Locality-constrained autoregressive cum conditional normalizing flow for lattice field theory simulations

Abstract: Normalizing flow-based sampling methods have been successful in tackling computational challenges traditionally associated with simulating lattice quantum field theories. Further works have incorporated gauge and translational invariance of the action integral in the underlying neural networks, which have led to efficient training and inference in those models. In this paper, we incorporate locality of the action integral which leads to simplifications to the input domain of conditional normalizing flows that sample constant time sub-lattices in an autoregressive process, dubbed local-Autoregressive Conditional Normalizing Flow (l-ACNF). We find that the autocorrelation times of l-ACNF models outperform an equivalent normalizing flow model on the full lattice by orders of magnitude when sampling $\phi^{4}$ theory on a 2 dimensional lattice.