Nonequilibrium thermodynamics of feedback-control: a phase-space perspective

What the math gives to ML

The paper develops fluctuation relations for feedback systems when the controller observes only a finite-resolution or singular projection of phase space. Its transferable mechanism is the separation between total acquired information and unavailable information: measurement resolution can increase without increasing the useful information available for control. In neural networks, this suggests treating gradients and optimizer state as partially observed feedback signals, retaining only the components that predict future loss reduction. The key falsifiable prediction is that optimization benefit saturates as observation resolution increases, while information acquisition and update noise continue to grow.