mlsanityData to 7 Oct 2026

End-to-End Differentiable Proving

arXiv 1705.11040 ↗First posted 31 May 2017cs.NE cs.AI cs.LGcited by 159

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Cited by 36 in LLM reasoning, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules.

Key facts. Cited by 159 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 May 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 34; 2022: 37; 2023: 32; 2024: 15; 2025: 22; 2026: 19.

159 papers.

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  1. 2022Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thoughtcited by 334
  2. 2021Proof Artifact Co-training for Theorem Proving with Language Modelscited by 130
  3. 2022A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multimodalcited by 106
  4. 2023NeurASP: Embracing Neural Networks into Answer Set Programmingcited by 92
  5. 2023Large Language Models can Learn Rulescited by 66
  6. 2021DeepStochLog: Neural Stochastic Logic Programmingcited by 58
  7. 2021Inductive logic programming at 30cited by 46
  8. 2021Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use casescited by 39
  9. 2021A Survey on Neural-symbolic Learning Systemscited by 39
  10. 2021Systematic Generalization with Edge Transformerscited by 38
  11. 2021TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learningcited by 37
  12. 2021Neuro-Symbolic Inductive Logic Programming with Logical Neural Networkscited by 36
38 more
  1. 2024Learning Iterative Reasoning through Energy Diffusioncited by 36
  2. 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
  3. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 34
  4. 2022FaiRR: Faithful and Robust Deductive Reasoning over Natural Languagecited by 29
  5. 2023Logic-induced Diagnostic Reasoning for Semi-supervised Semantic Segmentationcited by 29
  6. 2022HAKE: A Knowledge Engine Foundation for Human Activity Understandingcited by 28
  7. 2021Learning Algebraic Representation for Systematic Generalization in Abstract Reasoningcited by 27
  8. 2021Differentiable Inductive Logic Programming for Structured Examplescited by 26
  9. 2021Neural Multi-Hop Reasoning With Logical Rules on Biomedical Knowledge Graphscited by 25
  10. 2023Neural-Logic Human-Object Interaction Detectioncited by 25
  11. 2023Neural Probabilistic Logic Programming in Discrete-Continuous Domainscited by 24
  12. 2021Neuro-Symbolic Hierarchical Rule Inductioncited by 23
  13. 2022RobustLR: Evaluating Robustness to Logical Perturbation in Deductive Reasoningcited by 22
  14. 2023Dual Algorithmic Reasoningcited by 21
  15. 2023Complex Query Answering on Eventuality Knowledge Graph with Implicit Logical Constraintscited by 21
  16. 2024TILP: Differentiable Learning of Temporal Logical Rules on Knowledge Graphscited by 21
  17. 2022Deep Symbolic Learning: Discovering Symbols and Rules from Perceptionscited by 20
  18. 2023Neural Compositional Rule Learning for Knowledge Graph Reasoningcited by 20
  19. 2022Knowledge Graph Reasoning with Logics and Embeddings: Survey and Perspectivecited by 18
  20. 2023Improved Logical Reasoning of Language Models via Differentiable Symbolic Programmingcited by 18
  21. 2022Logical Reasoning with Span-Level Predictions for Interpretable and Robust NLI Modelscited by 17
  22. 2023Learning by Self-Explainingcited by 17
  23. 2023LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoningcited by 17
  24. 2021Neuro-Symbolic Forward Reasoningcited by 16
  25. 2022NELLIE: A Neuro-Symbolic Inference Engine for Grounded, Compositional, and Explainable Reasoningcited by 16
  26. 2021FF-NSL: Feed-Forward Neural-Symbolic Learnercited by 15
  27. 2022Multi-Step Deductive Reasoning Over Natural Language: An Empirical Study on Out-of-Distribution Generalisationcited by 15
  28. 2023Relational Concept Bottleneck Modelscited by 15
  29. 2022HEAT: Hyperedge Attention Networkscited by 13
  30. 2023Sequential Query Encoding For Complex Query Answering on Knowledge Graphscited by 13
  31. 2022Neural-Symbolic Recursive Machine for Systematic Generalizationcited by 12
  32. 2023On the Correspondence Between Monotonic Max-Sum GNNs and Datalogcited by 12
  33. 2023Learning Differentiable Logic Programs for Abstract Visual Reasoningcited by 12
  34. 2024Evaluating Deep Unlearning in Large Language Modelscited by 12
  35. 2021Is Multi-Hop Reasoning Really Explainable? Towards Benchmarking Reasoning Interpretabilitycited by 10
  36. 2022Learning Signal Temporal Logic through Neural Network for Interpretable Classificationcited by 10
  37. 2023Assessing SATNet's Ability to Solve the Symbol Grounding Problemcited by 10
  38. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10

50 most cited of 159 All 159 (JSON)