PhyGHT: Physics-Guided HyperGraph Transformer for Signal Purification at the HL-LHC

Mohammed Rakib; Luke Vaughan; Shivang Patel; Flera Rizatdinova; Alexander Khanov; Atriya Sen

hep-exFeb 24, 2026

PhyGHT: Physics-Guided HyperGraph Transformer for Signal Purification at the HL-LHC

Authors: Mohammed Rakib, Luke Vaughan, Shivang Patel, Flera Rizatdinova, Alexander Khanov, Atriya Sen

Organizations: Department of Computer Science Oklahoma State University, USA · Department of Physics Oklahoma State University, USA

Abstract

The High-Luminosity Large Hadron Collider (HL-LHC) at CERN will produce unprecedented datasets capable of revealing fundamental properties of the universe. However, realizing its discovery potential faces a significant challenge: extracting small signal fractions from overwhelming backgrounds dominated by approximately 200 simultaneous pileup collisions. This extreme noise severely distorts the physical observables required for accurate reconstruction. To address this, we introduce the Physics-Guided Hypergraph Transformer (PhyGHT), a hybrid architecture that combines distance-aware local graph attention with global self-attention to mirror the physical topology of particle showers formed in proton-proton collisions. Crucially, we integrate a Pileup Suppression Gate (PSG), an interpretable, physics-constrained mechanism that explicitly learns to filter soft noise prior to hypergraph aggregation. To validate our approach, we release a novel simulated dataset of top-quark pair production to model extreme pileup conditions. PhyGHT outperforms state-of-the-art baselines from the ATLAS and CMS experiments in predicting the signal's energy and mass correction factors. By accurately reconstructing the top quark's invariant mass, we demonstrate how machine learning innovation and interdisciplinary collaboration can directly advance scientific discovery at the frontiers of experimental physics and enhance the HL-LHC's discovery potential. The dataset and code are available at https://github.com/rAIson-Lab/PhyGHT

Figures & tables

Figure 1. Signal Collision (Blue) covered in Pileup Collisions (Red) in the HL-LHC Environment

Panel of Figure 2 — Figure 2. A Phoenix Event Display ( et al., 2024 ) depicting an event in the ATLAS inner tracking system in the HL-LHC conditions at $\langle\mu\rangle=60$ (left) and $\langle\mu\rangle=200$ (right) for signal (blue) and background (red) particles with $p_{T}>1.0$ GeV.

Figure 3. Overview of PhyGHT. It takes a heterogeneous graph of Tracks and Jets as input. It processes tracks through the Local Geometric (DA-GAT) block, followed by the Global Context block. The fused representations are filtered by the Pileup Suppression Gate (PSG) before being aggregated into the Jet representation via Hypergraph Attention for final regression.

$\bm{\langle\mu\rangle}$	Target	Baselines								Ours
$\bm{\langle\mu\rangle}$	Target	Transformer	GNN	HGNN	GAT	HGAT	PUPPI	ParticleNet	PUMINet	PhyGHT
60	Energy	0.812	0.841	0.821	0.839	0.792	0.769	0.869	0.934	0.943
60	Mass	0.634	0.694	0.662	0.683	0.621	0.549	0.748	0.838	0.869
200	Energy	0.778	0.837	0.798	0.792	0.756	0.348	0.853	0.926	0.932
200	Mass	0.567	0.643	0.587	0.591	0.595	0.114	0.693	0.805	0.836

Table 1. Performance Comparison on the Test Set. We report the Coefficient of Determination (

R^{2}

) for the energy (

\hat{y}_{E}

) and mass (

\hat{y}_{M}

) correction factors across two pileup scenarios:

\langle\mu\rangle\in\{60,200\}

Panel of Figure 4 — Figure 4. 1D distribution and 2D correlation plots for Energy ( $\hat{y}_{E}$ ) and Mass ( $\hat{y}_{M}$ ) at $\langle\mu\rangle=60$ (top row) and $\langle\mu\rangle=200$ (bottom row).

Panel of Figure 5 — Figure 5. Comparison of Energy and Mass Resolutions of PhyGHT with baselines at $\langle\mu\rangle=60$ and $\langle\mu\rangle=200$ .

$\bm{\langle\mu\rangle}$	Model	Energy	Mass	Params	Latency
$\bm{\langle\mu\rangle}$	Model	( $R^{2}$ ) $\uparrow$	( $R^{2}$ ) $\uparrow$	(M) $\downarrow$	(ms) $\downarrow$
60	ParticleNet	0.869	0.748	0.17	130.1
	PUMINet	0.934	0.838	0.85	12.4
	PhyGHT	0.943	0.869	0.95	10.0
200	ParticleNet	0.853	0.693	0.17	353.1
	PUMINet	0.926	0.805	0.85	78.2

Table 2. Comparison of performance, model size, and inference latency across a single event for 1000 runs.

Model	Energy	Mass	Latency
	( $R^{2}$ ) $\uparrow$	( $R^{2}$ ) $\uparrow$	(ms) $\downarrow$
ParticleNet	0.888	0.754	348
PUMINet	0.938	0.831	75
PhyGHT	0.946	0.864	39

Table 3. Cross-process generalization performance. Trained on

t\bar{t}

dataset and evaluated on the unseen di-Higgs dataset.

