red star, two bins are activated in the target magnitude output (shown in dark red) while the other bins remain null (shown in light blue). One bin is activated in each of the two corresponding redshift outputs (before using readjusted soft labels in step 3), while the remaining redshift outputs have a flat response over all bins (shown in light red).

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