{"title":"利用机器学习选择符号集成算法:LSTM 与树状 LSTM","authors":"Rashid Barket, Matthew England, Jürgen Gerhard","doi":"arxiv-2404.14973","DOIUrl":null,"url":null,"abstract":"Computer Algebra Systems (e.g. Maple) are used in research, education, and\nindustrial settings. One of their key functionalities is symbolic integration,\nwhere there are many sub-algorithms to choose from that can affect the form of\nthe output integral, and the runtime. Choosing the right sub-algorithm for a\ngiven problem is challenging: we hypothesise that Machine Learning can guide\nthis sub-algorithm choice. A key consideration of our methodology is how to\nrepresent the mathematics to the ML model: we hypothesise that a representation\nwhich encodes the tree structure of mathematical expressions would be well\nsuited. We trained both an LSTM and a TreeLSTM model for sub-algorithm\nprediction and compared them to Maple's existing approach. Our TreeLSTM\nperforms much better than the LSTM, highlighting the benefit of using an\ninformed representation of mathematical expressions. It is able to produce\nbetter outputs than Maple's current state-of-the-art meta-algorithm, giving a\nstrong basis for further research.","PeriodicalId":501033,"journal":{"name":"arXiv - CS - Symbolic Computation","volume":"45 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs\",\"authors\":\"Rashid Barket, Matthew England, Jürgen Gerhard\",\"doi\":\"arxiv-2404.14973\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Computer Algebra Systems (e.g. Maple) are used in research, education, and\\nindustrial settings. One of their key functionalities is symbolic integration,\\nwhere there are many sub-algorithms to choose from that can affect the form of\\nthe output integral, and the runtime. Choosing the right sub-algorithm for a\\ngiven problem is challenging: we hypothesise that Machine Learning can guide\\nthis sub-algorithm choice. A key consideration of our methodology is how to\\nrepresent the mathematics to the ML model: we hypothesise that a representation\\nwhich encodes the tree structure of mathematical expressions would be well\\nsuited. We trained both an LSTM and a TreeLSTM model for sub-algorithm\\nprediction and compared them to Maple's existing approach. Our TreeLSTM\\nperforms much better than the LSTM, highlighting the benefit of using an\\ninformed representation of mathematical expressions. It is able to produce\\nbetter outputs than Maple's current state-of-the-art meta-algorithm, giving a\\nstrong basis for further research.\",\"PeriodicalId\":501033,\"journal\":{\"name\":\"arXiv - CS - Symbolic Computation\",\"volume\":\"45 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Symbolic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2404.14973\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Symbolic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.14973","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
计算机代数系统(如 Maple)广泛应用于研究、教育和工业领域。它们的主要功能之一是符号积分,其中有许多子算法可供选择,这些算法会影响输出积分的形式和运行时间。为特定问题选择合适的子算法具有挑战性:我们假设机器学习可以指导子算法的选择。我们的方法论的一个关键考虑因素是如何向机器学习模型表示数学:我们假设,对数学表达式的树形结构进行编码的表示方法将非常适合。我们训练了一个 LSTM 模型和一个 TreeLSTM 模型来进行亚算法预测,并将它们与 Maple 的现有方法进行了比较。我们的 TreeLSTM 比 LSTM 的表现要好得多,这凸显了使用数学表达式的知情表示法的好处。它能够产生比 Maple 目前最先进的元算法更好的输出结果,为进一步的研究奠定了坚实的基础。
Symbolic Integration Algorithm Selection with Machine Learning: LSTMs vs Tree LSTMs
Computer Algebra Systems (e.g. Maple) are used in research, education, and
industrial settings. One of their key functionalities is symbolic integration,
where there are many sub-algorithms to choose from that can affect the form of
the output integral, and the runtime. Choosing the right sub-algorithm for a
given problem is challenging: we hypothesise that Machine Learning can guide
this sub-algorithm choice. A key consideration of our methodology is how to
represent the mathematics to the ML model: we hypothesise that a representation
which encodes the tree structure of mathematical expressions would be well
suited. We trained both an LSTM and a TreeLSTM model for sub-algorithm
prediction and compared them to Maple's existing approach. Our TreeLSTM
performs much better than the LSTM, highlighting the benefit of using an
informed representation of mathematical expressions. It is able to produce
better outputs than Maple's current state-of-the-art meta-algorithm, giving a
strong basis for further research.