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
We made 5 specific revisions. 1. We evaluated the covariance spectrum of a latent variable model proposed by Morrell et al. 2. We included a comparison with the findings of Manley et al. regarding the issue of saturating dimension in the Discussion section, highlighting the methodological differences and their implications. 3. We added a new mathematical derivation in the Methods section, elucidating the bounded dimensionality using the spectral properties of our model. 4. We have added a sentence in the Discussion section to further emphasize the robustness of our findings by demonstrating their consistency across diverse datasets and experimental techniques. 5. We have incorporated a brief discussion on the implications for neural coding and Fisher information, as highlighted in the recent work by Moosavi et al.
