Transformers to Predict the Applicability of Symbolic Integration Routines
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909373771546624 |
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| author | Barket, Rashid Shafiq, Uzma England, Matthew Gerhard, Juergen |
| author_facet | Barket, Rashid Shafiq, Uzma England, Matthew Gerhard, Juergen |
| contents | Symbolic integration is a fundamental problem in mathematics: we consider how machine learning may be used to optimise this task in a Computer Algebra System (CAS). We train transformers that predict whether a particular integration method will be successful, and compare against the existing human-made heuristics (called guards) that perform this task in a leading CAS. We find the transformer can outperform these guards, gaining up to 30% accuracy and 70% precision. We further show that the inference time of the transformer is inconsequential which shows that it is well-suited to include as a guard in a CAS. Furthermore, we use Layer Integrated Gradients to interpret the decisions that the transformer is making. If guided by a subject-matter expert, the technique can explain some of the predictions based on the input tokens, which can lead to further optimisations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23948 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transformers to Predict the Applicability of Symbolic Integration Routines Barket, Rashid Shafiq, Uzma England, Matthew Gerhard, Juergen Machine Learning Symbolic Computation Symbolic integration is a fundamental problem in mathematics: we consider how machine learning may be used to optimise this task in a Computer Algebra System (CAS). We train transformers that predict whether a particular integration method will be successful, and compare against the existing human-made heuristics (called guards) that perform this task in a leading CAS. We find the transformer can outperform these guards, gaining up to 30% accuracy and 70% precision. We further show that the inference time of the transformer is inconsequential which shows that it is well-suited to include as a guard in a CAS. Furthermore, we use Layer Integrated Gradients to interpret the decisions that the transformer is making. If guided by a subject-matter expert, the technique can explain some of the predictions based on the input tokens, which can lead to further optimisations. |
| title | Transformers to Predict the Applicability of Symbolic Integration Routines |
| topic | Machine Learning Symbolic Computation |
| url | https://arxiv.org/abs/2410.23948 |