Title: Inferring High-Dimensional Signal Geometry in Neural Data
Abstract: Recent advances in large-scale neural recording technology have spurred 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. I address this problem by developing new tools for the accurate estimation of high-dimensional signal geometry. I apply these tools to investigate the geometry of representations in mouse primary visual cortex (V1). Theoretical work has suggested that these representations follow a power law, in which the ith principal component decays as 1/i. Here, I show that response geometry in V1 is better described by a broken power law, in which two distinct exponents govern the falloff of early and late eigenmodes of population activity. My analysis reveals that later modes decay more rapidly than previously predicted, resulting in a substantially lower-dimensional representation that is concentrated in the early modes. Finally, I discuss extensions of my approach to other quantities of scientific interest that can be derived from the generalized trace.