# LeapfrogLayers: A Trainable Framework for Effective Topological Sampling

arXiv: https://arxiv.org/abs/2112.01582 · HTML: https://mlsanity.com/paper/2112.01582/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 2 Dec 2021.

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

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Generalizing Hamiltonian Monte Carlo with Neural Networks](https://mlsanity.com/paper/1711.09268/) (2017)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [Introduction to Normalizing Flows for Lattice Field Theory](https://mlsanity.com/paper/2101.08176/) (2021)
- [Involutive MCMC: a Unifying Framework](https://mlsanity.com/paper/2006.16653/) (2020)
- [A Neural Network MCMC sampler that maximizes Proposal Entropy](https://mlsanity.com/paper/2010.03587/) (2020)
- [Deep Learning Hamiltonian Monte Carlo](https://mlsanity.com/paper/2105.03418/) (2021)
- [You say Normalizing Flows I see Bayesian Networks](https://mlsanity.com/paper/2006.00866/) (2020)
- [Orbital MCMC](https://mlsanity.com/paper/2010.08047/) (2020)

## Built on by (most cited first, 3 of 3)

- [Aspects of scaling and scalability for flow-based sampling of lattice QCD](https://mlsanity.com/paper/2211.07541/) (2022)
- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Practical applications of machine-learned flows on gauge fields](https://mlsanity.com/paper/2404.11674/) (2024)

## Abstract (arXiv)

We introduce LeapfrogLayers, an invertible neural network architecture that can be trained to efficiently sample the topology of a 2D U(1) lattice gauge theory. We show an improvement in the integrated autocorrelation time of the topological charge when compared with traditional HMC, and look at how different quantities transform under our model. Our implementation is open source, and is publicly available on github at https://github.com/saforem2/l2hmc-qcd.