Channel selection at identically vanishing dissipation difference: isolating the frenetic sector of the overdamped path measure

What the math gives to ML

The paper separates path selection into a time-antisymmetric entropy term and a time-symmetric dynamical-activity (frenesy) term, then constructs cases where the entropy contribution is exactly zero and all selection comes from local transverse geometry. Its most transferable mathematical asset is the invariant ratio of transverse Hessian-diffusion determinants: shared spectator directions cancel, leaving only modes whose stiffness differs between alternatives. This suggests a curvature-based routing mechanism for neural networks that compares candidate branches using a relative log-determinant rather than an absolute Hessian statistic, improving robustness to nuisance dimensions and coordinate reparameterization. The cleanest first target is mixture-of-experts routing, with Hessians estimated in a small routing subspace using Gauss-Newton or Fisher curvature.