Shortcuts to Parameter Sweeps

What the math gives to ML

The paper introduces a controlled finite-time parameter sweep that transports a stochastic system along a prescribed family of instantaneous stationary distributions, avoiding repeated relaxation at every parameter value. Its transferable mechanism is an auxiliary drift satisfying a stationary-density continuity equation, combined with an exact covariance response identity that applies even when the stationary distribution is unknown. In neural networks, this can accelerate SGLD, Bayesian weight sampling, or optimizer-state exploration across temperature, weight decay, noise scale, or another hyperparameter. The main falsifiable prediction is that controlled sweeps exhibit substantially smaller stationary lag than uncontrolled sweeps and that covariance-based response estimates agree with independently equilibrated reference runs.