Fisher Information Metric as a model-free measure of proximity to criticality in neural systems
Year: 2026
Type: preprint
Abstract: Critical phenomena are widespread across many disciplines and have recently become a topic of deep interest in the study of biological and artificial neural networks. A distinct signature of criticality is the emergence of avalanches with power-law-distributed sizes and durations. However, empirically estimating the critical exponents remains challenging, and their interpretation is often model-dependent. In this work, we demonstrate how the Fisher Information Metric (FIM), a measure of generalized susceptibility, provides a comprehensive, model-agnostic characterization of the critical region in neural systems. We validate this approach across models of increasing biological complexity, from prototypical branching processes to spiking and whole-brain models, showing that FIM of each model's control parameter reliably tracks the system's degree of criticality. To emulate the study of real-world systems, where the control parameter is unknown, we additionally calculate FIM of the observed branching ratio of neural activity. The resulting FIM peaks where activity growth and decay balance, with the peak sharpening as the system approaches criticality. Hence, FIM peak width and height yield continuous, model-free readouts of proximity to criticality without requiring knowledge of the true control parameter, offering a robust tool for probing criticality in neural systems.
Source: arXiv (Cornell University)
Institution: Imperial College London
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Imperial College London
OpenAlex ID: W7212037880