Speaker
Description
Neural simulation-based inference (NSBI) has emerged as a powerful methodology for unbinned likelihood analyses in high-energy physics (HEP), with recent ATLAS [1] results at the Large Hadron Collider (LHC) demonstrating substantial sensitivity gains over binned methods. The dominant NSBI variant in HEP, Neural Likelihood-Ratio Estimation (NLRE), owes its popularity to the simplicity of the likelihood-ratio trick [2]. Despite this success, the implementation of NLRE methods suffers from several structural problems within the context of the profile-likelihood machinery common in HEP analyses. The quality of likelihood ratio estimators (LREs) are highly dependent on the support match, or mismatch, of the classes used in the training of the classifier [3]. When faced with composite likelihoods, often multiple LREs (e.g. one per signal) are used to build the likelihood model of the data, each carrying their own support-mismatch risk, leading to additive calibration/miss-specification errors on the composite likelihood. Continuous parameter scans require parameterised LREs, which consequently requires the base class (y = 0) dataset to be very large, since assigning randomised parameter values to reference events dilutes the effective sample size at each scan point. In contrast, Neural Likelihood Estimation (NLE) returns absolute densities that slot directly into the profile-likelihood workflow, often avoiding these structural problems. Unfortunately, standard NLE routes, such as normalising flows or diffusion models that yield log-densities via trajectory integration, are computationally expensive to train and/or evaluate. The latter is particularly problematic when dealing with the high data volumes of experiments at the LHC, and is a key prohibiting factor in the use of diffusion models for NSBI driven statistical inference tasks.
To address these problems we introduce a hybrid NLRE-NLE methodology that can learn a log-density of the data x conditioned on a set of parameters of interest (POI) θ (log(p (x | θ))), from a single classifier. Referred to as a Density Ratio Diffusion Probabilistic Model (DRDPM), the DRDPM method replaces the binary classifier of a NLRE method with a multi-class classifier over the discrete timesteps (t) of a diffusion process that interpolates between the data distribution and a standard Gaussian anchor. Applying Bayes’ rule to the classifier’s outputs at the two boundary classes (t = 0 clean data and t = T Gaussian anchor), the conditional log-likelihood of the data can be recovered in a closed form as the difference of the two boundary logits. In summary, the resulting hybrid NLRE–NLE method trains by classification alone, inheriting the classifier-training simplicity of NLRE, and returns a per-event likelihood estimate at inference-time (evaluation) that is O(10 − 100) times faster than current trajectory based Ordinary(Stochastic) Differential Equation (O(S)DE) solver-based solutions, since only a single neural function evaluation call is required per event. We demonstrate this methodology on a representative High Energy Physics problem of proton-proton collisions at the LHC, and benchmark the fast inferential capabilities using a three-body decay toy dataset within the NEEDLE project [4] (a inter-experiment collaboration across the ATLAS, CMS, and ALICE Collaborations).
[1] The ATLAS Collaboration. Measurement of off-shell higgs boson production in the h → ZZ → 4ℓ decay channel using a neural simulation-based inference technique in 13 TeV pp collisions with the ATLAS detector. Reports on Progress in Physics, 88(5):057803, may 2025.
[2] Kyle Cranmer, Juan Pavez, and Gilles Louppe. Approximating likelihood ratios with calibrated discriminative classifiers, 2016.
[3] Benjamin Rhodes, Kai Xu, and Michael U. Gutmann. Telescoping density-ratio estimation. In Advances in Neural Information Processing Systems, volume 33, pages 4905–4916. Curran Associates, Inc., 2020.
[4] NEEDLE Collaboration. NEEDLE: Neural-based Diffusion Likelihood Estimations. https:://needle-sbi.github.io/, 2026. Orchestration framework and toolkit for the deployment of Neural Simulation-based Inference (NSBI) methods in High Energy Physics. Accessed: July 31, 2026.