mlsanityData to 14 Oct 2026

A Semantic Loss Function for Deep Learning with Symbolic Knowledge

arXiv 1711.11157 ↗First posted 29 Nov 2017cs.AI cs.LG cs.LOcited by 270

Not on the map. Why?

Cited by 32 in LLM reasoning, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures how close the neural network is to satisfying the constraints on its output. An experimental evaluation shows that it effectively guides the learner to achieve (near-)state-of-the-art results on semi-supervised multi-class classification. Moreover, it significantly increases the ability of the neural network to predict structured objects, such as rankings and paths. These discrete concepts are tremendously difficult to learn, and benefit from a tight integration of deep learning and symbolic reasoning methods.

Key facts. Cited by 270 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 Nov 2017.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 39; 2022: 33; 2023: 49; 2024: 56; 2025: 42; 2026: 51.

270 papers.

Sort:

By area:

  1. 2022Semantic Probabilistic Layers for Neuro-Symbolic Learningcited by 103
  2. 2023NeurASP: Embracing Neural Networks into Answer Set Programmingcited by 92
  3. 2021A Survey on Interpretable Reinforcement Learningcited by 73
  4. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  5. 2023Scallop: A Language for Neurosymbolic Programmingcited by 63
  6. 2023Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscited by 63
  7. 2021Incorporating Domain Knowledge into Deep Neural Networkscited by 56
  8. 2021Neuro-Symbolic Artificial Intelligence: Current Trendscited by 54
  9. 2023On the Constrained Time-Series Generation Problemcited by 54
  10. 2022A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inferencecited by 50
  11. 2021MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networkscited by 44
  12. 2022Deep Learning with Logical Constraintscited by 44
38 more
  1. 2021Constrained Learning with Non-Convex Lossescited by 42
  2. 2023Safe Reinforcement Learning via Probabilistic Logic Shieldscited by 42
  3. 2021Modular Design Patterns for Hybrid Learning and Reasoning Systems: a taxonomy, patterns and use casescited by 39
  4. 2021A Survey on Neural-symbolic Learning Systemscited by 39
  5. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
  6. 2021Multi-Label Classification Neural Networks with Hard Logical Constraintscited by 36
  7. 2021Neural Network Robustness as a Verification Property: A Principled Case Studycited by 35
  8. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 35
  9. 2022NeuPSL: Neural Probabilistic Soft Logiccited by 34
  10. 2022ROAD-R: The Autonomous Driving Dataset with Logical Requirementscited by 34
  11. 2022SIMPLE: A Gradient Estimator for k-Subset Samplingcited by 34
  12. 2022Character-Centric Story Visualization via Visual Planning and Token Alignmentcited by 33
  13. 2023Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsalcited by 33
  14. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
  15. 2021EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use casecited by 30
  16. 2024Logically Consistent Language Models via Neuro-Symbolic Integrationcited by 30
  17. 2023Logic-induced Diagnostic Reasoning for Semi-supervised Semantic Segmentationcited by 29
  18. 2024How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Datacited by 29
  19. 2023TABLET: Learning From Instructions For Tabular Datacited by 28
  20. 2022Neuro-Symbolic Entropy Regularizationcited by 27
  21. 2023Neural Probabilistic Logic Programming in Discrete-Continuous Domainscited by 25
  22. 2023Neural-Logic Human-Object Interaction Detectioncited by 25
  23. 2024Scaling Tractable Probabilistic Circuits: A Systems Perspectivecited by 23
  24. 2023A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraintscited by 22
  25. 2022Deep Symbolic Learning: Discovering Symbols and Rules from Perceptionscited by 21
  26. 2023Neurosymbolic AI for Reasoning over Knowledge Graphs: A Surveycited by 21
  27. 2023Learning to Solve Constraint Satisfaction Problems with Recurrent Transformercited by 21
  28. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  29. 2023Improved Logical Reasoning of Language Models via Differentiable Symbolic Programmingcited by 18
  30. 2024On the Independence Assumption in Neurosymbolic Learningcited by 18
  31. 2024Concept-Based Explanations in Computer Vision: Where Are We and Where Could We Go?cited by 18
  32. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
  33. 2023LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoningcited by 17
  34. 2024Interpretable Concept-Based Memory Reasoningcited by 17
  35. 2021Neuro-Symbolic Forward Reasoningcited by 16
  36. 2024Softened Symbol Grounding for Neuro-symbolic Systemscited by 16
  37. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  38. 2024KLay: Accelerating Arithmetic Circuits for Neurosymbolic AIcited by 16

50 most cited of 270 All 270 (JSON)