mlsanityData to 7 Oct 2026

Deep Learning with Logical Constraints

arXiv 2205.00523 ↗First posted 1 May 2022cs.AI cs.LG cs.LOcited by 44

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Abstract (arXiv)

In recent years, there has been an increasing interest in exploiting logically specified background knowledge in order to obtain neural models (i) with a better performance, (ii) able to learn from less data, and/or (iii) guaranteed to be compliant with the background knowledge itself, e.g., for safety-critical applications. In this survey, we retrace such works and categorize them based on (i) the logical language that they use to express the background knowledge and (ii) the goals that they achieve.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). Builds on 21 of its 67 references that are in the map. First posted on arXiv 1 May 2022.

Builds on

21 of 67 references.

References · 21

  1. 2015Distilling the Knowledge in a Neural Networkcited by 10,076
  2. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 389
  3. 2017A Semantic Loss Function for Deep Learning with Symbolic Knowledgecited by 267
  4. 2019Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systemscited by 203
  5. 2020Logic Tensor Networkscited by 197
  6. 2019Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoningcited by 149
  7. 2016Harnessing Deep Neural Networks with Logic Rulescited by 135
  8. 2020Analyzing Differentiable Fuzzy Logic Operatorscited by 100
  9. 2017Logic Tensor Networks for Semantic Image Interpretationcited by 92
  10. 2016Label-Free Supervision of Neural Networks with Physics and Domain Knowledgecited by 74
  11. 2020Coherent Hierarchical Multi-Label Classification Networkscited by 65
  12. 2021Incorporating Domain Knowledge into Deep Neural Networkscited by 56
9 more
  1. 2019Embedding Symbolic Knowledge into Deep Networkscited by 49
  2. 2018Adversarially Regularising Neural NLI Models to Integrate Logical Background Knowledgecited by 45
  3. 2021MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networkscited by 44
  4. 2021Multi-Label Classification Neural Networks with Hard Logical Constraintscited by 36
  5. 2020On Tractable Representations of Binary Neural Networkscited by 34
  6. 2022Label Relation Graphs Enhanced Hierarchical Residual Network for Hierarchical Multi-Granularity Classificationcited by 29
  7. 2017DeepGO: Predicting protein functions from sequence and interactions using a deep ontology-aware classifiercited by 20
  8. 2020Analyzing Differentiable Fuzzy Implicationscited by 15
  9. 2021Neuro-Symbolic Constraint Programming for Structured Predictioncited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 7; 2023: 6; 2024: 17; 2025: 8; 2026: 6.

44 papers.

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  1. 2022Semantic Probabilistic Layers for Neuro-Symbolic Learningcited by 103
  2. 2023Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscited by 63
  3. 2022A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inferencecited by 50
  4. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 36
  5. 2022ROAD-R: The Autonomous Driving Dataset with Logical Requirementscited by 34
  6. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 34
  7. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  8. 2024On the Independence Assumption in Neurosymbolic Learningcited by 18
  9. 2023LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoningcited by 17
  10. 2023Predicated Diffusion: Predicate Logic-Based Attention Guidance for Text-to-Image Diffusion Modelscited by 16
  11. 2023Logic of Differentiable Logics: Towards a Uniform Semantics of DLcited by 15
  12. 2024Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programscited by 14
32 more
  1. 2025A Survey on Deep Learning Approaches for Tabular Data Generation: Utility, Alignment, Fidelity, Privacy, Diversity, and Beyondcited by 13
  2. 2025Neural Network Verification is a Programming Language Challengecited by 12
  3. 2022Refining neural network predictions using background knowledgecited by 11
  4. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  5. 2024ULLER: A Unified Language for Learning and Reasoningcited by 9
  6. 2022Hierarchical Interdisciplinary Topic Detection Model for Research Proposal Classificationcited by 8
  7. 2024Naturally Supervised 3D Visual Grounding with Language-Regularized Concept Learnerscited by 8
  8. 2023Concept-Centric Transformers: Enhancing Model Interpretability through Object-Centric Concept Learning within a Shared Global Workspacecited by 7
  9. 2024EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logiccited by 6
  10. 2024Exploiting T-norms for Deep Learning in Autonomous Drivingcited by 4
  11. 2024Improving deep learning with prior knowledge and cognitive models: A survey on enhancing explainability, adversarial robustness and zero-shot learningcited by 4
  12. 2024Semantic Objective Functions: A distribution-aware method for adding logical constraints in deep learningcited by 4
  13. 2024stl2vec: Semantic and Interpretable Vector Representation of Temporal Logiccited by 3
  14. 2025ABS: Enforcing Constraint Satisfaction On Generated Sequences Via Automata-Guided Beam Searchcited by 3
  15. 2025Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AIcited by 3
  16. 2024PiShield: A PyTorch Package for Learning with Requirementscited by 2
  17. 2024Informed deep hierarchical classification: a non-standard analysis inspired approachcited by 2
  18. 2025Integrating Background Knowledge in Medical Semantic Segmentation with Logic Tensor Networkscited by 2
  19. 2026To Neuro-Symbolic Classification and Beyond by Compiling Description Logic Ontologies to Probabilistic Circuitscited by 2
  20. 2022ESC-Rules: Explainable, Semantically Constrained Rule Setscited by 1
  21. 2024Convex and Bilevel Optimization for Neuro-Symbolic Inference and Learningcited by 1
  22. 2025Proof-Carrying Neuro-Symbolic Codecited by 1
  23. 2025A General Framework for Property-Driven Machine Learningcited by 1
  24. 2026Neuro-Symbolic Artificial Intelligence: A Task-Directed Survey in the Black-Box Models Eracited by 1
  25. 2023Co-creating a globally interpretable model with human inputcited by 0
  26. 2024Creating a Formally Verified Neural Network for Autonomous Navigation: An Experience Reportcited by 0
  27. 2024Bi-ICE: An Inner Interpretable Framework for Image Classification via Bi-directional Interactions between Concept and Input Embeddingscited by 0
  28. 2025Combining Abstract Argumentation and Machine Learning for Efficiently Analyzing Low-Level Process Event Streamscited by 0
  29. 2026Quantitative Linear Logic for Neuro-Symbolic Learning and Verificationcited by 0
  30. 2026Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Modelscited by 0
  31. 2026DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layerscited by 0
  32. 2026Engineering Reliable Autonomous Systems: Challenges and Solutionscited by 0