# Scaling of Stochastic Normalizing Flows in SU(3) lattice gauge theory

arXiv: https://arxiv.org/abs/2412.00200 · HTML: https://mlsanity.com/paper/2412.00200/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 29 Nov 2024.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [NETS: A Non-Equilibrium Transport Sampler](https://mlsanity.com/paper/2410.02711/) (2024)
- [Targeted free energy estimation via learned mappings](https://mlsanity.com/paper/2002.04913/) (2020)
- [An invitation to sequential Monte Carlo samplers](https://mlsanity.com/paper/2007.11936/) (2020)
- [Aspects of scaling and scalability for flow-based sampling of lattice QCD](https://mlsanity.com/paper/2211.07541/) (2022)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [On learning higher-order cumulants in diffusion models](https://mlsanity.com/paper/2410.21212/) (2024)
- [Generative models for scalar field theories: how to deal with poor scaling?](https://mlsanity.com/paper/2301.01504/) (2023)
- [Practical applications of machine-learned flows on gauge fields](https://mlsanity.com/paper/2404.11674/) (2024)

## Built on by (most cited first, 10 of 10)

- [Physics-Conditioned Diffusion Models for Lattice Gauge Theory](https://mlsanity.com/paper/2502.05504/) (2025)
- [Scaling flow-based approaches for topology sampling in SU(3) gauge theory](https://mlsanity.com/paper/2510.25704/) (2025)
- [Group-Equivariant Diffusion Models for Lattice Field Theory](https://mlsanity.com/paper/2510.26081/) (2025)
- [Toward Scalable Normalizing Flows for the Hubbard Model](https://mlsanity.com/paper/2601.18273/) (2026)
- [NeuMC -- a package for neural sampling for lattice field theories](https://mlsanity.com/paper/2503.11482/) (2025)
- [A scalable flow-based approach to mitigate topological freezing](https://mlsanity.com/paper/2601.20708/) (2026)
- [Stochastic normalizing flows for Effective String Theory](https://mlsanity.com/paper/2412.19109/) (2024)
- [Studying Effective String Theory using deep generative models](https://mlsanity.com/paper/2508.20610/) (2025)
- [Machine learning for four-dimensional SU(3) lattice gauge theories](https://mlsanity.com/paper/2604.12416/) (2026)
- [Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery](https://mlsanity.com/paper/2610.12293/) (2026)

## Abstract (arXiv)

Non-equilibrium Markov Chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. By driving a base probability distribution out of equilibrium, observables are computed without the need to thermalize. If the base distribution is characterized by mild autocorrelations, this approach provides a way to mitigate critical slowing down. Out-of-equilibrium evolutions share the same framework of flow-based approaches and they can be naturally combined into a novel architecture called Stochastic Normalizing Flows (SNFs). In this work we present the first implementation of SNFs for SU(3) lattice gauge theory in 4 dimensions, defined by introducing gauge-equivariant layers between out-of-equilibrium Monte Carlo updates. The core of our analysis is focused on the promising scaling properties of this architecture with the degrees of freedom of the system, which are directly inherited from NE-MCMC. Finally, we discuss how systematic improvements of this approach can realistically lead to a general and yet efficient sampling strategy at fine lattice spacings for observables affected by long autocorrelation times.