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Extended Mean-Field Theories for Networks of Real Neurons
Luca Di Carlo1, Francesca Mignacco1,2, Christopher W Lynn3
1Princeton University, Joseph Henry Laboratories of Physics and Lewis-Sigler Institute, Princeton, New Jersey 08544, USA.
Physical Review Letters
|July 23, 2026
Summary
Simple mean-field theories do not capture neural network activity patterns. An extended theory is consistent and suggests neural networks are poised near a critical point, aiding analysis of large neural datasets.
Area of Science:
- Computational Neuroscience
- Statistical Physics
Background:
- Mean-field theories simplify complex systems by using collective variables.
- Understanding emergent behavior in large neural networks is crucial.
Purpose of the Study:
- To investigate the applicability of mean-field theories to real neural networks.
- To explore the critical dynamics of neural network activity.
Main Methods:
- Comparing simple mean-field theories with observed neural activity patterns.
- Developing and applying an extended mean-field theory accounting for collective variable distributions.
Main Results:
- Simple mean-field approaches inadequately describe neural network activity.
- The extended mean-field theory shows consistency with observed data.
- Evidence suggests neural networks operate near a critical point.
Conclusions:
- Extended mean-field theories offer a more robust framework for analyzing neural networks.
- The critical state of neural networks may be a key feature for information processing.
- This work provides a method for analyzing large-scale neural data.
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Overview