Renormalization Group Flow Matching for Scalable Local Generative Modeling

What the math gives to ML

The paper provides a principled way to obtain globally coherent generation from local computation: evolve samples from long wavelengths to short wavelengths using an exact or approximate renormalization-group probability path. Its transferable asset is the quasi-locality bound, which says that the velocity field at RG scale \(\Lambda\) can be approximated using a spatial radius growing only as \(\Lambda^{-1}[\ln L+\ln(1/\varepsilon)]\), rather than requiring global context. A neural implementation should therefore use a coarse-to-fine pyramid of latent grids, train a separate scale-conditioned local velocity field at each grid resolution, and refine only after the coarse field has established global structure. This is more specific than simply using dilated convolutions: the receptive field should be tied to the current physical RG scale and error tolerance.