High-dimensional geometry of the cortical population code revealed by 10,000-neuron recordings

Abstract: We used 2-photon calcium imaging and improved analysis methods to record the responses of >10,000 neurons in the visual cortex of awake mice, to thousands of natural images. The recorded population code was high-dimensional, with the variance of its dimensions following a power law. This power law did not reflect the statistics of natural images, as it persisted even when presenting spatially whitened stimuli. A mathematical analysis showed that neural rate vectors lying in a set of fractal dimension d must have variances bounded by a power law of exponent 1+2/d. By recording responses to stimulus ensembles of varying dimension, we showed this bound is saturated. We conclude that the manifold of neural responses is as rough as is possible without exhibiting fractal geometry.