arXiv:2608.24689 2026 Optimization 1 ideas extracted · analyzed Sep 1, 2026
The paper identifies a concrete dynamical mechanism for higher-order motion: a persistent Ornstein-Uhlenbeck active force combined with thresholded dry friction produces non-smooth, jerk-dominated transients rather than ordinary inertial acceleration. This structure can be transferred to optimization by giving parameters an inertial state, driving them with a correlated auxiliary force, and applying a friction threshold that suppresses small updates while allowing motion once the effective force exceeds a threshold. The most practical first test is an optimizer module, not a new network architecture: compare correlated active forcing and dry friction against SGD, AdamW, and momentum on small vision tasks, measuring loss descent, update sparsity, and stability.
Replace the usual momentum state in an optimizer with a persistent Ornstein-Uhlenbeck-driven velocity subject to a dry-friction threshold. Correlated forcing can help traverse shallow noisy regions, while the friction term suppresses parameter motion when the effective force is small, potentially reducing update noise and improving late-stage stability.