mlsanityData to 13 Oct 2026

Logical Neural Networks

arXiv 2006.13155 ↗First posted 23 Jun 2020cs.AI cs.LG cs.LOcited by 118

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Cited by 24 in LLM reasoning, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.

Key facts. Cited by 118 papers in the map (data through 13 Oct 2026). First posted on arXiv 23 Jun 2020.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 21; 2022: 17; 2023: 19; 2024: 23; 2025: 16; 2026: 22.

118 papers.

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  1. 2024Mechanistic Interpretability for AI Safety -- A Reviewcited by 420
  2. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  3. 2021Incorporating Domain Knowledge into Deep Neural Networkscited by 56
  4. 2023Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstractioncited by 45
  5. 2022Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Reviewcited by 38
  6. 2021Neuro-Symbolic Inductive Logic Programming with Logical Neural Networkscited by 36
  7. 2021Neuro-Symbolic Reinforcement Learning with First-Order Logiccited by 30
  8. 2021Differentiable Inductive Logic Programming for Structured Examplescited by 26
  9. 2024Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AIcited by 24
  10. 2022Neuro-Symbolic Causal Reasoning Meets Signaling Game for Emergent Semantic Communicationscited by 21
  11. 2023Neurosymbolic AI for Reasoning over Knowledge Graphs: A Surveycited by 21
  12. 2022Deep Symbolic Learning: Discovering Symbols and Rules from Perceptionscited by 20
38 more
  1. 2021Logic Embeddings for Complex Query Answeringcited by 17
  2. 2023A Universal Question-Answering Platform for Knowledge Graphscited by 17
  3. 2025Reasoning in Computer Vision: Taxonomy, Models, Tasks, and Methodologiescited by 17
  4. 2021Neuro-Symbolic Forward Reasoningcited by 16
  5. 2023Joint Edge-Model Sparse Learning is Provably Efficient for Graph Neural Networkscited by 16
  6. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  7. 2021FF-NSL: Feed-Forward Neural-Symbolic Learnercited by 15
  8. 2022Neuro-Symbolic Learning of Answer Set Programs from Raw Datacited by 12
  9. 2023Reliable Natural Language Understanding with Large Language Models and Answer Set Programmingcited by 12
  10. 2023Learning Differentiable Logic Programs for Abstract Visual Reasoningcited by 12
  11. 2021LNN-EL: A Neuro-Symbolic Approach to Short-text Entity Linkingcited by 11
  12. 2024The Role of Foundation Models in Neuro-Symbolic Learning and Reasoningcited by 11
  13. 2022Knowledge-augmented Deep Learning and Its Applications: A Surveycited by 10
  14. 2024Learning Interpretable Differentiable Logic Networkscited by 10
  15. 2024Neuro-Symbolic AI: Explainability, Challenges, and Future Trendscited by 10
  16. 2025DMWM: Dual-Mind World Model with Long-Term Imaginationcited by 10
  17. 2021pix2rule: End-to-end Neuro-symbolic Rule Learningcited by 9
  18. 2024LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulationcited by 8
  19. 2021Combining Rules and Embeddings via Neuro-Symbolic AI for Knowledge Base Completioncited by 7
  20. 2022Neuro-symbolic Models for Interpretable Time Series Classification using Temporal Logic Descriptioncited by 7
  21. 2023PDSketch: Integrated Planning Domain Programming and Learningcited by 7
  22. 2023Neuro-symbolic Rule Learning in Real-world Classification Taskscited by 7
  23. 2023Towards Safe Autonomous Driving Policies using a Neuro-Symbolic Deep Reinforcement Learning Approachcited by 7
  24. 2024Towards Efficient Neuro-Symbolic AI: From Workload Characterization to Hardware Architecturecited by 7
  25. 2021LOA: Logical Optimal Actions for Text-based Interaction Gamescited by 6
  26. 2023Extensions to Generalized Annotated Logic and an Equivalent Neural Architecturecited by 6
  27. 2024Strong hallucinations from negation and how to fix themcited by 6
  28. 2024AdapTable: Test-Time Adaptation for Tabular Data via Shift-Aware Uncertainty Calibrator and Label Distribution Handlercited by 6
  29. 2024Dspy-based Neural-Symbolic Pipeline to Enhance Spatial Reasoning in LLMscited by 6
  30. 2025Unlocking the Potential of Generative AI through Neuro-Symbolic Architectures: Benefits and Limitationscited by 6
  31. 2021Neural Network for Weighted Signal Temporal Logiccited by 5
  32. 2024Logic Rules as Explanations for Legal Case Retrievalcited by 5
  33. 2025A Study on Neuro-Symbolic Artificial Intelligence: Healthcare Perspectivescited by 5
  34. 2021Eye of the Beholder: Improved Relation Generalization for Text-based Reinforcement Learning Agentscited by 4
  35. 2021Weighted Graph-Based Signal Temporal Logic Inference Using Neural Networkscited by 4
  36. 2021Logical Credal Networkscited by 4
  37. 2023Diagrammatization and Abduction to Improve AI Interpretability With Domain-Aligned Explanations for Medical Diagnosiscited by 4
  38. 2023Utterance Classification with Logical Neural Network: Explainable AI for Mental Disorder Diagnosiscited by 4

50 most cited of 118 All 118 (JSON)