Rethinking Mean-Field Theory for Neural Networks
Even the most complex biological and physical systems can sometimes be understood using just a few variables that describe the system’s collective behavior. This apparent simplicity suggests that each of the system’s components responds to the average influence of all the others—the guiding principle of so-called mean-field theory. Now Luca Di Carlo at Princeton University and his colleagues have investigated whether mean-field theory can be applied to networks of biological neurons [1]. They have found that simple versions of the theory fail to describe such networks’ activity patterns and have devised an improved version that succeeds in this task.
To explore the suitability of mean-field theory, the researchers developed statistical models built from activity recordings of more than 1000 networked mouse brain neurons. They first considered naive mean-field theory and generalized extensions that account for variations in collective neural activity. Such frameworks predicted statistics that were inconsistent with those seen in the models. The researchers then derived a new mean-field theory that incorporates the full distribution of collective activity patterns. This framework accurately reproduced the observed statistics.
The success of the team’s mean-field theory suggests that the neural networks from which the recordings were obtained exist near a critical point, in agreement with some observations. At such a critical point, these networks would display long-range correlations, scale-free behavior, and a maximal sensitivity to perturbations. The researchers point out that their theory can currently capture only the time-averaged statistics of neural activity. They plan to extend the framework to also describe how activity patterns evolve over time during animal behavior.
–Ryan Wilkinson
Ryan Wilkinson is a Corresponding Editor for Physics Magazine based in Durham, UK.
References
- L. Di Carlo et al., “Extended mean-field theories for networks of real neurons,” Phys. Rev. Lett. 137, 018401 (2026).