SciPost Submission Page
Lorentz-Equivariance without Limitations
by Luigi Favaro, Gerrit Gerhartz, Fred A. Hamprecht, Peter Lippmann, Sebastian Pitz, Tilman Plehn, Huilin Qu, Jonas Spinner
Submission summary
| Authors (as registered SciPost users): | Luigi Favaro · Tilman Plehn · Jonas Spinner |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2508.14898v2 (pdf) |
| Code repository: | https://github.com/heidelberg-hepml/lloca |
| Data repository: | https://github.com/heidelberg-hepml/lloca-experiments |
| Date submitted: | Nov. 11, 2025, 8:53 p.m. |
| Submitted by: | Luigi Favaro |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Computational |
Disclosure of Generative AI use
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
The usage of large language models is limited to formatting and writing improvements.
Abstract
Lorentz Local Canonicalization (LLoCa) ensures exact Lorentz-equivariance for arbitrary neural networks with minimal computational overhead. For the LHC, it equivariantly predicts local reference frames for each particle and propagates any-order tensorial information between them. We apply it to graph networks and transformers. We showcase its cutting-edge performance on amplitude regression, end-to-end event generation, and jet tagging. For jet tagging, we introduce a large top tagging dataset to benchmark LLoCa versions of a range of established benchmark architectures and highlight the importance of symmetry breaking.
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:
In refereeing
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2026-1-25 (Invited Report)
Disclosure of Generative AI use
The referee discloses that the following generative AI tools have been used in the preparation of this report:
LLM was used to improve English/grammar
Strengths
- The paper introduces a novel approach to Lorentz equivariance that works as a "wrapper" around arbitrary neural network architectures, rather than requiring specialized equivariant layers. I find this a significant advance.
- Comprehensive experimental validation across three important LHC tasks. This demonstrates the relevance of this approach in a broad range of applications.
- The ~4x speedup over L-GATr for similar performance is very interesting.
- I find very valuable the symmetry breaking analysis in Section 2.5.
- The code and data availability as well as the clear documentation seem sufficient for reproducibility of the results.
Weaknesses
- The numerical stability requires tuning specific to each application. For instance the \gamma < 3 clipping for event generation and various regularization parameters discuss in Appendix A suggest the method isn't fully plug-and-play. How strongly the performance depends on those parameters ?
- Eq. (21): Frames-Net seems to be central for the algorithm. Yet I think more discussion could be useful. e.g., it basically learns a weighted average of pairwise sums. Is this expressive enough? What if the optimal frame depends on higher order correlations between particles?
- Appendix C shows the simple MLP Frames-Net performs better than PELICAN and L-GATr variants for jet tagging. I find this interesting and I believe it should be promoted to the main body of the paper.
- Training time is nice to know, but what I would find more important/useful is the inference time/latency. Please include it.
- The results in the jet tagging task depend strongly on input features and training strategy. It is not clear in the paper which are the differences between the new work detailed in the paper and the existing algorithms.
- The TopTagXL dataset is a very welcome contribution to the community. However, it would be significantly more useful if the jets were generated including pileup (especially in view of the HL-LHC era).
Report
The paper presents LLoCa, a method to make arbitrary neural networks Lorentz-equivariant by learning local reference frames for each particle and transforming features between frames during message passing. The approach is tested on three important tasks at the LHC: amplitude regression, event generation, and jet tagging.
The work is solid and the scope is very comprehensive: amplitude regression, conditional-flow event generation, and jet tagging are all studied with consistent design logic. In amplitude regression, the LLoCa-Transformer reaches accuracy comparable to (or better than) specialized Lorentz-equivariant transformers while keeping the backbone standard and significantly reducing compute compared to L-GATr in the reported setup. In jet tagging, LLoCa variants are competitive with established state-of-the-art methods on multiple benchmarks, and the paper provides a useful set of ablation studies on residual symmetries and internal representations.
However, in several comparisons, the performance differences between methods are very small and uncertainty estimates are sometimes missing. This makes it difficult to assess whether the observed improvements are statistically significant.
Overall, I consider the paper strong with results important for the community, with clear originality in providing a portable Lorentz-equivariant upgrade mechanism that enables controlled symmetry breaking and fair comparisons to non-equivariant approaches. I would recommend publication after the authors address my points below.
The work is solid and the scope is very comprehensive: amplitude regression, conditional-flow event generation, and jet tagging are all studied with consistent design logic. In amplitude regression, the LLoCa-Transformer reaches accuracy comparable to (or better than) specialized Lorentz-equivariant transformers while keeping the backbone standard and significantly reducing compute compared to L-GATr in the reported setup. In jet tagging, LLoCa variants are competitive with established state-of-the-art methods on multiple benchmarks, and the paper provides a useful set of ablation studies on residual symmetries and internal representations.
However, in several comparisons, the performance differences between methods are very small and uncertainty estimates are sometimes missing. This makes it difficult to assess whether the observed improvements are statistically significant.
Overall, I consider the paper strong with results important for the community, with clear originality in providing a portable Lorentz-equivariant upgrade mechanism that enables controlled symmetry breaking and fair comparisons to non-equivariant approaches. I would recommend publication after the authors address my points below.
Requested changes
- Quantify how often the gamma < 3 clip activates in event generation and estimate the resulting equivariance violation.
- Add a table showing the distribution of boost factors in the predicted frames across different applications.
- Move the Frames-Net architecture comparison from Appendix C to the main text.
- Report latency (ms/event or events/second) for the jet tagging models.
- Acknowledge in Section 2 that the regularizations introduce small equivariance violations and estimate their magnitude.
- Add error estimates to the background rejection rates in Table 10
- Extend the discussion around Eq (21). e..g, Can you construct frames that depend on 3-body or higher correlations, or is it limited to pairwise information?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)