On the Subspace Invariance of Population Responses

In cat primary 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 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, represented by a median angular deviation of ~55 deg. The reason for this departure is a strong, negative correlation between the mean responses a neuron to the individual gratings and its response to the plaid. We show that contrast invariance, a special case of subspace invariance, also fails, meaning that the direction of the population vector changes with the contrast of a stimulus. This result is partly due to a sub-population of neurons that see their activity suppressed with increasing contrast, while other cells increase their activity with contrast. Altogether the data show that that subspace and contrast invariance do not hold in mouse V1. These findings rule out possible models of population coding, including vector averaging, some versions of normalization and temporal multiplexing.