Full Event Particle-Level Unfolding with Variable-Length Latent Variational Diffusion

TL;DR

This work tackles the problem of detector-effects unfolding in collider data by extending generative diffusion models to variable-length, full-event outputs. It introduces a Particle VAE, a Detector Encoder, and a Multiplicity Predictor to build a set-valued latent representation $(X|Y)$, and trains a Latent Diffusion Process with a set-aware denoising network to model $P(X|Y)$. The model is learned via an end-to-end ELBO that combines Prior Loss, Reconstruction Loss, Denoising Loss, and Multiplicity Loss, with inference sampling the event multiplicity from a Gamma distribution and performing reverse diffusion to produce particle-level observables. Applied to semi-leptonic $t\bar{t}$ events at the LHC, the method achieves close agreement with truth-level distributions across many observables and demonstrates robustness to prior changes, highlighting a path toward post-hoc re-interpretation of unfolded data while noting areas for improvement in sharp features and top-quark kinematics.

Abstract

The measurements performed by particle physics experiments must account for the imperfect response of the detectors used to observe the interactions. One approach, unfolding, statistically adjusts the experimental data for detector effects. Recently, generative machine learning models have shown promise for performing unbinned unfolding in a high number of dimensions. However, all current generative approaches are limited to unfolding a fixed set of observables, making them unable to perform full-event unfolding in the variable dimensional environment of collider data. A novel modification to the variational latent diffusion model (VLD) approach to generative unfolding is presented, which allows for unfolding of high- and variable-dimensional feature spaces. The performance of this method is evaluated in the context of semi-leptonic top quark pair production at the Large Hadron Collider.

Figures (24)

• Figure 1: A Flow diagram of the components of Particle VLD. Pairs of particle level (${\mathcal{O}_P}$) and detector level (${\mathcal{O}_D}$) events are used to train the model using the loss functions introduced in Ref. Shmakov:2023kjj. At inference time, a detector level event is used to produce a multiplicity prediction and mapped to a latent embedding through the detector encoder. The multiplicity prediction and the latent representation of the detector level event are then used to condition the diffusion process, resulting in a sample from the latent space of the particle VAE. A particle decoder is then applied to produce a sample from the learned conditional distribution $P(X|Y)$. During training, the particle encoder is used to produce latent samples instead of the diffusion process. The special vector $y_0$ is a learnable input vector trained alongside the network weights.
• Figure 2: A simplified block diagram of the particle denoising network and all of the inputs. Each of the inputs is a pre-processed and concatenated collection of various features. We introduce a variable-length conditional noise-prediction model by providing the transformer with both the noisy particles, as well as the detector inputs. The detector outputs are ignored and the particle outputs are interpreted as the noise prediction.
• Figure 3: A representative Feynman diagram of $t\bar{t}$ production in the semi-leptonic decay mode.
• Figure 4: Example learned noise schedule for each object. Independent noise schedules are learned for each unfolded object, ordered by true $p_T$. The "Event" represents the event level observables. Shown are (\ref{['subfig:noise']}) the signal-to-noise ratio (SNR) learned during training and (\ref{['subfig:beta']}) the equivalent $\beta$ schedule used during inference, following the DDPM framework ddpm.
• Figure 5: Inclusive kinematic distributions for jets in the SM testing dataset, comparing the true particle-level jets (dashed blue), the unfolded particle-level jets (solid red), and the detector-level jets (dotted green). The unfolded distributions include error bounds estimated by sampling each event 128 times.