2022/06/08 by Aurélien Dersy, Matthew D. Schwartz, Dersy, Aurélien +3 · 2 citations
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #History and Theory of Mathematics #Machine Learning (cs.LG) #Mathematical Physics (math-ph) #Mathematics, Computing, and Information Processing #Statistics Education and Methodologies
paper · pdf · doi:10.48550/arxiv.2206.04115
openalex publication_date 2022/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.