Pairton: Iterative Reconstruction of Short-Lived Particles

Andreas Hermansen; Chris Scheulen; Tobias Golling

hep-phAug 14, 2026

Pairton: Iterative Reconstruction of Short-Lived Particles

Authors: Andreas Hermansen, Chris Scheulen, Tobias Golling

Organizations: Département de physique nucléaire et corpusculaire, University of Geneva

Abstract

We present Pairton, an iterative framework for reconstructing short-lived particles in high-energy collision events. By formulating particle reconstruction as a masked prediction process over graph structures, Pairton learns conditional distributions consistent with a factorised decomposition of decay products and iteratively predicts edges in the adjacency matrix representing particle decay relationships. Leveraging a pairformer-based architecture with dynamically updated pairwise representations, our method incorporates global event consistency. We demonstrate state-of-the-art performance on fully hadronic $t\bar{t}$ decays. Pairton provides a general, flexible paradigm for particle reconstruction and can be readily extended to other topologies, bridging ideas from modern generative modelling and high-energy physics.

Figures & tables

Figure 1: Representation of an all-hadronic

t\bar{t}

event with eight jets as (left) a graph of the decay products of the individual tops and (right) the combined view of the corresponding top and

W

boson adjacency matrices

A^{t}

and

A^{W}

, respectively. In the chosen example, one top quark decays into the jets 1, 4, and 7, where jet 7 originates from the

b

quark while jets 1 and 4 originate from the subsequent

W

boson decay. Similarly, the other top quark decays into jets 2, 3, and 6 with jet 3 originating from the

b

quark. Jets 5 and 8 are additional jets not originating from the top quark decays. In the adjacency matrix view, grey entries correspond to zeros, while the coloured entries correspond to graph edges (including self-loops) corresponding to the graph assignment on the left: Blue entries and solid edges are ones in both

A^{t}

and

A^{W}

, green entries and dashed edges are ones in

A^{t}

only, and purple entries are ones in

A^{W}

only.

Figure 2: Sequential reconstruction of

W

bosons and top quarks in three steps for the event depicted in Figure 1 following the same visual style. Additionally, white entries indicate unknown adjacency, while the scratched entries indicate that no edge can exist in the

W

boson edge-set, so that the associated jets cannot be decay products of the same

W

boson, but might still be part of the top quark edge-set.

Figure 3: Visual illustration of the model during training and inference. During training, the mask level is chosen at random and used together with the true adjacency matrices to construct the visible adjacency matrices given to the model. During inference, the visible adjacency matrices are constructed iteratively. The true adjacency matrices are also used as targets for the loss calculation during training.

Feature	Feature(s) after Transformation
$E$	$\log(E/$ \mathrm{Ge\kern-1.00006pt{}V} $)-4.5$
$p_{\text{T}}$	$\log(p_{\text{T}}/$ \mathrm{Ge\kern-1.00006pt{}V} $)-4.5$
$\varphi$	$\cos\varphi$
$\varphi$	$\sin\varphi$
$\Delta\varphi_{ij}$	$\Delta\varphi_{ij}$
	$\Delta(\sin\varphi)_{ij}$

Table 1: Feature transformation applied for both single- and pairwise jet features. Only features for which transformations are applied are listed, while the other features mentioned in the text are propagated to Pairton as is.

	Jets	SPANet	Topograph	HyPER	Pairton
$\varepsilon_{t\bar{t}}$	6	$0.801$	$0.805$	$0.816$	$\textbf{0.8298}\pm 0.0004$
	7	$0.654$	$0.649$	$0.672$	$\textbf{0.6988}\pm 0.0011$
	$\geq 8$	$0.487$	$0.472$	$0.513$	$\textbf{0.5459}\pm 0.0004$
	Inclusive	$0.651$	$0.645$	$0.670$	$\textbf{0.6944}\pm 0.0003$
$\varepsilon_{t}$	6	$0.667$	$0.658$	$0.663$	$\textbf{0.6760}\pm 0.0008$
	7	$0.649$	$0.638$	$0.654$	$\textbf{0.6693}\pm 0.0005$

Table 2: Comparison of model reconstruction efficiencies for full-event (

\varepsilon_{t\bar{t}}

), top quark (

\varepsilon_{t}

), and

W

boson (

\varepsilon_{W}

) reconstruction. The values for SPANet, Topograph, and HyPER are taken from Reference [ 9 ] . The uncertainties of Pairton were calculated by varying the initial random initialisation and shuffling the training batches five times. Since only statistical uncertainties of the test dataset size were considered for the other models, we only quote the central value for these, and note that the statistical uncertainties are generally around

0.001

. While only fully reconstructible events were considered for the full-event reconstruction efficiencies, reconstructible

W

bosons and top quarks from partially reconstructible events were additionally considered for their respective particle reconstruction efficiencies.

Figure 4: Event reconstruction efficiencies of the different models in dependence on

m_{t\bar{t}}

, the invariant mass of the

t\bar{t}

system as determined from truth-matched final-state reconstructed jets. While Pairton consistently outperforms the other methods with HyPER showing the second-highest efficiencies, Topograph outperforms SPANet in the low-mass region while their ordering is reversed for high

m_{t\bar{t}}

. The performance metrics of HyPER, SPANet, and Topograph are taken from Reference [ 9 ] .

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Name	Value
Number of pairformer blocks	$4$
Sequence embedding dimension	$128$
Pairwise embedding dimension	$64$
Optimiser	AdamW
Learning rate	$0.001$
Learning rate scheduler	Cosine annealing

Appendix

Table 3: Summary of the most important hyperparameters.

