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Simplifying Polylogarithms with Machine Learning
Aurelien Dersy · Matthew Schwartz · Xiaoyuan Zhang

In particle physics calculations are centered around Feynman integrals, which are commonly expressed using polylogarithmic functions such as the logarithm or the dilogarithm. Although the resulting expressions usually simplify with an astute application of polylogarithmic identities, it is often difficult to know which identities to apply and in what order. We explore the extent to which machine learning methods are able to help with this creative step. We implement two simplification strategies, one based on an intuitive application of reinforcement learning and one showcasing the potential of language models such as transformers. We demonstrate that the transformer approach is more flexible and holds promise for practical use in symbolic manipulation tasks relevant to mathematical physics.

Author Information

Aurelien Dersy (Harvard University)
Matthew Schwartz (Harvard University)
Xiaoyuan Zhang (Harvard University)

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