Revisiting the high-dimensional geometry of population responses in the visual cortex

Recent advances in large-scale recording technology have spurred inquiries into the high-dimensional geometry of the neural code. However, characterizing this geometry from noisy neural responses, particularly in datasets with more neurons than trials, poses major statistical challenges. We address this problem by developing tools for the accurate estimation of high-dimensional signal geometry. We apply these tools to investigate the geometry of representations in the mouse primary visual cortex. Previous work has argued that these representations exhibit a power law, in which the ith principal component falls off as 1/i. Here, we show that response geometry in V1 is better described by a broken power law, in which two different exponents govern the falloff of early and late eigenmodes of population activity. Our analysis reveals that later modes decay more rapidly than previously suggested, resulting in a substantially lower-dimensional representation that is concentrated in early modes. We thus characterize the stimulus encoding of these dominant population modes. We find properties of population coding in the mouse primary visual cortex that underscore its greater tractability relative to single-neuron characterization. Specifically, we find these modes encode visual features with far higher fidelity than single neurons, and these features are easier to characterize than the tuning of single neurons: both classical and deep network models of V1 achieve more than 25% better predictive performance for eigenmodes than single neurons. Overall, our approach overturns prior results and reveals emergent structure in a population sensory representation.