# Machine Learning meets Algebraic Combinatorics: A Suite of Datasets Capturing Research-level Conjecturing Ability in Pure Mathematics

arXiv: https://arxiv.org/abs/2503.06366 · HTML: https://mlsanity.com/paper/2503.06366/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 9 Mar 2025.

## Builds on (most cited first, 22 of 22)

- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [Teaching Arithmetic to Small Transformers](https://mlsanity.com/paper/2307.03381/) (2023)
- [The CLRS Algorithmic Reasoning Benchmark](https://mlsanity.com/paper/2205.15659/) (2022)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Why are Sensitive Functions Hard for Transformers?](https://mlsanity.com/paper/2402.09963/) (2024)
- [On the Symmetries of Deep Learning Models and their Internal Representations](https://mlsanity.com/paper/2205.14258/) (2022)
- [Constructions in combinatorics via neural networks](https://mlsanity.com/paper/2104.14516/) (2021)
- [Seeing is Believing: Brain-Inspired Modular Training for Mechanistic Interpretability](https://mlsanity.com/paper/2305.08746/) (2023)
- [PatternBoost: Constructions in Mathematics with a Little Help from AI](https://mlsanity.com/paper/2411.00566/) (2024)
- [Quiver Mutations, Seiberg Duality and Machine Learning](https://mlsanity.com/paper/2006.10783/) (2020)
- [Machine learning detects terminal singularities](https://mlsanity.com/paper/2310.20458/) (2023)
- [Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Search](https://mlsanity.com/paper/2311.03583/) (2023)
- [Machine Learning Clifford invariants of ADE Coxeter elements](https://mlsanity.com/paper/2310.00041/) (2023)
- [Machine Learning Algebraic Geometry for Physics](https://mlsanity.com/paper/2204.10334/) (2022)
- [Machines and Mathematical Mutations: Using GNNs to Characterize Quiver Mutation Classes](https://mlsanity.com/paper/2411.07467/) (2024)

## Built on by (most cited first, 5 of 5)

- [A Human-AI Collaborative Workflow for Mathematical Discovery: A Case Study in Grover-Compatible Riemannian Optimization](https://mlsanity.com/paper/2512.09443/) (2025)
- [Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems](https://mlsanity.com/paper/2505.23881/) (2025)
- [Numbers Already Carry Their Own Embeddings](https://mlsanity.com/paper/2606.14108/) (2026)
- [PermuFormer: Multi-Task Pretraining for Permutation Representation in Algebraic Combinatorics](https://mlsanity.com/paper/2609.25438/) (2026)
- [CrowdMath: A Dataset of Crowdsourced Mathematical Research Discussions](https://mlsanity.com/paper/2606.06526/) (2026)

## Abstract (arXiv)

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.