On the Subspace Invariance of Population Responses

Abstract

The response of a neural population in cat primary visual cortex 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 cause of this departure is a strong, negative correlation between the mean responses a neuron to the individual gratings and its response to the plaid. We suggest that an early nonlinearity may distort the power distribution of grating and plaid stimuli such that plaids have a prominent power component at {+/-}45 deg off the fundamental orientations. We conclude that subspace invariance does not hold in mouse V1. This finding rules out a large class of possible models of population coding, including vector averaging and gain control.