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Embedding Symbolic Knowledge into Deep Networks

arXiv 1909.01161 ↗First posted 3 Sep 2019cs.AI cs.CV cs.MMcited by 49

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Abstract (arXiv)

In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph Convolutional Network (GCN). To generate semantically-faithful embeddings, we develop techniques to recognize node heterogeneity, and semantic regularization that incorporate structural constraints into the embedding. Experiments show that our approach improves the performance of models trained to perform entailment checking and visual relation prediction. Interestingly, we observe a connection between the tractability of the propositional theory representation and the ease of embedding. Future exploration of this connection may elucidate the relationship between knowledge compilation and vector representation learning.

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Sep 2019.

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Citing papers per year: 2021: 13; 2022: 11; 2023: 8; 2024: 11; 2025: 5; 2026: 1.

49 papers.

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  1. 2024Hallucination is Inevitable: An Innate Limitation of Large Language Modelscited by 329
  2. 2025InternVLA-M1: A Spatially Guided Vision-Language-Action Framework for Generalist Robot Policycited by 83
  3. 2021Incorporating Domain Knowledge into Deep Neural Networkscited by 56
  4. 2021Neuro-Symbolic Artificial Intelligence: Current Trendscited by 54
  5. 2022Deep Learning with Logical Constraintscited by 44
  6. 2021A Survey on Neural-symbolic Learning Systemscited by 39
  7. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 34
  8. 2023Neural-Logic Human-Object Interaction Detectioncited by 25
  9. 2021Relation-aware Compositional Zero-shot Learning for Attribute-Object Pair Recognitioncited by 19
  10. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  11. 2023LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoningcited by 17
  12. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
37 more
  1. 2021Embedding Symbolic Temporal Knowledge into Deep Sequential Modelscited by 11
  2. 2022CARE: Certifiably Robust Learning with Reasoning via Variational Inferencecited by 10
  3. 2022Knowledge-augmented Deep Learning and Its Applications: A Surveycited by 10
  4. 2024Weakly Supervised Anomaly Detection via Knowledge-Data Alignmentcited by 10
  5. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  6. 2022Tractable Boolean and Arithmetic Circuitscited by 9
  7. 2023Sample-Efficient Learning of Novel Visual Conceptscited by 8
  8. 2024Naturally Supervised 3D Visual Grounding with Language-Regularized Concept Learnerscited by 8
  9. 2024LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulationcited by 8
  10. 2026ST4VLA: Spatially Guided Training for Vision-Language-Action Modelscited by 8
  11. 2021AI Descartes: Combining Data and Theory for Derivable Scientific Discoverycited by 7
  12. 2021A Critical Review of Inductive Logic Programming Techniques for Explainable AIcited by 7
  13. 2022Neuro-Symbolic Learning: Principles and Applications in Ophthalmologycited by 7
  14. 2025Symbolic Knowledge Extraction and Injection with Sub-symbolic Predictors: A Systematic Literature Reviewcited by 7
  15. 2021Inclusion of Domain-Knowledge into GNNs using Mode-Directed Inverse Entailmentcited by 6
  16. 2022Logical Reasoning for Task Oriented Dialogue Systemscited by 5
  17. 2025The Need for Verification in AI-Driven Scientific Discoverycited by 5
  18. 2021Neuro-Symbolic VQA: A review from the perspective of AGI desideratacited by 4
  19. 2024Semantic Objective Functions: A distribution-aware method for adding logical constraints in deep learningcited by 4
  20. 2021SYNERGY: Building Task Bots at Scale Using Symbolic Knowledge and Machine Teachingcited by 3
  21. 2024stl2vec: Semantic and Interpretable Vector Representation of Temporal Logiccited by 3
  22. 2023Learning from Noisy Crowd Labels with Logicscited by 2
  23. 2023Parallel Neurosymbolic Integration with Concordiacited by 2
  24. 2023Towards Unbiased Exploration in Partial Label Learningcited by 2
  25. 2022Differentiable Fuzzy ALC: A Neural-Symbolic Representation Language for Symbol Groundingcited by 1
  26. 2022Neural Controller Synthesis for Signal Temporal Logic Specifications Using Encoder-Decoder Structured Networkscited by 1
  27. 2023A Novel Neural-symbolic System under Statistical Relational Learningcited by 1
  28. 2023Spatial Knowledge-Infused Hierarchical Learning: An Application in Flood Mapping on Earth Imagerycited by 1
  29. 2024Bridging the Intent Gap: Knowledge-Enhanced Visual Generationcited by 1
  30. 2025Bridging Logic and Learning: Decoding Temporal Logic Embeddings via Transformerscited by 1
  31. 2021A Review of Some Techniques for Inclusion of Domain-Knowledge into Deep Neural Networkscited by 0
  32. 2021Incorporation of Deep Neural Network & Reinforcement Learning with Domain Knowledgecited by 0
  33. 2021Integrating Regular Expressions with Neural Networks via DFAcited by 0
  34. 2022Scalable Regularization of Scene Graph Generation Models using Symbolic Theoriescited by 0
  35. 2022A Roadmap to Domain Knowledge Integration in Machine Learningcited by 0
  36. 2024Social and Ethical Risks Posed by General-Purpose LLMs for Settling Newcomers in Canadacited by 0
  37. 2025Physics-Inspired Spatial Temporal Graph Neural Networks for Predicting Industrial Chain Resiliencecited by 0