# A Guide to Constraining Effective Field Theories with Machine Learning

arXiv: https://arxiv.org/abs/1805.00020 · HTML: https://mlsanity.com/paper/1805.00020/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2018.

## Built on by (most cited first, 25 of 25)

- [Machine Learning in the Search for New Fundamental Physics](https://mlsanity.com/paper/2112.03769/) (2021)
- [A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithful](https://mlsanity.com/paper/2110.06581/) (2021)
- [E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once](https://mlsanity.com/paper/2101.07263/) (2021)
- [Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference](https://mlsanity.com/paper/2310.04395/) (2023)
- [A Cautionary Tale of Decorrelating Theory Uncertainties](https://mlsanity.com/paper/2109.08159/) (2021)
- [Learning Likelihood Ratios with Neural Network Classifiers](https://mlsanity.com/paper/2305.10500/) (2023)
- [Scaling laws for amplitude surrogates](https://mlsanity.com/paper/2601.13308/) (2026)
- [ELSA -- Enhanced latent spaces for improved collider simulations](https://mlsanity.com/paper/2305.07696/) (2023)
- [Optimal Equivariant Architectures from the Symmetries of Matrix-Element Likelihoods](https://mlsanity.com/paper/2410.18553/) (2024)
- [Inferring dark matter substructure with astrometric lensing beyond the power spectrum](https://mlsanity.com/paper/2110.01620/) (2021)
- [Data-driven Science and Machine Learning Methods in Laser-Plasma Physics](https://mlsanity.com/paper/2212.00026/) (2022)
- [Exploration of Parameter Spaces Assisted by Machine Learning](https://mlsanity.com/paper/2207.09959/) (2022)
- [New Machine Learning Techniques for Simulation-Based Inference: InferoStatic Nets, Kernel Score Estimation, and Kernel Likelihood Ratio Estimation](https://mlsanity.com/paper/2210.01680/) (2022)
- [FAIR Universe HiggsML Uncertainty Dataset and Competition](https://mlsanity.com/paper/2410.02867/) (2024)
- [Neural Quasiprobabilistic Likelihood Ratio Estimation with Negatively Weighted Data](https://mlsanity.com/paper/2410.10216/) (2024)
- [Data-Driven High-Dimensional Statistical Inference with Generative Models](https://mlsanity.com/paper/2506.06438/) (2025)
- [Neural simulation-based inference of the Higgs trilinear self-coupling via off-shell Higgs production](https://mlsanity.com/paper/2507.02032/) (2025)
- [Profiling systematic uncertainties in Simulation-Based Inference with Factorizable Normalizing Flows](https://mlsanity.com/paper/2602.13184/) (2026)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [Factorizable Normalizing Flows for parameter-dependent density morphing](https://mlsanity.com/paper/2606.30489/) (2026)
- [An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning](https://mlsanity.com/paper/2607.21702/) (2026)
- [Mixture Density Network Estimation of Continuous Variable Maximum Likelihood Using Discrete Training Samples](https://mlsanity.com/paper/2103.13416/) (2021)
- [Learning to discover: expressive Gaussian mixture models for multi-dimensional simulation and parameter inference in the physical sciences](https://mlsanity.com/paper/2108.11481/) (2021)
- [Designing Observables for Measurements with Deep Learning](https://mlsanity.com/paper/2310.08717/) (2023)
- [Hybrid Neural Simulation-Based Inference for Robust Applications and Limited-Budget Scenarios](https://mlsanity.com/paper/2609.36044/) (2026)

## Abstract (arXiv)

We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator. This augmented data can be used to train neural networks that precisely estimate the likelihood ratio. The new methods scale well to many observables and high-dimensional parameter spaces, do not require any approximations of the parton shower and detector response, and can be evaluated in microseconds. Using weak-boson-fusion Higgs production as an example process, we compare the performance of several techniques. The best results are found for likelihood ratio estimators trained with extra information about the score, the gradient of the log likelihood function with respect to the theory parameters. The score also provides sufficient statistics that contain all the information needed for inference in the neighborhood of the Standard Model. These methods enable us to put significantly stronger bounds on effective dimension-six operators than the traditional approach based on histograms. They also outperform generic machine learning methods that do not make use of the particle physics structure, demonstrating their potential to substantially improve the new physics reach of the LHC legacy results.