# Event Generation with Parallel Langevin Sampling and Learned Stein Diagnostics

arXiv: https://arxiv.org/abs/2606.14854 · HTML: https://mlsanity.com/paper/2606.14854/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 85 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [Measuring Sample Quality with Kernels](https://mlsanity.com/paper/1703.01717/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Mirrored Langevin Dynamics](https://mlsanity.com/paper/1802.10174/) (2018)
- [Optimal dimension dependence of the Metropolis-Adjusted Langevin Algorithm](https://mlsanity.com/paper/2012.12810/) (2020)
- [Stein's Method Meets Computational Statistics: A Review of Some Recent Developments](https://mlsanity.com/paper/2105.03481/) (2021)
- [The Tamed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1710.05559/) (2017)
- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [Estimating Density Models with Truncation Boundaries using Score Matching](https://mlsanity.com/paper/1910.03834/) (2019)
- [Optimal Preconditioning and Fisher Adaptive Langevin Sampling](https://mlsanity.com/paper/2305.14442/) (2023)
- [Neural Network-Based Approach to Phase Space Integration](https://mlsanity.com/paper/1810.11509/) (2018)
- [Optimising simulations for diphoton production at hadron colliders using amplitude neural networks](https://mlsanity.com/paper/2106.09474/) (2021)
- [Differentiable Matrix Elements with MadJax](https://mlsanity.com/paper/2203.00057/) (2022)
- [Scaling laws for amplitude surrogates](https://mlsanity.com/paper/2601.13308/) (2026)
- [Standardisation-function Kernel Stein Discrepancy: A Unifying View on Kernel Stein Discrepancy Tests for Goodness-of-fit](https://mlsanity.com/paper/2106.12105/) (2021)
- [Approximate Stein Classes for Truncated Density Estimation](https://mlsanity.com/paper/2306.00602/) (2023)

## Abstract (arXiv)

Efficient event generation is a major computational challenge for precision collider phenomenology, especially for high-multiplicity final states where matrix-element evaluations are expensive and rejection-sampling efficiencies are low. We study an alternative approach based on many parallel underdamped Langevin chains, retaining one terminal state from each chain to obtain unweighted events while avoiding within-chain autocorrelation. A learned Stein discrepancy is used as a convergence diagnostic, providing a data-driven estimate of the relaxation time. We apply the method to tree-level ubar u→ Z+n g event generation and find that relaxation requires only a modest number of exact-target Langevin steps, with mild growth over the multiplicities studied. Finally, we show that simple neural-network surrogate initialization can substantially reduce the required number of exact matrix-element and gradient evaluations.