Using renormalization group methods to study how the brain processes information

Using renormalization group methods to study how the brain processes information

This is a screenshot taken from a numerical simulation of a 2D Wilson Cowan model with random input (equivalent (3) in our paper). Yellow (blue) pixels represent high (low) activity. Credit: Tiberi et al.

Previous neuroscience research suggests that biological neural networks in the brain can regulate themselves in a critical state. In physics, the critical state is essentially a point that indicates the transition between the phases of organized and disordered matter.

Researchers at the Jülich Research Center, RWTH University Aachen and the Sorbonne University recently presented a theory that could help explain the critical importance of the brain. This theory was presented in a research paper published in Physical Review Lettersbased on typical neural field theory, known as the “Wilson-Cowan stochastic equation.”

“Previous work has provided evidence that the brain is operating at a critical point,” Lorenzo Tiberi, Jonas Stubmans, Tobias Kuhn, Thomas Law, David Dahmen and Moritz Helias, the researchers who conducted the study, said by email. “However, it is unclear which of the many potential types of criticality are specifically executed by the brain, and how the latter can exploit the critical importance of optimal computation.”

To classify the different types of criticality, physicists typically use methods within the so-called renormalization group (RG). These are basically formal approaches that can be used to systematically investigate changes in a physical system at different levels.

Using renormalization group methods to study how the brain processes information

Abstract figure illustrating the Renormalization Group (RG) approach. When observing the system on scales of coarser lengths (indicated by concentric circles and the arrow in front of the brain), the strength of nonlinear interactions (represented by the Feynman diagram on the left) decreases only slowly and, in particular, remains distinct from zero even at large spatial scales (pointed curve). coloured). Background: Same as Figure 1, but a different color scheme. Credit: Tiberi et al.

In their study, the researchers adapted these traditional methods and combined them with a typical neural field model first proposed by Wilson and Cowan. Then they specifically applied it in the field of neuroscience to examine the significance in biological neural networks.

“In our work, we study well-established Wilson-Cowan equations with random inputs, so the model we use is not new,” said Tibery, Stepmans and their colleagues. “However, using RG techniques, we arrive at an original result.”

to complete Arithmetic tasksand cognitive tasks involving computations, the the human mind It must be able to save the input data it receives and then combine it in complex ways. This, in turn, allows it to process information and solve a computational problem.

“We discovered that critical significance in the Wilson-Kwan neural field model is that of Gil-Man-Lo, which, of all the critical types, specifically provides an ideal balance between archiving and combining input data in complex ways,” said Tiberi, Stapmanns and colleagues.

Using renormalization group methods to study how the brain processes information

Figure illustrating the investigation of the computational capabilities of the model. A stimulus (structured input) is added to the system (with x and y spatial coordinates) which evolves over time t while the network is also triggered by random input (noisy drive). Linear reading is trained to reconstruct or categorize the input stimulus from a snapshot of the activity in the system. The rebuild task tests system memory, while the classification task requires nonlinear interactions. Credit: Tiberi et al.

Using RG methods, the researchers were able to study the effects of nonlinear interactions in the Wilson-Kwan model, which are crucial to understanding how the brain processes information. This is a remarkable achievement, as average field methods used by other teams in the past have not been able to capture these effects, especially when the interactions are strong enough to shape brain dynamics on a microscopic scale.

“We expect RG methods to be useful for studying other nonlinear processes in neural networks,” the team explained. Moreover, we draw links to other areas of physics: the concept of Gell-Man-Low criticality arises from quantum field theory The Kardar-Parisi-Zhang model, which is closely related to our model, was originally used to describe the dynamic growth of facades. “

In the future, the theory presented by this team of researchers can be used to examine brain dynamics and various other neural processes, beyond criticality. In addition, it could eventually pave the way towards the introduction of other theoretical constructs that integrate physics and neuroscience.

“In the brain, the strength of connections between neurons is so highly variable that in a first rough estimate it can be described as stochastic,” the researchers added. “We now plan to apply our methods to neural models that include this feature and see what effect, if any, this has on the kind of significance we find.”


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more information:
Lorenzo Tiberi et al., Jill-Mann – Low criticality in neural networks, Physical Review Letters (2022). DOI: 10.1103/ PhysRevLett.128.168301

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