# Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects

arXiv: https://arxiv.org/abs/2410.14466 · HTML: https://mlsanity.com/paper/2410.14466/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (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)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Practical applications of machine-learned flows on gauge fields](https://mlsanity.com/paper/2404.11674/) (2024)

## Built on by (most cited first, 13 of 13)

- [Multilevel Generative Samplers for Investigating Critical Phenomena](https://mlsanity.com/paper/2503.08918/) (2025)
- [Scaling flow-based approaches for topology sampling in SU(3) gauge theory](https://mlsanity.com/paper/2510.25704/) (2025)
- [Aspects of holographic entanglement using physics-informed-neural-networks](https://mlsanity.com/paper/2509.25311/) (2025)
- [SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows](https://mlsanity.com/paper/2505.19619/) (2025)
- [Estimation of the reduced density matrix and entanglement entropies using autoregressive networks](https://mlsanity.com/paper/2506.04170/) (2025)
- [Toward Scalable Normalizing Flows for the Hubbard Model](https://mlsanity.com/paper/2601.18273/) (2026)
- [Simulating the Hubbard Model with Equivariant Normalizing Flows](https://mlsanity.com/paper/2501.07371/) (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)
- [Variational Autoregressive Networks with probability priors](https://mlsanity.com/paper/2605.16020/) (2026)
- [Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions](https://mlsanity.com/paper/2608.25606/) (2026)

## Abstract (arXiv)

We introduce a novel technique to numerically calculate R'enyi entanglement entropies in lattice quantum field theory using generative models. We describe how flow-based approaches can be combined with the replica trick using a custom neural-network architecture around a lattice defect connecting two replicas. Numerical tests for the φ4 scalar field theory in two and three dimensions demonstrate that our technique outperforms state-of-the-art Monte Carlo calculations, and exhibit a promising scaling with the defect size.