mlsanityData to 7 Oct 2026

Neural Logic Machines

arXiv 1904.11694 ↗First posted 26 Apr 2019cs.AI cs.LG stat.MLcited by 144

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Cited by 25 in LLM reasoning, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifiers. After being trained on small-scale tasks (such as sorting short arrays), NLMs can recover lifted rules, and generalize to large-scale tasks (such as sorting longer arrays). In our experiments, NLMs achieve perfect generalization in a number of tasks, from relational reasoning tasks on the family tree and general graphs, to decision making tasks including sorting arrays, finding shortest paths, and playing the blocks world. Most of these tasks are hard to accomplish for neural networks or inductive logic programming alone.

Key facts. Cited by 144 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Apr 2019.

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Citing papers per year: 2021: 30; 2022: 24; 2023: 31; 2024: 21; 2025: 24; 2026: 14.

144 papers.

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  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,302
  2. 2022Least-to-Most Prompting Enables Complex Reasoning in Large Language Modelscited by 1,397
  3. 2022Measuring and Narrowing the Compositionality Gap in Language Modelscited by 1,054
  4. 2022Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thoughtcited by 334
  5. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  6. 2021A Survey on Interpretable Reinforcement Learningcited by 70
  7. 2023Interpretable Neural-Symbolic Concept Reasoningcited by 56
  8. 2021Inductive logic programming at 30cited by 46
  9. 2024R2-Guard: Robust Reasoning Enabled LLM Guardrail via Knowledge-Enhanced Logical Reasoningcited by 41
  10. 2022Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Reviewcited by 37
  11. 2021Neuro-Symbolic Inductive Logic Programming with Logical Neural Networkscited by 36
  12. 2024Learning Iterative Reasoning through Energy Diffusioncited by 36
38 more
  1. 2021From Machine Learning to Robotics: Challenges and Opportunities for Embodied Intelligencecited by 35
  2. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 34
  3. 2022A Review of Emerging Research Directions in Abstract Visual Reasoningcited by 33
  4. 2023Skills-in-Context Prompting: Unlocking Compositionality in Large Language Modelscited by 33
  5. 2023What's Left? Concept Grounding with Logic-Enhanced Foundation Modelscited by 33
  6. 2023Learning Domain-Independent Heuristics for Grounded and Lifted Planningcited by 31
  7. 2021EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use casecited by 30
  8. 2021Neuro-Symbolic Reinforcement Learning with First-Order Logiccited by 30
  9. 2022HAKE: A Knowledge Engine Foundation for Human Activity Understandingcited by 28
  10. 2021Learning Algebraic Representation for Systematic Generalization in Abstract Reasoningcited by 27
  11. 2024Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AIcited by 24
  12. 2021Neuro-Symbolic Hierarchical Rule Inductioncited by 23
  13. 2021Neuro-Symbolic AI: An Emerging Class of AI Workloads and their Characterizationcited by 22
  14. 2021Reinforcement Learning for Classical Planning: Viewing Heuristics as Dense Reward Generatorscited by 21
  15. 2024LLMs for Relational Reasoning: How Far are We?cited by 21
  16. 2023Hierarchical Programmatic Reinforcement Learning via Learning to Compose Programscited by 20
  17. 2021Differentiable Logic Machinescited by 18
  18. 2022GALOIS: Boosting Deep Reinforcement Learning via Generalizable Logic Synthesiscited by 16
  19. 2023Symbol-LLM: Leverage Language Models for Symbolic System in Visual Human Activity Reasoningcited by 16
  20. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  21. 2021Modeling Hierarchical Structures with Continuous Recursive Neural Networkscited by 15
  22. 2023Scalable Neural-Probabilistic Answer Set Programmingcited by 14
  23. 2024Neuro-symbolic Learning Yielding Logical Constraintscited by 12
  24. 2025Parameter-Efficient Continual Fine-Tuning: A Surveycited by 11
  25. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  26. 2024Neuro-Symbolic AI: Explainability, Challenges, and Future Trendscited by 10
  27. 2021Learning Symbolic Rules for Interpretable Deep Reinforcement Learningcited by 9
  28. 2021pix2rule: End-to-end Neuro-symbolic Rule Learningcited by 9
  29. 2021Weakly Supervised Explainable Phrasal Reasoning with Neural Fuzzy Logiccited by 9
  30. 2021Learning Symbolic Rules for Reasoning in Quasi-Natural Languagecited by 9
  31. 2021Interpretable Model-based Hierarchical Reinforcement Learning using Inductive Logic Programmingcited by 8
  32. 2021Neural Unification for Logic Reasoning over Natural Languagecited by 8
  33. 2022AdaLoGN: Adaptive Logic Graph Network for Reasoning-Based Machine Reading Comprehensioncited by 8
  34. 2023Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learningcited by 8
  35. 2023What Planning Problems Can A Relational Neural Network Solve?cited by 8
  36. 2024LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulationcited by 8
  37. 2021Combining Rules and Embeddings via Neuro-Symbolic AI for Knowledge Base Completioncited by 7
  38. 2021A Critical Review of Inductive Logic Programming Techniques for Explainable AIcited by 7

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