Speaker
Description
The renormalisation group considers general coarse-graining transformations in lattice systems and more broadly speaking field theories or data spaces and is based on an analytically known optimal transport equation.
This framework has a natural correspondence with modern generative architectures in terms of pooling and convolutions, but differs in terms of the non-linearity with corresponds to a general field/variable transformation, the physics-informed kernel (PIK) [1,2]. The PIK is a can be chosen in an informed manner to suit the generative task:
We discuss several examples which are encompassed by this framework, ranging from Langevin evolutions to sampling of complex probability distributions with a sign problem [3].
[1] FI, Pawlowski, Annals Phys. 481 (2025) 170177
[2] FI, R. Kapust, J. M. Pawlowski , arXiv:2510.26678
[3] FI, R. Kapust, J. M. Pawlowski , arXiv:2603.03159