Advancing Tools for Simulation-Based Inference

TL;DR

The paper develops and benchmarks a suite of SBI tools tailored for LHC analyses, embedding physics structure through morphing and derivative learning, and enhancing training with fractional smearing and Lorentz-equivariant networks (L-GATr). On a toy model and a pp→WZ SMEFT application, derivative learning provides accurate reco-level likelihood estimates with low uncertainty, while morphing offers stability under favorable basis choices; fractional smearing and L-GATr further improve training efficiency and reconstruction-level discrimination. The results demonstrate improved numerical control and stability over traditional rate- or histogram-based methods, with robust uncertainty estimation via repulsive ensembles and conservative empirical coverage. These advances pave the way for unbinned, high-dimensional likelihood inference in HL-LHC contexts and will be integrated into public SBI tooling in the MadGraph/MadMiner ecosystem.

Abstract

We study the benefit of modern simulation-based inference to constrain particle interactions at the LHC. We explore ways to incorporate known physics structures into likelihood estimation, specifically morphing-aware estimation and derivative learning. Technically, we introduce a new and more efficient smearing algorithm, illustrate how uncertainties can be approximated through repulsive ensembles, and show how equivariant networks can improve likelihood estimation. After illustrating these aspects for a toy model, we target di-boson production at the LHC and find that our improvements significantly increase numerical control and stability.

Figures (13)

• Figure 1: Likelihoods for local and non-local cases. Both show the full $p(x|\theta)$ for $\theta=0$ and $\theta=0.4$.
• Figure 2: Comparison between the likelihood ratios estimated using the morphing-aware and derivative learning approaches for $\alpha=1.5$ (left) and $\alpha=3$ (right). The truth value is $\theta = 0.6$.
• Figure 3: Likelihood ratio estimated using the single neural network morphing-aware implementation of Ref. Brehmer:2018eca, compared to the truth.
• Figure 4: Histogram of the reco-level second derivative $R_{\theta^2}$, for the original dataset (blue) and the fractionally-smeared dataset (orange).
• Figure 5: Left: learned second derivative as a function $x$ for various setups compared to the truth. Right: expectation value of the learned likelihood ratio as a function of $\theta$ compared to the true likelihood ratio.