SciPost Submission Page
Generating particle physics Lagrangians with transformers
by Yong Sheng Koay, Rikard Enberg, Stefano Moretti, Eliel Camargo-Molina
Submission summary
| Authors (as registered SciPost users): | Rikard Enberg · Yong Sheng Koay |
| Submission information | |
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| Preprint Link: | scipost_202507_00009v1 (pdf) |
| Code repository: | https://huggingface.co/JoseEliel/BART-Lagrangian |
| Data repository: | https://huggingface.co/datasets/JoseEliel/lagrangian_generation |
| Date submitted: | July 2, 2025, 3:27 p.m. |
| Submitted by: | Yong Sheng Koay |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating Lagrangians as complex, rule-based constructs similar to linguistic expressions, we trained a transformer model --- proven to be effective in natural language tasks --- to predict the Lagrangian corresponding to a given list of particles. We report on the transformer's performance in constructing Lagrangians respecting the Standard Model $\mbox{SU}(3)\times \mbox{SU}(2)\times \mbox{U}(1)$ gauge symmetries. The resulting model is shown to achieve high accuracies (over 90\%) with Lagrangians up to six matter fields, with the capacity to generalize beyond the training distribution, albeit within architectural constraints. We show through an analysis of input embeddings that the model has internalized concepts such as group representations and conjugation operations as it learned to generate Lagrangians. We make the model and training datasets available to the community. An interactive demonstration can be found at: \url{https://huggingface.co/spaces/JoseEliel/generate-lagrangians}.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
In particular the out of domain-section is clearly written and explains the method well. Quantification of abstract similarity is particularly nicely carried out.
Weaknesses
1 - While interesting in its own right, I am wondering how, on the longer term, the Lagrangian-generating AI might be applied: To my understanding it generates EFT-Lagrangians, and would it be imaginable that subsequent processing determines for instance S-matrix elements and scattering amplitudes?
2 - Many intellectual achievements in the construction of the standard model of particle physics seem to be implicitly assumed in the proposed generative AI, or are beyond the scope of what the algorithm would be able to provide: Could you comment on this, in particular with these two points in mind?
2a - Many choices in the construction of Lagrangians are implicit: restriction to squares of first derivatives in the kinetic terms disallow derivative couplings or Ostrogradsky-unstable theories, explicitly constructed differences between left- and right-handed fermion doubles already codify P-violation. Can you please be more explicit in what implicit or hidden assumptions are at the basis of the Lagrange-construction?
2b - Similarly, adding more particles for instance with SU(3) symmetries would have them co-exist with possible interactions - but there would not be a larger symmetry group accommodating them, right?
3 - There are studies for automatic generation of Lagrange-functions from data through symbolic regression. Can you please add a comment on how the two are related? To my understanding, your methods looks for mathematical consistency, and tying in to my first remark, does not take direct input from experimental data?
4 - Similarly, it'd be good to emphasise that the gauge particle content and their group structure in this work is fixed, and the matter particle content is variable. On a related note - there is no concept of quark mixing, right?
5 - Would the generative AI find Lagrange-densities with V-A coupling, i.e. explicit parity violation?
Report
The decision to relegate the technical parts to the appendices is understandable, but did not help me to access the paper. It was only after working through the appendix that things became apparent. I'd argue that the appendices are vital to the understanding of the paper.
Requested changes
Please take account of the points listed under "weakness" in the evaluation. Further points would be:
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I find it difficult to assess whether the number of Lagrange densities for instance in the training data set is large or not. Can you make a combinatorial argument what fraction of Lagrange densities is contained?
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I've been playing with the online tool for Lagrangian generation, which I find a great addition to the paper and a prime example of accessibility. Would it be imaginable that the coupling terms are non-polynomial?
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Could you please explain how you quantify "hallucination" and what measures to take against it?
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Would the boundary between well-constructed Lagrange-densities and faulty ones as a function of the number of fields (discussed in the OOD-section) shift towards more fields if more fields are contained in the training data? In other words, is there anything peculiar about 6 fields?
Recommendation
Ask for minor revision