Abstract
Understanding neural activity organization is vital for deciphering brain function. By recording whole-brain calcium activity in larval zebrafish during hunting and spontaneous behaviors, we find that the shape of the neural activity space, described by the neural covariance spectrum, is scale-invariant: a smaller, randomly sampled cell assembly resembles the entire brain. This phenomenon can be explained by Euclidean Random Matrix theory, where neurons are reorganized from anatomical to functional positions based on their correlations. Three factors contribute to the observed scale invariance: slow neural correlation decay, higher functional space dimension, and neural activity heterogeneity. In addition to matching data from zebrafish and mice, our theory and analysis demonstrate how the geometry of neural activity space evolves with population sizes and sampling methods, thus revealing an organizing principle of brain-wide activity.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
First, with new theoretical analysis and experimental verification, we uncover a fundamental principle underlying the brain's information processing capabilities: the invariant geometry and dimensionality of the neural activity space. This principle suggests a universal strategy employed by the brain to efficiently encode and process information across various scales of brain organization. To reflect these substantial improvements and new insights, we have revised our manuscript with a new title: " The Geometry and Dimensionality of Brain-wide Activity". Second, in an effort to bridge theoretical insights and experimental applications, we show that the configuration of neural activity space can evolve distinctly across scales under different recording techniques commonly used in neuroscience. This revision aims to enhance the accessibility of our work for experimentalists.