Ornstein-Uhlenbeck Process Driven by Multiple Dichotomous Noises
arXiv:2608.29226
2026
Dynamics
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper gives an exact construction for bounded, finite-correlation-time nonequilibrium fluctuations: a stable linear relaxation process driven by independent dichotomous telegraph signals. Its transferable assets are a hard stationary support bound, analytically predictable variance and autocorrelation, and a controlled crossover from strongly non-Gaussian behavior at small K to Gaussian behavior at large K. The most direct neural-network transfer is to replace unbounded Gaussian noise in optimizer momentum or latent-state sampling with this bounded colored-noise process. The implementation has sharp falsifiable signatures: the injected state must remain below a known amplitude bound, and its measured moments and correlation curve should match the closed-form predictions.
Ideas from this paper
✗ Mechanism failed
2026
Add a bounded colored exploration force to an optimizer by filtering a sum of independent two-state telegraph signals through a stable linear relaxation equation. Unlike Gaussian momentum noise, the perturbation has a strict amplitude bound and a tunable finite correlation time, reducing rare destructive parameter excursions while retaining structured exploration.
Useful7/10
Difficulty4/10
Novelty7/10
Unverified
2026
Use the OU process driven by multiple dichotomous noises as a bounded colored-noise module for latent-variable or diffusion sampling. Its stationary forcing is compactly supported for fixed amplitudes, while heterogeneous amplitudes and switching rates create controllable non-Gaussian structure before the large-K Gaussian limit.
Useful6/10
Difficulty5/10
Novelty8/10