Self-supervised In-context Operator Learning for Stochastic Mean-Field Control

What the math gives to ML

The paper combines two transferable constructions: triangular invertible coupling maps with exact inverse and log-determinant, and amortized task-conditioned learning of entire controlled distributional dynamics rather than solving one control problem at a time. The invertibility gives an explicit likelihood and score route without numerical Jacobian determinants, while the probability-flow reformulation converts stochastic Fokker–Planck evolution into deterministic particle trajectories. The most promising transfer is a task-conditioned invertible trajectory module that can represent distributions, evaluate density-derived forces, and optimize control costs without supervised optimal trajectories. This is especially relevant to amortized diffusion control, distributional planning, and reusable controllers over families of tasks.