# Learning the Simplicity of Scattering Amplitudes

arXiv: https://arxiv.org/abs/2408.04720 · HTML: https://mlsanity.com/paper/2408.04720/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 8 Aug 2024.

## Builds on (most cited first, 18 of 18)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [Investigating the Limitations of Transformers with Simple Arithmetic Tasks](https://mlsanity.com/paper/2102.13019/) (2021)
- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning](https://mlsanity.com/paper/2102.09756/) (2021)
- [Point Cloud Transformers applied to Collider Physics](https://mlsanity.com/paper/2102.05073/) (2021)
- [Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory](https://mlsanity.com/paper/2405.06107/) (2024)
- [Simplifying Polylogarithms with Machine Learning](https://mlsanity.com/paper/2206.04115/) (2022)
- [PASCL: Supervised Contrastive Learning with Perturbative Augmentation for Particle Decay Reconstruction](https://mlsanity.com/paper/2402.11538/) (2024)

## Built on by (most cited first, 6 of 6)

- [Generating particle physics Lagrangians with transformers](https://mlsanity.com/paper/2501.09729/) (2025)
- [Unraveling particle dark matter with Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.17597/) (2025)
- [Learning the S-matrix from data: Rediscovering gravity from gauge theory via symbolic regression](https://mlsanity.com/paper/2602.15169/) (2026)
- [Machine learning modularity](https://mlsanity.com/paper/2601.01779/) (2026)
- [Reconstructing conformal field theoretical compositions with Transformers](https://mlsanity.com/paper/2605.01072/) (2026)
- [Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding](https://mlsanity.com/paper/2606.10698/) (2026)

## Abstract (arXiv)

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 .