mlsanityData to 14 Oct 2026

Semantic Probabilistic Layers for Neuro-Symbolic Learning

arXiv 2206.00426 ↗First posted 1 Jun 2022cs.LG cs.AIcited by 103

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Abstract (arXiv)

We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer (SPL) can model intricate correlations, and hard constraints, over a structured output space all while being amenable to end-to-end learning via maximum likelihood. SPLs combine exact probabilistic inference with logical reasoning in a clean and modular way, learning complex distributions and restricting their support to solutions of the constraint. As such, they can faithfully, and efficiently, model complex SOP tasks beyond the reach of alternative neuro-symbolic approaches. We empirically demonstrate that SPLs outperform these competitors in terms of accuracy on challenging SOP tasks including hierarchical multi-label classification, pathfinding and preference learning, while retaining perfect constraint satisfaction.

Key facts. Cited by 103 papers in the map (data through 14 Oct 2026). Builds on 40 of its 100 references that are in the map. First posted on arXiv 1 Jun 2022.

Builds on

40 of 100 references.

References · 40

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28 more
  1. 2020Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuitscited by 103
  2. 2021Implicit MLE: Backpropagating Through Discrete Exponential Family Distributionscited by 98
  3. 2020Coherent Hierarchical Multi-Label Classification Networkscited by 65
  4. 2021Incorporating Domain Knowledge into Deep Neural Networkscited by 56
  5. 2021Neuro-Symbolic Artificial Intelligence: Current Trendscited by 54
  6. 2020Fast and Accurate Neural CRF Constituency Parsingcited by 50
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  8. 2021MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networkscited by 44
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 4; 2023: 18; 2024: 35; 2025: 28; 2026: 18.

103 papers.

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  1. 2023Tractable Control for Autoregressive Language Generationcited by 65
  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. 2023Safe Reinforcement Learning via Probabilistic Logic Shieldscited by 42
  5. 2024Towards Scientific Discovery with Generative AI: Progress, Opportunities, and Challengescited by 41
  6. 2023Subtractive Mixture Models via Squaring: Representation and Learningcited by 39
  7. 2025Neuro-Symbolic AI in 2024: A Systematic Reviewcited by 38
  8. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
  9. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 35
  10. 2022SIMPLE: A Gradient Estimator for k-Subset Samplingcited by 34
  11. 2023Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsalcited by 33
  12. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
38 more
  1. 2024Logically Consistent Language Models via Neuro-Symbolic Integrationcited by 30
  2. 2024How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Datacited by 29
  3. 2024Scaling Tractable Probabilistic Circuits: A Systems Perspectivecited by 23
  4. 2023Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learningcited by 22
  5. 2023A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraintscited by 22
  6. 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
  7. 2023Neurosymbolic AI for Reasoning over Knowledge Graphs: A Surveycited by 21
  8. 2024Sum of Squares Circuitscited by 21
  9. 2023How to Turn Your Knowledge Graph Embeddings into Generative Modelscited by 20
  10. 2023Random-Set Neural Networks (RS-NN)cited by 19
  11. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  12. 2024On the Independence Assumption in Neurosymbolic Learningcited by 18
  13. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
  14. 2024KLay: Accelerating Arithmetic Circuits for Neurosymbolic AIcited by 16
  15. 2024On the Relationship Between Monotone and Squared Probabilistic Circuitscited by 14
  16. 2023CuTS: Customizable Tabular Synthetic Data Generationcited by 13
  17. 2025Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lenscited by 13
  18. 2023Semantic Strengthening of Neuro-Symbolic Learningcited by 12
  19. 2024Building Expressive and Tractable Probabilistic Generative Models: A Reviewcited by 12
  20. 2022Refining neural network predictions using background knowledgecited by 11
  21. 2024Controllable Generation via Locally Constrained Resamplingcited by 11
  22. 2025A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfactioncited by 11
  23. 2024Learning with Logical Constraints but without Shortcut Satisfactioncited by 10
  24. 2024Neuro-Symbolic AI: Explainability, Challenges, and Future Trendscited by 10
  25. 2024A Compositional Atlas for Algebraic Circuitscited by 10
  26. 2023A Unified Approach to Count-Based Weakly-Supervised Learningcited by 9
  27. 2024COLEP: Certifiably Robust Learning-Reasoning Conformal Prediction via Probabilistic Circuitscited by 9
  28. 2024ULLER: A Unified Language for Learning and Reasoningcited by 9
  29. 2024On the Hardness of Probabilistic Neurosymbolic Learningcited by 9
  30. 2025Scaling Probabilistic Circuits via Monarch Matricescited by 9
  31. 2025Fast and Expressive Multi-Byte Prediction with Probabilistic Circuitscited by 9
  32. 2023Machine Learning with Requirements: a Manifestocited by 8
  33. 2023Characteristic Circuitscited by 8
  34. 2025Defining neurosymbolic AIcited by 8
  35. 2023Bayesian Structure Scores for Probabilistic Circuitscited by 7
  36. 2024Error Detection and Constraint Recovery in Hierarchical Multi-Label Classification without Prior Knowledgecited by 7
  37. 2024Restructuring Tractable Probabilistic Circuitscited by 7
  38. 2025The Need for Verification in AI-Driven Scientific Discoverycited by 7

50 most cited of 103 All 103 (JSON)

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  5. 2024Softened Symbol Grounding for Neuro-symbolic Systems
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