mlsanityData to 14 Oct 2026

Premise Selection for Theorem Proving by Deep Graph Embedding

arXiv 1709.09994 ↗First posted 28 Sep 2017cs.AI cs.LG cs.LOcited by 44

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Abstract (arXiv)

We propose a deep learning-based approach to the problem of premise selection: selecting mathematical statements relevant for proving a given conjecture. We represent a higher-order logic formula as a graph that is invariant to variable renaming but still fully preserves syntactic and semantic information. We then embed the graph into a vector via a novel embedding method that preserves the information of edge ordering. Our approach achieves state-of-the-art results on the HolStep dataset, improving the classification accuracy from 83% to 90.3%.

Key facts. Cited by 44 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Sep 2017.

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Citing papers per year: 2021: 9; 2022: 6; 2023: 5; 2024: 12; 2025: 8; 2026: 4.

44 papers.

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  1. 2022Formal Mathematics Statement Curriculum Learningcited by 142
  2. 2022Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Proverscited by 98
  3. 2024Premise Order Matters in Reasoning with Large Language Modelscited by 72
  4. 2024Lean Copilot: Large Language Models as Copilots for Theorem Proving in Leancited by 58
  5. 2024A Survey on Deep Learning for Theorem Provingcited by 57
  6. 2023Magnushammer: A Transformer-Based Approach to Premise Selectioncited by 50
  7. 2021LIME: Learning Inductive Bias for Primitives of Mathematical Reasoningcited by 46
  8. 2021TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learningcited by 37
  9. 2025Solving Formal Math Problems by Decomposition and Iterative Reflectioncited by 35
  10. 2021Learning to Guide a Saturation-Based Theorem Provercited by 15
  11. 2021Embedding Symbolic Temporal Knowledge into Deep Sequential Modelscited by 11
  12. 2024Learn from Failure: Fine-Tuning LLMs with Trial-and-Error Data for Intuitionistic Propositional Logic Provingcited by 11
32 more
  1. 2025ProofAug: Efficient Neural Theorem Proving via Fine-grained Proof Structure Analysiscited by 11
  2. 2021Vampire With a Brain Is a Good ITP Hammercited by 10
  3. 2025MPS-Prover: Advancing Stepwise Theorem Proving by Multi-Perspective Search and Data Curationcited by 10
  4. 2022A Survey in Mathematical Language Processingcited by 9
  5. 2021SyGNS: A Systematic Generalization Testbed Based on Natural Language Semanticscited by 7
  6. 2024Learning Guided Automated Reasoning: A Brief Surveycited by 7
  7. 2024ATG: Benchmarking Automated Theorem Generation for Generative Language Modelscited by 6
  8. 2023CoProver: A Recommender System for Proof Constructioncited by 5
  9. 2025Neural Theorem Proving: Generating and Structuring Proofs for Formal Verificationcited by 5
  10. 2021A Study of Continuous Vector Representationsfor Theorem Provingcited by 4
  11. 2023An Ensemble Approach for Automated Theorem Proving Based on Efficient Name Invariant Graph Neural Representationscited by 4
  12. 2021Graph Contrastive Pre-training for Effective Theorem Reasoningcited by 3
  13. 2023Lemmas: Generation, Selection, Applicationcited by 3
  14. 2024Exploring the Limits of Fine-grained LLM-based Physics Inference via Premise Removal Interventionscited by 3
  15. 2026COMPOSE: Composing Future Theorems from Citations and Formal Structurecited by 3
  16. 2024Learning Structure-Aware Representations of Dependent Typescited by 2
  17. 2024BAIT: Benchmarking (Embedding) Architectures for Interactive Theorem-Provingcited by 2
  18. 2022Exploring Representation of Horn Clauses using GNNs (Extended Technical Report)cited by 1
  19. 2022Learning to Prove Trigonometric Identitiescited by 1
  20. 2022Neural Controller Synthesis for Signal Temporal Logic Specifications Using Encoder-Decoder Structured Networkscited by 1
  21. 2024Learning Better Representations From Less Data For Propositional Satisfiabilitycited by 1
  22. 2024Guiding Word Equation Solving using Graph Neural Networks (Extended Technical Report)cited by 1
  23. 2025Hierarchical Attention Generates Better Proofscited by 1
  24. 2025Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspectivecited by 1
  25. 2026MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Researchcited by 1
  26. 2021Learning Heuristics for Template-based CEGIS of Loop Invariants with Reinforcement Learningcited by 0
  27. 2023Safety without alignmentcited by 0
  28. 2024EvoGPT-f: An Evolutionary GPT Framework for Benchmarking Formal Math Languagescited by 0
  29. 2025When GNNs Met a Word Equations Solver: Learning to Rank Equations (Extended Technical Report)cited by 0
  30. 2025Partial Label Learning for Automated Theorem Provingcited by 0
  31. 2026Automated Proving of Shannon-Type Entropy Inequalities via Fine-Tuned Language Models and Guided Tree Searchcited by 0
  32. 2026When Does Structured Knowledge Help Neural Theorem Proving?cited by 0