This is SParTA: A modular, efficient and scalable transformer architecture for jet-tagging
Authors: Rajneil Baruah, Subhadeep Mondal, Sunando Kumar Patra, Satyajit Roy
Organizations: Department of Physics, SEAS, Bennett University, Greater Noida, Uttar Pradesh, 201310, India · Department of Physics, Bangabasi Evening College, Kolkata, 700009, West Bengal, India
We present the Sparse Particle-interaction Transformer Architecture (SParTA), a modular, scalable, and efficient transformer for jet tagging at high-energy colliders. Exploiting the steeply falling transverse-momentum (pT) spectrum of jet constituents, SParTA factorizes constituent processing into two topological regimes. Ordered by descending pT, only the N hardest constituents (the hard core) participate in quadratic O(N2) differential interaction attention driven by pairwise physical and learned relational features. The remaining soft constituents are integrated via linear O(lN) cross-attention to the hard core, preserving soft-radiation and color-flow information while avoiding the O(l2) memory bottleneck of full self-attention over all l constituents. Pairwise interaction features are computed dynamically in-network from constituent four-momenta and conditioned on global jet-level substructure observables. On the quark-gluon tagging benchmark, a 300K-parameter SParTA model achieves an AUC of 92.02% and accuracy of 85.06%, matching the 2.14M-parameter Particle Transformer (ParT) at one-seventh the parameter count and outperforming IAFormer by 21% in background rejection at 30% signal efficiency. On the boosted top-tagging benchmark, SParTA outperforms ParT and ParticleNet with 511K parameters, while we analyze the architectural trade-offs relative to fully dense multi-layer interaction networks.
Figures & tables
Figure 1: Schematics of the SParT Architecture.
Quark–gluon
Top tagging
Signal / background
q / g
t / QCD
Generator
Pythia 8
Pythia 8
Detector sim.
none
Delphes (ATLAS)
Jet radius R
0.4
0.8
Jet pT (GeV)
500–550
550–650
Rapidity cut
∣y∣<1.7
∣η∣<2
Table 1: Properties of the two datasets and of the inputs built from them.
Feature
Description
1
Δη=η−ηjet
pseudorapidity offset from the jet axis
2
Δϕ=ϕ−ϕjet
azimuthal offset from the jet axis
3
m
constituent mass
4
logpT
transverse momentum
5
logE
energy
6
log(\pt/\ptjet)
momentum fraction
Table 2: Per-constituent input features. The PID feature is available for the QG dataset only ( v=9 ); top tagging uses the first eight ( v=8 ).
Group
Features
No.
Jet kinematics
pTjet , ηjet , ϕjet , mjet
4
Multiplicity
Ncons
1
N-subjettiness ( Thaler and Van Tilburg, 2011 ; Thaler and Van Tilburg, 2012 )
D -series ( Larkoski et al., 2014 ; Larkoski et al., 2016 ; Larkoski et al., 2015 ; Bhattacherjee et al., 2024 )
D2(α,β) , α,β∈{1,2} ; four D3 variants
8
U -series ( Moult et al., 2016 )
U1,U2,U3 ; β=0.5,1,2
9
Table 3: The 53 jet-level (global) features used for both datasets. β is the angular exponent; (α,β) label the two exponents of D2(α,β) .
Figure 2: Schematics of the SParTA Block.
Hyperparameter
Symbol
Values scanned
Embedding dimension
E
40, 60, 80
Hard-core size
N
60, 80
Feed-forward width
F
3E , 4E
Number of SParTA blocks
B
2, 4, 6
Table 4: Hyperparameters scanned. The number of attention heads is fixed at 20.
Rank
B
E
N
Dp
FFN
Params (k)
FLOPs (M)
AUC (%)
R50
R30
1
6
40
80
0.2
120
185.3
416.1
91.86
46.2
126.5
2
6
80
80
0.3
320
757.3
695.8
91.80
44.8
124.1
3
6
40
80
0.2
160
214.9
424.4
91.79
45.1
126.3
4
4
40
80
0.2
160
146.9
293.1
91.78
45.4
121.4
5*
4
60
80
0.3
240
300.4
376.5
91.77
45.2
123.1
6
4
80
80
0.3
320
511.5
474.6
91.77
44.9
126.5
Table 5: All 30 scanned SParTA configurations on the QG test set, ranked by AUC, before fine-tuning. B : blocks; E : embedding dimension; N : hard-core size; Dp: dropout; FFN: feed-forward width F . R50 and R30 are the background rejections 1/ϵB at ϵS=0.5 and 0.3 . ⋆ Configuration used, after fine-tuning, for the results of Table 7 .
