mlsanityData to 7 Oct 2026

PatternBoost: Constructions in Mathematics with a Little Help from AI

arXiv 2411.00566 ↗First posted 1 Nov 2024math.CO cs.LGcited by 32

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Abstract (arXiv)

We introduce PatternBoost, a flexible method for finding interesting constructions in mathematics. Our algorithm alternates between two phases. In the first ``local'' phase, a classical search algorithm is used to produce many desirable constructions. In the second ``global'' phase, a transformer neural network is trained on the best such constructions. Samples from the trained transformer are then used as seeds for the first phase, and the process is repeated. We give a detailed introduction to this technique, and discuss the results of its application to several problems in extremal combinatorics. The performance of PatternBoost varies across different problems, but there are many situations where its performance is quite impressive. Using our technique, we find the best known solutions to several long-standing problems, including the construction of a counterexample to a conjecture that had remained open for 30 years.

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). Builds on 11 of its 43 references that are in the map. First posted on arXiv 1 Nov 2024.

Builds on

11 of 43 references.

References · 11

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Language Models are Few-Shot Learnerscited by 32,199
  3. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 13,958
  4. 2018Neural Ordinary Differential Equationscited by 3,733
  5. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  6. 2019Deep Learning for Symbolic Mathematicscited by 266
  7. 2021Investigating the Limitations of Transformers with Simple Arithmetic Taskscited by 136
  8. 2021Constructions in combinatorics via neural networkscited by 46
  9. 2024Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformerscited by 29
  10. 2023Finding Increasingly Large Extremal Graphs with AlphaZero and Tabu Searchcited by 8
  11. 2019Convergence rates for ordinal embeddingcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 14; 2026: 15.

32 papers.

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  2. 2025ThetaEvolve: Test-time Learning on Open Problemscited by 52
  3. 2025Self-Improving Transformers Overcome Easy-to-Hard and Length Generalization Challengescited by 30
  4. 2024Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learningcited by 11
  5. 2025Generative Modeling for Mathematical Discoverycited by 9
  6. 2026Reinforced Generation of Combinatorial Structures: Ramsey Numberscited by 8
  7. 2026LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematicscited by 7
  8. 2026Autonomous Research Agents: A Survey of AI Scientists and the Verification Gapcited by 6
  9. 2025CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphscited by 5
  10. 2025Machine Learning meets Algebraic Combinatorics: A Suite of Datasets Capturing Research-level Conjecturing Ability in Pure Mathematicscited by 5
  11. 2025Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformerscited by 5
  12. 2025Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?cited by 4
20 more
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  4. 2026Flow-based Extremal Mathematical Structure Discoverycited by 3
  5. 2024A Note on Small Percolating Sets on Hypercubes via Generative AIcited by 2
  6. 2025From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithmcited by 2
  7. 2026Can Neural Networks Learn Small Algebraic Worlds? An Investigation Into the Group-theoretic Structures Learned By Narrow Models Trained To Predict Group Operationscited by 2
  8. 2025Int2Int: a framework for mathematics with transformerscited by 1
  9. 2025CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)cited by 1
  10. 2025An AI enhanced approach to the tree unimodality conjecturecited by 1
  11. 2026Improved Upper Bounds for Slicing the Hypercubecited by 1
  12. 2026LLM Framework for Discovering Major Mathematical Conjectures: AI's Quest for the Next Riemann Hypothesiscited by 1
  13. 2025Reinforcement learning for graph theory, Parallelizing Wagner's approachcited by 0
  14. 2026Reconstructing conformal field theoretical compositions with Transformerscited by 0
  15. 2026Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Toolscited by 0
  16. 2026Genetic Algorithms with Optimization Guided Operatorscited by 0
  17. 2026Stable Menus of Public Goods: AI-Enabled Progresscited by 0
  18. 2026Geometry-Aware MCTS for Extremal Problems in Combinatorial Geometrycited by 0
  19. 2026Generating Special Triangulations with Transformerscited by 0
  20. 2026Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codescited by 0