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Augmenting Neural Networks with First-order Logic

arXiv 1906.06298 ↗First posted 14 Jun 2019cs.LG cs.CL stat.MLcited by 51

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Abstract (arXiv)

Today, the dominant paradigm for training neural networks involves minimizing task loss on a large dataset. Using world knowledge to inform a model, and yet retain the ability to perform end-to-end training remains an open question. In this paper, we present a novel framework for introducing declarative knowledge to neural network architectures in order to guide training and prediction. Our framework systematically compiles logical statements into computation graphs that augment a neural network without extra learnable parameters or manual redesign. We evaluate our modeling strategy on three tasks: machine comprehension, natural language inference, and text chunking. Our experiments show that knowledge-augmented networks can strongly improve over baselines, especially in low-data regimes.

Key facts. Cited by 51 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Jun 2019.

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Citing papers per year: 2021: 11; 2022: 13; 2023: 12; 2024: 7; 2025: 5; 2026: 3.

51 papers.

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  1. 2023Evaluating the Logical Reasoning Ability of ChatGPT and GPT-4cited by 202
  2. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  3. 2021GrooMeD-NMS: Grouped Mathematically Differentiable NMS for Monocular 3D Object Detectioncited by 66
  4. 2021Incorporating Domain Knowledge into Deep Neural Networkscited by 56
  5. 2023Symbol-LLM: Towards Foundational Symbol-centric Interface For Large Language Modelscited by 38
  6. 2022Is Neuro-Symbolic AI Meeting its Promise in Natural Language Processing? A Structured Reviewcited by 37
  7. 2021Multi-Label Classification Neural Networks with Hard Logical Constraintscited by 36
  8. 2022ROAD-R: The Autonomous Driving Dataset with Logical Requirementscited by 34
  9. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 34
  10. 2023GLoRE: Evaluating Logical Reasoning of Large Language Modelscited by 13
  11. 2021DomiKnowS: A Library for Integration of Symbolic Domain Knowledge in Deep Learningcited by 12
  12. 2023Semantic Strengthening of Neuro-Symbolic Learningcited by 12
38 more
  1. 2024Do Large Language Models Understand Logic or Just Mimick Context?cited by 10
  2. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  3. 2025DMWM: Dual-Mind World Model with Long-Term Imaginationcited by 10
  4. 2021Learning Constraints and Descriptive Segmentation for Subevent Detectioncited by 9
  5. 2021Does External Knowledge Help Explainable Natural Language Inference? Automatic Evaluation vs. Human Ratingscited by 9
  6. 2021Exploring Distantly-Labeled Rationales in Neural Network Modelscited by 8
  7. 2021Evaluating Relaxations of Logic for Neural Networks: A Comprehensive Studycited by 8
  8. 2022AdaLoGN: Adaptive Logic Graph Network for Reasoning-Based Machine Reading Comprehensioncited by 8
  9. 2023AutoML in The Wild: Obstacles, Workarounds, and Expectationscited by 8
  10. 2024Naturally Supervised 3D Visual Grounding with Language-Regularized Concept Learnerscited by 8
  11. 2021AI Descartes: Combining Data and Theory for Derivable Scientific Discoverycited by 7
  12. 2024EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logiccited by 6
  13. 2022A Solver-Free Framework for Scalable Learning in Neural ILP Architecturescited by 5
  14. 2024Logic Rules as Explanations for Legal Case Retrievalcited by 5
  15. 2025The Need for Verification in AI-Driven Scientific Discoverycited by 5
  16. 2022A Novel Multi-Task Learning Approach for Context-Sensitive Compound Type Identification in Sanskritcited by 4
  17. 2023Augmenting deep neural networks with symbolic knowledge: Towards trustworthy and interpretable AI for educationcited by 4
  18. 2024Exploiting T-norms for Deep Learning in Autonomous Drivingcited by 4
  19. 2022Knowledge Enhanced Neural Networks for relational domainscited by 3
  20. 2023LogicMP: A Neuro-symbolic Approach for Encoding First-order Logic Constraintscited by 3
  21. 2025LogiCoL: Logically-Informed Contrastive Learning for Set-based Dense Retrievalcited by 3
  22. 2022Memory Classifiers: Two-stage Classification for Robustness in Machine Learningcited by 2
  23. 2022Reduced Implication-bias Logic Loss for Neuro-Symbolic Learningcited by 2
  24. 2023Parallel Neurosymbolic Integration with Concordiacited by 2
  25. 2023The Integer Linear Programming Inference Cookbookcited by 2
  26. 2022Label Augmentation with Reinforced Labeling for Weak Supervisioncited by 1
  27. 2022Movement Analytics: Current Status, Application to Manufacturing, and Future Prospects from an AI Perspectivecited by 1
  28. 2022Neural DAEs: Constrained neural networkscited by 1
  29. 2023Current and Future Challenges in Knowledge Representation and Reasoningcited by 1
  30. 2024MedLogic-AQA: Enhancing Medical Question Answering with Abstractive Models Focusing on Logical Structurescited by 1
  31. 2021A Review of Some Techniques for Inclusion of Domain-Knowledge into Deep Neural Networkscited by 0
  32. 2022Constrained Training of Neural Networks via Theorem Provingcited by 0
  33. 2023Empirical Sufficiency Lower Bounds for Language Modeling with Locally-Bootstrapped Semantic Structurescited by 0
  34. 2023Improving Text Matching in E-Commerce Search with A Rationalizable, Intervenable and Fast Entity-Based Relevance Modelcited by 0
  35. 2025Bridging Neural Networks and Dynamic Time Warping for Adaptive Time Series Classificationcited by 0
  36. 2025Towards Scalable Lottery Ticket Networks using Genetic Algorithmscited by 0
  37. 2026On Improving Neurosymbolic Learning by Exploiting the Representation Spacecited by 0
  38. 2026Structure-Preserving Document Translation via Multi-Stage LLM Pipeline: A Case Study in Marathicited by 0

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