{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-to-discover-efficient-mathematical","title":"Learning to Discover Efficient Mathematical Identities","arxiv_id":"1406.1584","date":"2014-06-06","proceeding":"NeurIPS 2014 12","authors":["Wojciech Zaremba","Karol Kurach","Rob Fergus"],"abstract":"In this paper we explore how machine learning techniques can be applied to\nthe discovery of efficient mathematical identities. We introduce an attribute\ngrammar framework for representing symbolic expressions. Given a set of grammar\nrules we build trees that combine different rules, looking for branches which\nyield compositions that are analytically equivalent to a target expression, but\nof lower computational complexity. However, as the size of the trees grows\nexponentially with the complexity of the target expression, brute force search\nis impractical for all but the simplest of expressions. Consequently, we\nintroduce two novel learning approaches that are able to learn from simpler\nexpressions to guide the tree search. The first of these is a simple n-gram\nmodel, the other being a recursive neural-network. We show how these approaches\nenable us to derive complex identities, beyond reach of brute-force search, or\nhuman derivation.","url_abs":"http://arxiv.org/abs/1406.1584v3","url_pdf":"http://arxiv.org/pdf/1406.1584v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-to-discover-efficient-mathematical","repo_url":"https://github.com/kkurach/math_learning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"attribute","task_name":"Attribute"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1406.1584","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}