Learnability of Red-Green Opponency

Lennie, Haake, and Williams found that in the lateral geniculate nucleus (LGN), parvocellular unit responses are consistent with the hypothesis that their input connectivity is blind to the difference between middle-wavelength-sensitive (MWS) and long-wavelength-sensitive (LWS) cones. Most of their cells have a total MWS input weight opposite in sign and similar in magnitude to their total LWS input weight. If these weights are exactly balanced, the construction of a red-green opponent system from such units is simple: such units need only be aligned so the signs of their outputs agree. Ahumada and Mulligan described an associative learning process which can accomplish this alignment. If the units are not balanced (carry some luminance information), the strong overlap between the MWS and LWS spectral responses can cause units to agree more on the basis of luminance, and the associative process fails to produce red-green opponency. The learning theory requires that the LGN units be nearly balanced (more strongly encode chromaticity than luminance) and quantitatively expresses the requirement: the principal component of the LGN outputs must be in the red-green rather than the luminance direction. We show that the cone weights of the monkey LGN cells measured by Derrington, Krauskopf, and Lennie can satisfy this learnability criterion even if the MWS spectral response is close to the LWS spectral response, simulating anomalous trichromacy. The learnability theory provides a source of visual system variation for explaining why different anomalous trichromats may make the same average anomaloscope match (same pigments), but have either narrow (good opponent learning) or wide (poor learning) ranges of acceptable matches.