The Geometric Signatures of Brain State Transitions: Recursive Informational Curvature Reveals Hidden Dynamics in...

Recursive Informational Curvature (RIC) was recently introduced as an information-geometric framework for describing the balance between recursive structure and entropy change in dynamical systems. Here, we present the first empirical implementation and benchmark evaluation of its scalar curvature term, $K$ in high-density macaque electrocorticography (ECoG).

We analyzed 2 open-access datasets: a 128-channel eyes-open versus eyes-closed benchmark derived from the George anesthesia-and-sleep recording package, and a 64-channel food-tracking dataset with synchronized motion capture. Following standardized preprocessing and symbolic discretization, we extracted Shannon entropy, recursive gain, and empirical curvature for each channel and epoch. We then evaluated these features using single-feature, multichannel, and combined-feature models, together with ablation and sensitivity analyses across symbolic bin counts, epoch lengths, and classifier families.

In the primary eyes-open versus eyes-closed benchmark, multichannel curvature features supported near-perfect state discrimination. In the food-tracking task, the strongest performance was obtained from combined curvature and amplitude features. Across analyses, entropy alone was weak, whereas recursive gain and curvature showed closely matched performance profiles, indicating that in the present implementation much of the discriminative structure captured by curvature is concentrated in the recursive term.

These findings establish the empirical RIC curvature term as an interpretable and state-sensitive descriptor of neural dynamics in ECoG, provide a reproducible benchmark for future refinement of the framework, and clarify both the promise and the current limits of curvature-based analysis in neural states.