Population coding under the scale-invariance of high-dimensional noise

High-dimensional neural activities exhibiting scale-invariant, power-law noise spectra are ubiquitously observed across various brain regions and species. However, their impact on information coding remains unclear. We provide the scaling conditions for noise covariance that clarify the boundedness of information and establish a quantitative relation between information capacity and population size, based on the properties of scale-invariant noise covariance observed in stimulus-evoked activities of mouse V1 neurons. Our analysis reveals that sublinearly scaling small noise components align sufficiently with the signal direction, enabling neurons to convey stimulus information unboundedly as population size increases. These findings demonstrate that the quasi-universal scaling of neural noise covariance lays the foundation for understanding the scaling and boundedness of population codes, highlighting the critical need to consider the full spectrum of high-dimensional noise.