Appendix

Lety0 = g(,y), and assume that(,x,y) 7 (x,y0) is a one-to-one function. Given any (x,y0), by the one-to-one assumption, there is exactly one inverse(,x,y). Thisisgenerally notaconcern in practice, since standard ML setups have exactly one labely per examplex. This codebase applies random crops and random left-right flips tothe training images. To investigate this further, Figure 8a displays test loss as a function of the number of additional noisevaluesaddedtoys,yq.