# Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory

arXiv: https://arxiv.org/abs/2405.06107 · HTML: https://mlsanity.com/paper/2405.06107/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 61 references that are in the map.
- First posted on arXiv 9 May 2024.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Conformer: Convolution-augmented Transformer for Speech Recognition](https://mlsanity.com/paper/2005.08100/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Investigating the Limitations of Transformers with Simple Arithmetic Tasks](https://mlsanity.com/paper/2102.13019/) (2021)
- [A Length-Extrapolatable Transformer](https://mlsanity.com/paper/2212.10554/) (2022)
- [Teaching Arithmetic to Small Transformers](https://mlsanity.com/paper/2307.03381/) (2023)
- [Linear algebra with transformers](https://mlsanity.com/paper/2112.01898/) (2021)
- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [Learning the greatest common divisor: explaining transformer predictions](https://mlsanity.com/paper/2308.15594/) (2023)
- [SALSA: Attacking Lattice Cryptography with Transformers](https://mlsanity.com/paper/2207.04785/) (2022)
- [Simplifying Polylogarithms with Machine Learning](https://mlsanity.com/paper/2206.04115/) (2022)
- [SYMBA: Symbolic Computation of Squared Amplitudes in High Energy Physics with Machine Learning](https://mlsanity.com/paper/2206.08901/) (2022)

## Built on by (most cited first, 18 of 18)

- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [Large Physics Models: Towards a collaborative approach with Large Language Models and Foundation Models](https://mlsanity.com/paper/2501.05382/) (2025)
- [Meta-Designing Quantum Experiments with Language Models](https://mlsanity.com/paper/2406.02470/) (2024)
- [Can Transformers Do Enumerative Geometry?](https://mlsanity.com/paper/2408.14915/) (2024)
- [Transformer Normalisation Layers and the Independence of Semantic Subspaces](https://mlsanity.com/paper/2406.17837/) (2024)
- [Learning the Simplicity of Scattering Amplitudes](https://mlsanity.com/paper/2408.04720/) (2024)
- [Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning](https://mlsanity.com/paper/2502.05121/) (2025)
- [Machine-learning emergent spacetime from linear response in future tabletop quantum gravity experiments](https://mlsanity.com/paper/2411.16052/) (2024)
- [Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers](https://mlsanity.com/paper/2507.03732/) (2025)
- [Generating particle physics Lagrangians with transformers](https://mlsanity.com/paper/2501.09729/) (2025)
- [Can AI Follow In Einstein's Footsteps?](https://mlsanity.com/paper/2607.27794/) (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)
- [Learning First Integrals via Backward-Generated Data and Guided Reinforcement Learning](https://mlsanity.com/paper/2605.21160/) (2026)
- [Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding](https://mlsanity.com/paper/2606.10698/) (2026)
- [Generating Special Triangulations with Transformers](https://mlsanity.com/paper/2606.26660/) (2026)
- [Graph Neural Networks for the Graphical Bootstrap](https://mlsanity.com/paper/2607.03109/) (2026)

## Abstract (arXiv)

We pursue the use of deep learning methods to improve state-of-the-art computations in theoretical high-energy physics. Planar N = 4 Super Yang-Mills theory is a close cousin to the theory that describes Higgs boson production at the Large Hadron Collider; its scattering amplitudes are large mathematical expressions containing integer coefficients. In this paper, we apply Transformers to predict these coefficients. The problem can be formulated in a language-like representation amenable to standard cross-entropy training objectives. We design two related experiments and show that the model achieves high accuracy (> 98%) on both tasks. Our work shows that Transformers can be applied successfully to problems in theoretical physics that require exact solutions.