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EPiC-GAN: Equivariant Point Cloud Generation for Particle Jets

by Erik Buhmann, Gregor Kasieczka, Jesse Thaler

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Submission summary

Authors (as registered SciPost users): Erik Buhmann
Submission information
Preprint Link:  (pdf)
Code repository:
Date accepted: 2023-08-21
Date submitted: 2023-07-17 16:28
Submitted by: Buhmann, Erik
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Experiment
  • High-Energy Physics - Phenomenology
Approach: Computational


With the vast data-collecting capabilities of current and future high-energy collider experiments, there is an increasing demand for computationally efficient simulations. Generative machine learning models enable fast event generation, yet so far these approaches are largely constrained to fixed data structures and rigid detector geometries. In this paper, we introduce EPiC-GAN - equivariant point cloud generative adversarial network - which can produce point clouds of variable multiplicity. This flexible framework is based on deep sets and is well suited for simulating sprays of particles called jets. The generator and discriminator utilize multiple EPiC layers with an interpretable global latent vector. Crucially, the EPiC layers do not rely on pairwise information sharing between particles, which leads to a significant speed-up over graph- and transformer-based approaches with more complex relation diagrams. We demonstrate that EPiC-GAN scales well to large particle multiplicities and achieves high generation fidelity on benchmark jet generation tasks.

Author comments upon resubmission

We thank our colleagues for their thoughtful comments on the manuscript and the opportunity to resubmit. We have already provided direct responses to the reviewer comments. A detailed list of changes is provided as well.

List of changes

1- Softened our language in the Introduction: “For these applications, the generative models need to learn the underlying data distributions with help from the inductive bias of the model architecture.”

2- Softened our language in the Introduction: “Some very advanced generative modeling efforts for high-dimensional data in high energy physics (HEP) are currently undertaken for calorimeter shower simulations.”

3- Added to the third paragraph of the Introduction: ““Here, we introduce a novel kind of GAN architecture which could be applied to various applications. Of course, when applied to a specific physics analysis, the uncertainties derived from a generative model need to be critically examined depending on the use-case.”

4- We expanded on the application in the Introduction: “JetNet is a specifically designed toy dataset for the generation of hadronized jets used to compare point cloud generative models.” and “We further envision that our model could be applied to generate in-situ background events for anomaly detection methods such as CATHODE [34]. Additionally, the development of fast and lightweight generative models can support analysis by making Monte Carlo tuning or nuisance parameter variation computationally efficient.“

5- Citations: We added the following citations to the Introduction:
– S. Vallecorsa, F. Carminati and G. Khattak, 3D convolutional GAN for fast simulation, EPJ Web Conf. 214, 02010 (2019)
– M. Erdmann, J. Glombitza and T. Quast, Precise Simulation of Electromagnetic Calorimeter Showers Using a Wasserstein Generative Adversarial Network, Computing and Software for Big Science 3(1) (2019)
– G. R. Khattak, S. Vallecorsa, F. Carminati and G. M. Khan, Fast Simulation of a High
Granularity Calorimeter by Generative Adversarial Networks (2021), arXiv 2109.07388
– ATLAS Collaboration, Deep generative models for fast photon shower simulation in ATLAS (2022), arXiv 2210.06204
– E. Buhmann, S. Diefenbacher, E. Eren, F. Gaede, G. Kasieczka, A. Korol and K. Krüger,
Decoding Photons: Physics in the Latent Space of a BIB-AE Generative Network, EPJ Web of Conferences 251, 03003 (2021)
– J. C. Cresswell, B. L. Ross, G. Loaiza-Ganem, H. Reyes-Gonzalez, M. Letizia and A. L. Caterini, CaloMan: Fast generation of calorimeter showers with density estimation on learned manifolds (2022), arXiv 2211.15380

6- Figure 2: In the discriminator diagram the aggregation was supposed to be in front of the MLP phi_p^in, not behind.

7- Expanded on the end of Sec. 2.2: “We compared this approach to the regular GAN objective using the binary cross-entropy loss and found slightly improved training stability with the LSGAN objective as it avoids vanishing gradients. Additionally, we apply weight normalization to all hidden layers of both the generator and discriminator to improve the GAN stability.”

8- We added and streamlined Sec. 3.2. with a Table of the hyperparameters.

9- Added to Sec. 3.2.: “In principle, the discriminator could also be implemented with any other permutation-equivariant graph- or set-based architecture. However, replacing the EPiC discriminator with a simple Particle Flow Network -- equivalent to L_discriminator=0 EPiC layers -- led to worse results.”

10-Table 2: We recalculated the MPGAN metrics, now with the same post processing applied as to the EPiC GAN (centering of jets). The values changed just slightly within the margin of error for Gluon W1EFP from 0.6 +- 0.4 to 0.6 +- 0.3; for Top W1M from 0.4 +- 0.1 to 0.5+- 0.1; and for Top W1EFP from 0.9 +- 0.3 to 1.0 +- 0.7.

11- Added to the end of Sec. 3.3.4: “In practice, GAN samples need to be verified to have a sufficient fidelity for a given physics analysis task. The metrics for judging the fidelity depend on the simulation task, and there are approaches that could increase the fidelity such as a learned re-weighting of generated samples. Alternatively, important physics observables could be added to the loss function, i.e. in Ref. [20] the jet mass is added as a conditioning. However, even if certain observables are individually added to the loss function, their correlations might still be mismodeled. Therefore, using an unconditional model like the EPiC-GAN might be advantageous as certain correlations can be learned and directly encoded into the global attribute vector of the model.”

12- We expanded on the application in Sec. 3.5: “Further, the linear scaling of the EPiC-GAN also allows the model to be applicable to physics simulation tasks that are traditionally much more computationally expensive than the lightweight Pythia event generation, such as calorimeter shower simulation with Geant4.”

13- Clarified in the Conclusion: “Depending on the application, i.e. for proof-of-principle studies or large scale parameter scans, it may even be beneficial to opt for a model with slightly worse fidelity if it comes at a significantly lower cost.”

Published as SciPost Phys. 15, 130 (2023)

Reports on this Submission

Report 2 by Tilman Plehn on 2023-7-20 (Invited Report)


Thank you for considering all my comments. Concerning the references, I am unhappy, because declaring detector-generative models and event-generative models too different to cite each other is not good for the scientific exchange and not good for the careers of theory students. For instance, the Rutgers and Heidelberg groups just wrote a paper combining calorimeter flows and event flows, illustrating the fruitful combination of the two task. In addition, are we not pretending that this exchange is really important for our grant applications? But this is clearly a choice of the authors, fine by me.

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Anonymous Report 1 on 2023-7-18 (Invited Report)


I am satisfied with the authors replies to my comments.

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