Recent advances in large-scale recording technology have spurred exciting new 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 new tools for the accurate estimation of high-dimensional signal geometry. We apply these tools to investigate the geometry of representations in mouse primary visual cortex. Previous work has argued that these representations exhibit a power law, in which the n ’th principal component falls off as 1 /n . 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 modes of population activity. Our analysis reveals that later modes decay more rapidly than previously suggested, resulting in a substantially larger fraction of signal variance contained in the early modes of population activity. We examined the signal representations of the early population modes and found them to have higher fidelity than even the most reliable neurons. Intriguingly there are many population modes not captured by classic models of primary visual cortex indicating there is highly redundant yet poorly characterized tuning across neurons. Furthermore, inhibitory neurons tend to co-activate in response to stimuli that drive the early modes consistent with a role in sharpening population level tuning. Overall, our novel and broadly applicable approach overturns prior results and reveals striking structure in a population sensory representation. Significance Statement The nervous system encodes the visual environment across millions of neurons. Such high-dimensional signals are difficult to estimate—and consequently—to characterize. We address this challenge with a novel statistical method that revises past conceptions of the complexity of encoding in primary visual cortex. We discover population encoding is dominated by approximately ten features while additional features account for much less of the representation than previously thought. Many dominant features are not explained by classic models indicating highly redundant encoding of poorly characterized nonlinear image features. Interestingly, inhibitory neurons respond in unison to dominant features consistent with a role in sharpening population representation. Overall, we discover striking properties of population visual representation with novel, broadly applicable, statistical tools.

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