Operator Spectroscopy of Trained Lattice Samplers

ArXi:2605.11199v1 Announce Type: cross Trained lattice samplers are usually judged by the ensembles they generate. Here we instead analyze the trained field-space function itself: a flow-matching velocity, a diffusion score, or a normalizing-flow action residual. We project these functions onto operator bases fixed before the fit, chosen from symmetry, exact Gaussian path limits, finite-volume modes, and gauge covariance. For two-dimensional lattice \(\phi^4\), a trained straight-flow teacher is not described by a local force basis alone.