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

arXiv: https://arxiv.org/abs/2304.01798 · HTML: https://mlsanity.com/paper/2304.01798/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [cuDNN: Efficient Primitives for Deep Learning](https://mlsanity.com/paper/1410.0759/) (2014)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review](https://mlsanity.com/paper/1611.00740/) (2016)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Sampling using SU(N) gauge equivariant flows](https://mlsanity.com/paper/2008.05456/) (2020)
- [Aspects of scaling and scalability for flow-based sampling of lattice QCD](https://mlsanity.com/paper/2211.07541/) (2022)
- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)
- [Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks](https://mlsanity.com/paper/2105.05650/) (2021)

## Abstract (arXiv)

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 φ4 theory on a 2 dimensional lattice.