A Nonlinear Information-Theoretic Approach Reveals the Low Dimensionality of Visual Neural Codes

A key debate in neuroscience is whether neural population codes are high-dimensional and efficient or low-dimensional and robust. Arguments for high dimensionality often rely on linear measures, where a slow power-law decay of the variance spectrum implies complexity, since many dimensions are needed to explain the variance. Yet it remains unclear whether this reflects a true feature or a consequence of linearity. Mutual Information (MI), which captures both linear and nonlinear dependencies, offers a promising alternative, though accurate MI estimation from finite data is notoriously difficult, especially in modern neuroscience high-dimensional settings. Neural network–based MI estimators address this by optimizing loss functions that nonlinearly embed high-dimensional data into lower-dimensional spaces. Using recent advances, we developed an open-source toolbox and applied it to a large-scale V1 dataset (N ≥ 10k neurons). We estimated "internal information," the MI between random halves of the population, as a function of embedding dimension d. Whereas the linear variance spectrum decays gradually, the nonlinear "information spectrum" drops sharply, revealing an intrinsic dimensionality of ~10. This suggests the apparent high dimensionality of V1 arises from linear analysis. Our toolbox enables reevaluation of such hypotheses across neuroscience and beyond.