Step
n
⟨ΔAUC⟩
Range
Up
⟨ΔR30⟩
B:2→4
10
+0.202
[+0.08,+0.43]
10
+5.5
N:60→80
12
+0.123
[+0.01,+0.26]
12
+1.1
F:3E→4E
15
+0.059
[−0.08,+0.33]
10
+2.7
B:4→6
10
−0.011
[−0.28,+0.14]
6
−0.5
E:60→80
6
−0.023
[−0.21,+0.09]
3
−0.5
E:40→60
12
−0.105
[−0.28,−0.01]
0
−3.5
Table 6: Change in test AUC (percentage points) and in R30 for one hyperparameter step, over all n pairs of configurations that differ only in that step; “Up” counts the pairs whose AUC improved. F is compared as a multiple of E ; the E:60→80 pairs all have N=80 .
Figure 3: Background rejection against cost for the scanned SParTA configurations on the QG test set. Point colour indicates the number of blocks (blue: 2, green: 4, orange: 6); red points joined by the dashed line form the Pareto front.
Figure 4: Main-effect variance fraction ηi2 , Eq. ( 6 ), of each scanned hyperparameter for the test AUC (yellow), R50 (blue) and the number of trainable parameters (green), over the 30 configurations of Table 5 .
Figure 5: Linear CKA, Eq. ( 7 ), between the outputs of the six blocks (B1–B6) of the fine-tuned E60H20N80F4D2B4 model on the QG test set.
Accuracy (%)
AUC (%)
1/ϵB
# of Params
Best
Dist.
Best
Dist.
ϵS=0.5
ϵS=0.3
ParticleNet Qu and Gouskos (2020)
84.0
91.16
39.8(2)
98.6(1.3)
370K
PFN Komiske et al. (2019b)
–
90.52
37.4(7)
–
86.1K
rPCN Shimmin (2021)
–
90.81
38.6(5)
–
–
Lorentz Invariance-
PELICAN Bogatskiy et al. (2024)
85.51
92.52
52.3(3)
149.8(2.4)
208K
based
LorentzNet Gong et al. (2022)
84.40
91.56
42.4(4)
110.2(1.3)
224K
Table 7: Performance of jet taggers on the QG test set. Numbers for SParTA are from this work: “Best” is the best of [ 10 ] trainings and “Dist.” the mean and standard deviation over them. All other numbers are taken from the cited references. The subscript full marks models that use additional weights for charged and neutral hadrons ( Qu et al., 2022b ) , and f.t. marks models pre-trained on JetClass and fine-tuned. Bold marks the best value in each column and italics the best within each group.
Accuracy (%)
AUC (%)
1/ϵB
# of Params
Best
Dist.
Best
Dist.
ϵS=0.5
ϵS=0.3
ParticleNet Qu and Gouskos (2020)
94.0
98.58
397(7)
1615(93)
370K
PFN Komiske et al. (2019b)
–
98.19
247(3)
888(17)
86.1K
rPCN Shimmin (2021)
–
98.40
364(9)
1642(93)
–
Lorentz Invariance-
PELICAN Bogatskiy et al. (2024)
94.26
98.70
–
2250(75)
208K
based
LorentzNet Gong et al. (2022)
94.2
98.68
498(18)
2195(173)
224K
Table 8: Performance of jet taggers on the top-tagging test set. Conventions as in Table 7 .
Table 10: AB: Additive Bias; AS: Attention Score; GC: Graph Convolution ✓ indicates the feature is present as described in the corresponding publication (and, where available, its reference implementation); – indicates it is absent or not applicable. † Feature not implemented in the current architecture, but is an option. ∗ A convolution operation takes place when the interaction tensor is used in the Particle Attention Blocks. ∼ denotes architectures that learn pairwise interaction features from embedded features but do not combine them with the physical interaction features in a single tensor. Marks refer to the architecture as published; several reference implementations expose additional options that are disabled in the published configuration. The “ Activation in FFN ” row reports the nonlinearity of the position-wise feed-forward sub-layer only; embedding-MLP and attention-coefficient activations may differ.