Metric $R^{2}$	PhyGHT	w/o Local	w/o Global	w/o PSG	w/o Hypergraph
Energy	0.943	0.903	0.848	0.915	0.891
Mass	0.869	0.813	0.715	0.837	0.824

Table 4. Impact of removing key components from PhyGHT.

Metric $R^{2}$	Neighbors ( $\bm{k}$ )
Metric $R^{2}$	0	2	4	8	16	20	32
Energy	0.903	0.932	0.938	0.943	0.934	0.928	0.921
Mass	0.813	0.851	0.856	0.869	0.858	0.853	0.849

Table 5. Impact of Local DA-GAT neighborhood size (

k

) on regression performance. For

k=0

, the local block is removed.

Metric $R^{2}$	Auxiliary Weight ( $\bm{\lambda_{aux}}$ )
Metric $R^{2}$	0.0	0.1	0.25	0.5	0.75	1.0
Energy	0.915	0.943	0.940	0.938	0.935	0.931
Mass	0.837	0.869	0.865	0.862	0.859	0.855

Table 6. Impact of the auxiliary classification loss weight (

\lambda_{aux}

) on overall regression performance.

Panel of Figure 6 — Figure 6. Mass Reconstruction after PhyGHT correction

Test Setting	ParticleNet		PUMINet		PhyGHT
	Energy	Mass	Energy	Mass	Energy	Mass
	( $R^{2}$ ) $\uparrow$	( $R^{2}$ ) $\uparrow$	( $R^{2}$ ) $\uparrow$	( $R^{2}$ ) $\uparrow$	( $R^{2}$ ) $\uparrow$	( $R^{2}$ ) $\uparrow$
Pythia Gen.	0.873	0.772	0.933	0.849	0.943	0.880
Inflated $d_{0},z_{0}$	0.869	0.748	0.934	0.839	0.944	0.869
Both	0.873	0.772	0.933	0.849	0.943	0.880

Table 7. Impact of generator and detector shifts on regression performance at

\langle\mu\rangle=200

without retraining.

PSG-Hypergraph Attention Relation	Percentage
High PSG & High Attention	26.8%
Low PSG & Low Attention	24.2%
High PSG & Low Attention	18.1%
Low PSG & High Attention	0.01%

Table 8. Agreement b/w PSG and hypergraph attention. High and low denote the top and bottom 20% of tracks within each jet. Percentages are calculated over all constituent-track instances after per-jet ranking.

Masking Setting	Energy	Mass
	( $R^{2}$ ) $\uparrow$	( $R^{2}$ ) $\uparrow$
No masking	0.932	0.836
Mask top 20%	0.459	0.093
Mask bottom 20%	0.932	0.836

Table 9. Effect of masking tracks ranked by PSG.

Figure 7. ROC Curve for PSG Track Classification at $\langle\mu\rangle=200$

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

$\bm{\langle\mu\rangle}$	Model	Energy ( $\hat{y}_{E}$ )				Mass ( $\hat{y}_{M}$ )
$\bm{\langle\mu\rangle}$	Model	MSE $\downarrow$	RMSE $\downarrow$	MAE $\downarrow$	$R^{2}$ $\uparrow$	MSE $\downarrow$	RMSE $\downarrow$	MAE $\downarrow$	$R^{2}$ $\uparrow$
60	ParticleNet	0.0044	0.0664	0.0429	0.8692	0.0030	0.0549	0.0366	0.7483
	PUMINet	0.0022	0.0472	0.0308	0.9341	0.0019	0.0440	0.0289	0.8389
	PhyGHT (Ours)	0.0019	0.0436	0.0281	0.9436	0.0016	0.0396	0.0257	0.8692
200	ParticleNet	0.0009	0.0305	0.0174	0.8536	0.0005	0.0212	0.0125	0.6935
	PUMINet	0.0005	0.0216	0.0124	0.9265	0.0003	0.0169	0.0097	0.8052

Appendix

Table 10. Detailed regression metrics for Energy (

\hat{y}_{E}

) and Mass (

\hat{y}_{M}

) correction factors across standard (

\langle\mu\rangle=60

) and high-pileup (

\langle\mu\rangle=200

) scenarios. Best results are bolded , second-best are underlined .

Panel of Figure 8 — Figure 8. Validation Plots for implementation of the PUPPI algorithm

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Using Line Segment Tracking to enable ML-based Track Reconstruction in CMS

Aashay Arora on behalf of the CMS Collaboration

University of California San Diego, La Jolla, CA, USA

High-Energy Physics

Open paper AskPDF arXiv

High-pileup conditions in CMS during the HL-LHC era make charged-particle tracking increasingly challenging as detector occupancy and combinatorics grow. We present a hybrid approach that exploits Line Segment Tracking (LST) objects rather than individual hits to enable the first CMS ML-based track reconstruction algorithm. The LST objects, namely the triplets used in this study, are built according to geometry- and physics-driven criteria and carry richer local structure, geometrical cues, and physics quantities such as transverse momentum, which helps the model incorporate detector-level information from the start. We apply a Transformer encoder with geometrically masked sparse self-attention to embed these objects in a learned latent space, and use object condensation to assemble full tracks in a single inference step. This object-based representation reduces complexity in dense environments and makes the model less sensitive to ambiguities introduced by high pileup. Evaluated on CMS Phase-2 simulation of

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