Fokker-Planck-Kolmogorov inclusions of the mean field type

What the math gives to ML

The paper provides a rigorous framework for stochastic dynamics whose drift and diffusion are selected from a convex, measure-dependent set rather than fixed in advance. This suggests replacing a neural layer's single vector field with a state-distribution-dependent differential inclusion, allowing the model to choose among admissible drift/noise pairs while retaining a compact family of stable trajectories. The most practical transfer is a particle-based stochastic layer with a learned convex coefficient set and an explicit per-step selection rule optimized for the task loss; the paper's existence theorem supplies qualitative well-posedness, while the engineering value must be tested empirically.