Real-time jet tagging is critical for identifying short-lived particle decays in the high-throughput detectors of the Large Hadron Collider, where real-time trigger systems responsible for deciding which collision events to store impose strict latency and accuracy constraints. While transformer architectures achieve the highest jet tagging accuracy when compute is unconstrained, their quadratic self-attention cost makes inference restrictive on trigger budget. Existing efficient variants reduce the computational cost, but hinder the classification performance. To address this limitation, we introduce the Patch Hierarchical Attention Transformer (PHAT-JeT), which combines two mechanisms: a physics-inspired geometric message-passing module that encodes local detector-plane structure, and a hierarchical patch-based attention scheme that computes exact attention within small particle groups while preserving global context through lightweight patch-token communication. Within a restricted budget, PHAT-JeT achieves state-of-the-art accuracy and background rejection among all resource-constrained jet tagging models on four benchmarks (hls4ml, JetClass, Top Tagging, and Quark--Gluon). Our code is available at https://github.com/aaronw5/PHAT-JeT.
Aaron Wang, Zihan Zhao, Alan Xia +5
University of Illinois Chicago Chicago, IL 60607, USA · University of California San Diego La Jolla, CA 92093, USA · California Institute of Technology Pasadena, CA 91125, USA +1
The Lund plane offers a physics-motivated, hierarchical representation of QCD radiation within jets, while transformer-based taggers have reached state-of-the-art performance by learning directly from raw particle constituents and their pairwise relations. We investigate whether transformers implicitly capture hierarchical QCD structure from constituent-level inputs, or whether explicit physics representations remain complementary. To test this, we introduce PLuM, a multimodal architecture that projects particle constituents and Lund plane splittings into a shared latent space, processing both jointly with a unified transformer. Cross-attention allows the model to probe whether structured QCD information provides discriminating power beyond what particles alone encode. We observe systematic gains for top-quark and H→bbˉ tagging, while finding no comparable improvement for H→ccˉ or H→4q topologies. This selective enhancement suggests that explicit hierarchical information about b-jet formation remains complementary to raw particle representations even in highly expressive architectures, while other topologies are already well-captured at constituent level. For high-impact LHC analyses such as Lorentz-boosted di-Higgs searches in the four b quark final state (HH(4b)), the gains are substantial: at a 25% di-Higgs efficiency working point, PLuM achieves 25% higher background rejection than the baseline. Our results indicate that physically structured representations of QCD radiation retain discriminating value in the transformer era, motivating further study into how different aspects of jet dynamics are encoded by deep learning algorithms.
Loukas Gouskos, Benedikt Maier
Brown University, Providence, USA · Imperial College of Science, Technology and Medicine, London, United Kingdom
Jet flavor tagging plays an important role in precise Standard Model measurement enabling the extraction of mass dependence in jet-quark interaction and quark-gluon plasma (QGP) interactions. They also enable inferring the nature of particles produced in high-energy particle collisions that contain heavy quarks. The classification of bottom jets is vital for exploring new Physics scenarios in proton-proton collisions. In this research, we present a hybrid deep learning architecture that integrates edge convolutions with transformer self-attention mechanisms, into one single architecture called the Edge Convolution Transformer (ECT) model for bottom-quark jet tagging. ECT processes track-level features (impact parameters, momentum, and their significances) alongside jet-level observables (vertex information and kinematics) to achieve state-of-the-art performance. The study utilizes the ATLAS simulation dataset. We demonstrate that ECT achieves 0.9333 AUC for b-jet versus combined charm and light jet discrimination, surpassing ParticleNet (0.8904 AUC) and the pure transformer baseline (0.9216 AUC). The model maintains inference latency below 0.060 ms per jet on modern GPUs, meeting the stringent requirements for real-time event selection at the LHC. Our results demonstrate that hybrid architectures combining local and global features offer superior performance for challenging jet classification tasks. The proposed architecture achieves good results in b-jet tagging, particularly excelling in charm jet rejection (the most challenging task), while maintaining competitive light-jet discrimination comparable to pure transformer models.
Diego F. Vasquez Plaza, Vidya Manian
Department of Electrical and Computer Engineering, University of Puerto Rico Mayaguez, PR 00681-9000, USA