Model	$\varepsilon_{t\bar{t}}$	$\varepsilon_{t}$	$\varepsilon_{W}$
Transformer	$0.635$	$0.623$	$0.655$
Transformer with bias	$0.668$	$0.649$	$0.678$
Pairformer	$0.688$	$0.656$	$0.682$
Iterative pairformer	$0.692$	$0.661$	$0.684$

Appendix

Table 4: Comparison of the reconstruction efficiencies from the ablation study comparing different neural network architectures. The efficiencies shown are the maximum efficiencies achieved on the validation set during model training.

Figure 5: Comparison of the reconstruction performance of the 3-step iterative pairformer model (towards the right) and a one-shot pairformer model (towards the left) on a total of

117\,487

fully reconstructible all-hadronic

t\bar{t}

events of the validation set. To directly compare the model behaviour, the reconstruction of the first

W

boson is common between the two methods. Afterwards, the iterative model reconstructs further particles in additional model passes using partial adjacency matrices from previous iterations as described in Section III . Meanwhile, all particles are reconstructed from the first model pass in a greedy approach for the one-shot model, whereby the first

W

boson selected is the one maximising the edge assignment heuristic detailed in Appendix D . In each reconstruction step, the number of correct and incorrect assignments, as well as their proportion with respect to the previous assignment outcome, are shown. For the

b

quark assignment, the number and proportion of partial correct assignments are additionally shown while respecting consistency in the top quark matching between possible correctly reconstructed

W

bosons and

b

quarks.

Model	$\varepsilon_{t\bar{t}}$	$\varepsilon_{t}$	$\varepsilon_{W}$
Pairformer	$0.688$	$0.656$	$0.682$
Pairformer HyPER	$0.688$	$0.657$	$0.681$
Iterative pairformer 3-step	$0.692$	$0.661$	$0.684$
Iterative pairformer 4-step	$0.691$	$0.660$	$0.684$
Pairformer deep	$0.687$	$0.658$	$0.684$

Appendix

Table 5: Comparison of the reconstruction efficiencies from the ablation study comparing different reconstruction methods. The efficiencies shown are the maximum efficiencies achieved on the validation set during model training.

Explore similar work

HEPTv2: End-to-End Efficient Point Transformer for Charged Particle Reconstruction
Jun 18, 2026Siqi Miao, Shitij Govil, Jack P. Rodgers +5Efficient Transformer Inference Transformer
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA. · Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA. · Department of Physics, University of California San Diego, La Jolla, CA, USA. +1
Prompting Particle Physics: Tokenized Multi-modal Foundation Models for Combinatorially Many Tasks
Sep 25, 2026Nilotpal Kakati, Daniel Murnane, Baran Hashemi +5Unified Multimodal Models High-Energy Physics
Weizmann Institute of Science, Rehovot, Israel · Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark · Lawrence Berkeley National Laboratory, Berkeley, CA, USA +3
Comprehensive reconstruction of collider events with hypergraph representation learning and graph-conditioned diffusion
Sep 16, 2026Lining Mao, Yvonne Peters, Ethan Simpson +1High-Energy Physics Hypergraph Learning
School of Physics and Astronomy, Shanghai Jiao Tong University, No.800 Dong Chuan Road, Shanghai 200240, PRC · Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK

Jun 18, 2026J/K move · Enter open · S save

HEPTv2: End-to-End Efficient Point Transformer for Charged Particle Reconstruction

Siqi Miao, Shitij Govil, Jack P. Rodgers, Mia Liu+4

School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA. · Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA. · Department of Physics, University of California San Diego, La Jolla, CA, USA.+1

Efficient Transformer Inference Transformer High-Energy Physics

Open paper AskPDF arXiv

Charged-particle tracking -- reconstructing trajectories from sparse detector measurements -- is a fundamental high-energy-physics inference problem and a canonical example of learning under extreme combinatorial ambiguity. At the High-Luminosity Large Hadron Collider (HL-LHC), tracking must remain accurate and efficient despite unprecedented collision densities. Graph neural networks perform strongly, but incur substantial costs from graph construction and processing, while transformer-based approaches rely on auxiliary stages that prevent end-to-end optimization. To address this, we present HEPTv2, an end-to-end point-transformer architecture that reconstructs tracks from detector hits in one trainable pipeline. HEPTv2 combines a locality-aware point encoder with a track decoder that predicts complete trajectories without graph-building, clustering, or filtering. The encoder uses locality-sensitive hashing in detector coordinate space to preserve tracking-relevant geometry while enabling efficient local attention. The decoder resolves ambiguities through sectorized decoding and direct hit-to-track prediction under joint encoder-decoder supervision, allowing the full pipeline to be optimized end-to-end. On TrackML, HEPTv2 achieves 98.6% double-majority tracking efficiency at a 0.8% fake rate, while requiring only

\sim

15~~ms inference time and 0.4~~GB peak memory per event on a NVIDIA A100 GPU. Latency and memory scale approximately linearly for events with up to

5\times10^5

hits. HEPTv2 establishes a new state of the art in the accuracy-latency trade-off, improving efficiency by 4.5% over the strongest prior transformer and by 1.1--2.2% over optimized graph-based pipelines, while reducing latency by factors of 7 and 38--52, respectively. These results show end-to-end transformers can deliver the accuracy and efficiency required for real-time particle reconstruction at the HL-LHC.

Abstract

Explore similar work

HEPTv2: End-to-End Efficient Point Transformer for Charged Particle Reconstruction

Prompting Particle Physics: Tokenized Multi-modal Foundation Models for Combinatorially Many Tasks

Comprehensive reconstruction of collider events with hypergraph representation learning and graph-conditioned diffusion