Density-Dependent McKean--Vlasov Diffusions: Subgaussian Occupancy Bounds and Polynomial Propagation of Chaos

What the math gives to ML

The paper develops a constructive replacement for dense kernel interactions in density-dependent particle dynamics: a clipped, randomly shifted histogram evaluated with occupied-cell hashing. Its transferable asset is the combination of local density conditioning, reduced grid-alignment error from random shifts, and expected linear-time evaluation instead of quadratic pairwise KDE computation. This suggests a scalable particle layer for diffusion samplers, latent particle models, and neural SDE architectures whose drift depends on the current empirical density. The explicit propagation-of-chaos bound also supplies a bandwidth rule and a falsifiable accuracy-versus-compute benchmark.