[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125729-en":3,"doc-seo-125729-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125729,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","MLFMF - Data Sets for Machine Learning for Mathematical Formalization","MLFMF introduces a collection of datasets for benchmarking recommendation systems that support mathematical formalization with proof assistants. The datasets target premise selection by identifying relevant prior entries—such as theorems, constructions, datatypes, and postulates—needed to prove a new theorem or build a new construction. Each dataset is derived from formalized mathematics libraries in Agda or Lean, including Mathlib for Lean 4 and major Agda libraries like the standard library, Agda-unimath, and TypeTopology.","MLFMF: Data Sets for Machine Learning for Mathematical Formalization  \narXiv :2310 . 16005v1 [ cs .LG] 24 Oct 2023  \nAndrej Bauer  \nFaculty of Mathematics and Physics University of Ljubljana  \nInstitute for Mathematics, Physics and Mechanics Ljubljana, Slovenia [andrej.bauer@fmf.uni-lj.si](andrej.bauer@fmf.uni-lj.si)  \nMatej Petkovi  \nFaculty of Mathematics and Physics University of Ljubljana Department of Knowledge Technologies Jožef Stefan Institute Ljubljana, Slovenia [matej.petkovic@fmf.uni-lj.si](matej.petkovic@fmf.uni-lj.si)  \nLjupo Todorovski  \nFaculty of Mathematics and Physics  \nUniversity of Ljubljana  \nDepartment of Knowledge Technologies  \nJožef Stefan Institute  \nLjubljana, Slovenia  \n[ljupco.todorovski@fmf.uni-lj.si](ljupco.todorovski@fmf.uni-lj.si)  \nAbstract  \nWe introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions, datatypes, and postulates) are relevant in proving a new theorem or carrying out anew construction. Each data set is derived from a library of formalized mathematics written in proof assistants Agda or Lean. The collection includes the largest Lean 4 library Mathlib, and some of the largest Agda libraries: the standard library, the library of univalent mathematics Agda-unimath, and the TypeTopology library.  \nEach data set represents the corresponding library in two ways: as a heterogeneous network, and as a list of s-expressions representing the syntax trees of all the entries in the library. The network contains the (modular) structure of the library and the references between entries, while the s-expressions give complete and easily parsed information about every entry. We report baseline results using standard graph and word embeddings, tree ensembles, and instance-based learning algorithms. The MLFMF data sets provide solid benchmarking support for further investigation of the numerous machine learning approaches to formalized mathematics. The methodology used to extract the networks and the s-expressions readily applies to other libraries, and is applicable to other proof assistants. With more than 250000 entries in total, this is currently the largest collection of formalized mathematical knowledge in machine learnable format.  \n1 Introduction  \nApplications of artificial intelligence to automation of mathematics have a long history, starting from early approaches based on a collection of hand-crafted heuristics for formalizing new mathematical concepts and conjectures related to them [Lenat, 1977] . In the last decade, there has been a growing interest in formalization of mathematics with proof assistants, which verify the formal correctness of  \n37th Conference on Neural Information Processing Systems (NeurIPS 2023) .  \nmathematical proofs and constructions, and help automate the tedious parts. The trend is correlated with the interest of machine learning community in aiding formalization efforts with its expertise. Machine learning methods are often used to address premise selection, i.e., recommendation of theorems that are useful for proving a given statement. DeepMath [Irving et al., 2016] proposes using convolutional and recurrent neural networks to predict the relevance of a premise for proving the given statement. While many other approaches [Polu and Sutskever, 2020, Welleck et al., 2022] use transformers and general language models, Paliwal et al. [2020] have shown that taking into account the higher-order structure of logical expressions used in formalizing mathematics can greatly improve the performance of premise selection and automated proving. Indeed, many approaches use graph neural networks to learn from the higher-order structures, e.g.,[Wang et al., 2017] . More recently, graph neural networks have also been proven useful for explorative, unsupervised approaches to automated theorem proving with","cbCaisfiowz4Bvdo","https://ap.wps.com/l/cbCaisfiowz4Bvdo","pdf",459894,1,19,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"What problem do MLFMF datasets address in mathematical formalization?\",\"answer\":\"They benchmark recommendation systems for premise selection, helping find which previous formal entries are relevant for proving a new theorem or constructing new objects.\"},{\"question\":\"How are the datasets derived and which proof assistants are used?\",\"answer\":\"Each dataset is extracted from formalized mathematics libraries written in Agda or Lean, including the Lean 4 Mathlib library and several large Agda libraries.\"},{\"question\":\"In what two representations are the libraries provided?\",\"answer\":\"As heterogeneous networks capturing the modular structure and references between entries, and as lists of s-expressions that encode syntax trees for each entry.\"}]","MLFMF - 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