Topical seminar: "Signal-to-Noise as a Transport Problem: Stein Geometry and Langevin Dynamics"

por Dr. Pietro Butti (U. Southern Denmark, QTC)

miércoles 22 abr. 2026 12:00 → 13:00 Europe/Madrid

1001-Primera-1-1-1 - Paterna. Seminario (Universe)

Abstract: We address the signal-to-noise problem in lattice field theory by recasting it as a problem in variance-optimal transport. The exponential degradation of the signal-to-noise ratio is identified as a consequence of poor overlap between the base and target distributions in a source reweighting scheme. We introduce an infinitesimal transport map and derive a perturbative expansion of the KL divergence that determines the optimal velocity field. The first-order term vanishes by Stein's identity, and the problem reduces to a Poisson equation for the generator of overdamped Langevin dynamics. For interacting theories, the Feynman–Kac formula provides a formal solution, establishing a connection to linear response theory and the fluctuation-dissipation theorem. We present preliminary numerical results for scalar lattice field theories.