ABSTRACT We release photometric redshifts, reaching ∼0.7, for ∼14M galaxies at r ≤ 20 in the 11 500 deg2 of the SDSS north and south Galactic caps. These estimates were inferred from a convolution neural network (CNN) trained on ugriz stamp images of galaxies labelled with a spectroscopic redshift from the SDSS, GAMA, and BOSS surveys. Representative training sets of ∼370k galaxies were constructed from the much larger combined spectroscopic data to limit biases, particularly those arising from the over-representation of luminous red galaxies. The CNN outputs a redshift classification that offers all the benefits of a well-behaved PDF, with a width efficiently signalling unreliable estimates due to poor photometry or stellar sources. The dispersion, mean bias, and rate of catastrophic failures of the median point estimate are of order σMAD = 0.014, <Δznorm>=0.0015, $η (|Δ z_{\rm norm}|\gt 0.05)=4{{\, \rm per\ cent}}$ on a representative test sample at r < 19.8, outperforming currently published estimates. The distributions in narrow intervals of magnitudes of the redshifts inferred for the photometric sample are in good agreement with the results of tomographic analyses. The inferred redshifts also match the photometric redshifts of the redMaPPer galaxy clusters for the probable cluster members.