# Operator-Guided Model Reduction for Generative Sampling in Lattice Field Theory

arXiv: https://arxiv.org/abs/2605.11199 · HTML: https://mlsanity.com/paper/2605.11199/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 5 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 1 of 1)

- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)

## Abstract (arXiv)

Neural generative samplers for lattice field theory can be costly to train and evaluate. When they miss modes or assign them incorrect relative weights, biased observables do not reveal which collective variables are responsible. We project a trained flow-matching velocity onto vector fields built from lattice operators and Fourier modes. In two-dimensional lattice φ4 theory, the projection separates changes in the overall magnetization from the lowest nonzero-momentum fluctuations and guides an explicit invertible proposal that treats them separately. Allowing the amplitude of the lowest nonzero-momentum fluctuations to depend on the magnetization improves the overlap between the proposal and target distributions, while the same two-parameter modification at higher momenta gives smaller improvements. The Metropolis--Hastings correction defines a Markov chain with the target Boltzmann distribution as its stationary law, and the normalized proposal density yields finite-volume partition-function estimates consistent with an independent HMC calculation. At the larger tested volume, the overlap between the proposal and target distributions deteriorates substantially, limiting the range over which the same parameterization remains effective.