The simplification and reorganization of complex expressions lies at the core of scientific progress, particularly in theoretical high-energy physics. This work explores the application of machine learning to a particular facet of this challenge: the task of simplifying scattering amplitudes expressed in terms of spinor-helicity variables. We demonstrate that an encoder-decoder transformer architecture achieves impressive simplification capabilities for expressions composed of handfuls of terms. Lengthier expressions are implemented in an additional embedding network, trained using contrastive learning, which isolates subexpressions that are more likely to simplify. The resulting framework is capable of reducing expressions with hundreds of terms - a regular occurrence in quantum field theory calculations - to vastly simpler equivalent expressions. Starting from lengthy input expressions, our networks can generate the Parke-Taylor formula for five-point gluon scattering, as well as new compact expressions for five-point amplitudes involving scalars and gravitons. An interactive demonstration can be found at https://spinorhelicity.streamlit.app .
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
Author comments upon resubmission
We thank the referees for their thorough review and insightful comments. We answered their comments or questions in the author replies and have adapted the manuscript to reflect their recommendations.
List of changes
- Modifications to the introduction: after Eq 1.3 ("and, to our ... expressions analytically")", on the top of p.3 ("In the field of ... purely symbolic"), near the end of the first paragraph on p.3 ("For those problems... model hallucinations") - Modifying footnote 1 - In the last paragraph before 2.2 adding "together with information from singular kinematic limits" - First paragraph of 2.2, adding "Following the ... backward generation." - Fixed typos in 2.8/2.9/2.10 - Added a paragraph before 2.4 "One could be ... training set." - Added references 49/50 in 2.4 - In second paragraph of 3.1 added "To reach 1500 ... amplitudes respectively" and "We ask for .... during training" - Modified footnote 4 - Minimal updates to Table 2 and Fig 2,3,5,6,10,13 to account for a small correction to the 6-pt training data (6-pt simplifier model is retrained and evaluated) - Moved the last paragraph of 4.1 upwards to the second paragraph of 4.1 "including in high-energy physics ... reconstruction tasks." - Fourth paragraph of 4.2 adding "lasting around 2h" - Adding standard deviations in Fig.8 and updating caption - Last paragraph before 4.3 adding "We note that ... We comment on this point further in" - Correcting typo below 4.6 "c(t) decreases" - Modifying footnote 14 - Minimal updates to Fig.9,14,15 after correcting a small bug in the contrastive model (no qualitative changes noticed) - In the conclusion adding "Crucially, ... numerical evaluations" and "or with factors .... systematically avoided". - Updating the legend and caption in Fig 12 - Adding a paragraph in Appendix F "For instance, taking ... less than 3 identities"
