Frequency-Resolved Directional Asymmetry in Neural Information Geometry: A Finsler Extension of Transfer Entropy

Directed information transfer in neural circuits exhibits frequency-dependent directional preferences. We show these arise from two mathematically separable sources of asymmetry, each captured by a distinct component of the Finsler extension of Fisher information geometry. The first, A^(dyn), arises from asymmetric connectivity and concentrates at low frequencies set by intrinsic timescales. The second, A^(T), arises from non-Gaussian statistics and concentrates at higher frequencies carried by transient events. We derive an explicit mapping between TE − ½GC and the squared norm of the Amari–Chentsov tensor. The framework unifies frequency-resolved observations from predictive coding, anesthetic pharmacology, and clinical neurophysiology.