Macroscopic fluctuation theory for the multi-time statistics of current in non-stationary diffusive systems

What the math gives to ML

The paper provides a constructive macroscopic-fluctuation-theory description of multi-time current fluctuations in non-stationary diffusive systems. Its transferable asset is a path-space action, together with perturbative multi-time correlation predictions, that distinguishes transient step-like profiles from spatially flat initial conditions rather than assuming a universal fractional-Brownian law. A neural-network analogue is to treat layerwise gradient or activation energy as a coarse-grained density, estimate its effective diffusivity and mobility from training trajectories, and use the resulting action as an instability monitor and learning-rate controller. The main falsifiable prediction is that rare bursts in the coarse-grained training current obey an approximately linear log-probability versus MFT action relation, while transient covariance decay follows the fitted diffusive spectrum.