Description: Gell-Mann–Low Criticality in Neural Networks

This title appears in the Scientific Report : 2022

Gell-Mann–Low Criticality in Neural Networks

Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of biological information processing to mean-field results. These methods neglect a key feature of critical systems: the inter...

Personal Name(s):	Tiberi, Lorenzo (Corresponding author)
	Stapmanns, Jonas / Kühn, Tobias / Luu, Thomas / Dahmen, David / Helias, Moritz
Contributing Institute:	Computational and Systems Neuroscience; INM-6 Theorie der starken Wechselwirkung; IKP-3 Theorie der Starken Wechselwirkung; IAS-4 Theoretical Neuroscience; IAS-6 Jara-Institut Brain structure-function relationships; INM-10
Published in:	Physical review letters, 128 (2022) 16, S. 168301
Imprint:	College Park, Md. APS 2022
DOI:	10.1103/PhysRevLett.128.168301
Document Type:	Journal Article
Research Program:	Transparent Deep Learning with Renormalized Flows Human Brain Project Specific Grant Agreement 3 Neuroscientific Foundations
Link:	OpenAccess
	Publikationsportal JuSER

Please use the identifier: http://dx.doi.org/10.1103/PhysRevLett.128.168301 in citations.
Please use the identifier: http://hdl.handle.net/2128/32544 in citations.

Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of biological information processing to mean-field results. These methods neglect a key feature of critical systems: the interaction between degrees of freedom across all length scales, required for complex nonlinear computation. We present a renormalized theory of a prototypical neural field theory, the stochastic Wilson-Cowan equation. We compute the flow of couplings, which parametrize interactions on increasing length scales. Despite similarities with the Kardar-Parisi-Zhang model, the theory is of a Gell-Mann–Low type, the archetypal form of a renormalizable quantum field theory. Here, nonlinear couplings vanish, flowing towards the Gaussian fixed point, but logarithmically slowly, thus remaining effective on most scales. We show this critical structure of interactions to implement a desirable trade-off between linearity, optimal for information storage, and nonlinearity, required for computation.