# MLFMF: Data Sets for Machine Learning for Mathematical Formalization

arXiv: https://arxiv.org/abs/2310.16005 · HTML: https://mlsanity.com/paper/2310.16005/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2023.

## Built on by (most cited first, 10 of 10)

- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [Process-Driven Autoformalization in Lean 4](https://mlsanity.com/paper/2406.01940/) (2024)
- [FormalAlign: Automated Alignment Evaluation for Autoformalization](https://mlsanity.com/paper/2410.10135/) (2024)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)
- [TheoremGraph: Bridging Formal and Informal Mathematics](https://mlsanity.com/paper/2606.25363/) (2026)
- [Artificial Intelligence and the Structure of Mathematics](https://mlsanity.com/paper/2604.06107/) (2026)
- [Approximating the universal thermal climate index using sparse regression with orthogonal polynomials](https://mlsanity.com/paper/2508.11307/) (2025)
- [Hierarchical Attention Generates Better Proofs](https://mlsanity.com/paper/2504.19188/) (2025)
- [Benchmarking Foundation Models with Retrieval-Augmented Generation in Olympic-Level Physics Problem Solving](https://mlsanity.com/paper/2510.00919/) (2025)
- [Combining Textual and Structural Information for Premise Selection in Lean](https://mlsanity.com/paper/2510.23637/) (2025)

## Abstract (arXiv)

We 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 a new 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. Each 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 250,000 entries in total, this is currently the largest collection of formalized mathematical knowledge in machine learnable format.