# Simplifying Polylogarithms with Machine Learning

arXiv: https://arxiv.org/abs/2206.04115 · HTML: https://mlsanity.com/paper/2206.04115/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 75 references that are in the map.
- First posted on arXiv 8 Jun 2022.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Distributed Representations of Sentences and Documents](https://mlsanity.com/paper/1405.4053/) (2014)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [Q-Prop: Sample-Efficient Policy Gradient with An Off-Policy Critic](https://mlsanity.com/paper/1611.02247/) (2016)
- [Reinforcement Learning of Theorem Proving](https://mlsanity.com/paper/1805.07563/) (2018)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Training Larger Networks for Deep Reinforcement Learning](https://mlsanity.com/paper/2102.07920/) (2021)
- [TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning](https://mlsanity.com/paper/2102.09756/) (2021)
- [Machine-learning hidden symmetries](https://mlsanity.com/paper/2109.09721/) (2021)
- [Towards Effective Context for Meta-Reinforcement Learning: an Approach based on Contrastive Learning](https://mlsanity.com/paper/2009.13891/) (2020)

## Built on by (most cited first, 15 of 15)

- [Length Generalization in Arithmetic Transformers](https://mlsanity.com/paper/2306.15400/) (2023)
- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [What is my math transformer doing? -- Three results on interpretability and generalization](https://mlsanity.com/paper/2211.00170/) (2022)
- [Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory](https://mlsanity.com/paper/2405.06107/) (2024)
- [Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression](https://mlsanity.com/paper/2211.08420/) (2022)
- [Can Transformers Do Enumerative Geometry?](https://mlsanity.com/paper/2408.14915/) (2024)
- [Learning the Simplicity of Scattering Amplitudes](https://mlsanity.com/paper/2408.04720/) (2024)
- [Oracle-Preserving Latent Flows](https://mlsanity.com/paper/2302.00806/) (2023)
- [A Perspective on Symbolic Machine Learning in Physical Sciences](https://mlsanity.com/paper/2502.17993/) (2025)
- [Seeking Truth and Beauty in Flavor Physics with Machine Learning](https://mlsanity.com/paper/2311.00087/) (2023)
- [Generating particle physics Lagrangians with transformers](https://mlsanity.com/paper/2501.09729/) (2025)
- [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)
- [Graph Neural Networks for the Graphical Bootstrap](https://mlsanity.com/paper/2607.03109/) (2026)

## Abstract (arXiv)

Polylogrithmic functions, such as the logarithm or dilogarithm, satisfy a number of algebraic identities. For the logarithm, all the identities follow from the product rule. For the dilogarithm and higher-weight classical polylogarithms, the identities can involve five functions or more. In many calculations relevant to particle physics, complicated combinations of polylogarithms often arise from Feynman integrals. Although the initial expressions resulting from the integration usually simplify, it is often difficult to know which identities to apply and in what order. To address this bottleneck, we explore to what extent machine learning methods can help. We consider both a reinforcement learning approach, where the identities are analogous to moves in a game, and a transformer network approach, where the problem is viewed analogously to a language-translation task. While both methods are effective, the transformer network appears more powerful and holds promise for practical use in symbolic manipulation tasks in mathematical physics.