  In cat visual cortex, the response of a neural population to the linear
combination of two sinusoidal gratings (a plaid) can be well approximated by a
weighted sum of the population responses to the individual gratings --- a
property we refer to as {\em subspace invariance}. We tested subspace
invariance in mouse primary visual cortex by measuring the angle between the
population response to a plaid and the plane spanned by the population
responses to its individual components. We found robust violations of subspace
invariance arising from a strong, negative correlation between the responses of
neurons to individual gratings and their responses to the plaid. Contrast
invariance, a special case of subspace invariance, also failed. The responses
of some neurons decreased with increasing contrast, while others increased.
Altogether the data show that subspace and contrast invariance do not hold in
mouse primary visual cortex. These findings rule out some models of population
coding, including vector averaging, some versions of normalization and temporal
multiplexing.
