mlsanityData to 14 Oct 2026

A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference

arXiv 2212.12393 ↗First posted 23 Dec 2022cs.LG cs.AI cs.LOcited by 50

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

We study the problem of combining neural networks with symbolic reasoning. Recently introduced frameworks for Probabilistic Neurosymbolic Learning (PNL), such as DeepProbLog, perform exponential-time exact inference, limiting the scalability of PNL solutions. We introduce Approximate Neurosymbolic Inference (A-NeSI): a new framework for PNL that uses neural networks for scalable approximate inference. A-NeSI 1) performs approximate inference in polynomial time without changing the semantics of probabilistic logics; 2) is trained using data generated by the background knowledge; 3) can generate symbolic explanations of predictions; and 4) can guarantee the satisfaction of logical constraints at test time, which is vital in safety-critical applications. Our experiments show that A-NeSI is the first end-to-end method to solve three neurosymbolic tasks with exponential combinatorial scaling. Finally, our experiments show that A-NeSI achieves explainability and safety without a penalty in performance.

Key facts. Cited by 50 papers in the map (data through 14 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 34 of its 64 references that are in the map. First posted on arXiv 23 Dec 2022.

Builds on

34 of 64 references.

Closest ancestors · 1

Same direction, newest first

  1. 2022NeuPSL: Neural Probabilistic Soft Logic27 May

Other references · 33

  1. 2017Attention Is All You Needcited by 60,361
  2. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  3. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  4. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  5. 2015Variational Inference with Normalizing Flowscited by 2,170
  6. 2017Modeling Relational Data with Graph Convolutional Networkscited by 1,694
  7. 2017A Distributional Perspective on Reinforcement Learningcited by 765
  8. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 394
  9. 2021Flow Network based Generative Models for Non-Iterative Diverse Candidate Generationcited by 392
  10. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 283
  11. 2017A Semantic Loss Function for Deep Learning with Symbolic Knowledgecited by 270
  12. 2022Trajectory balance: Improved credit assignment in GFlowNetscited by 251
21 more
  1. 2019On Completeness-aware Concept-Based Explanations in Deep Neural Networkscited by 239
  2. 2019Differentiation of Blackbox Combinatorial Solverscited by 226
  3. 2021Efficient and Modular Implicit Differentiationcited by 203
  4. 2020Logic Tensor Networkscited by 199
  5. 2016Variational Lossy Autoencodercited by 176
  6. 2015Gradient Estimation Using Stochastic Computation Graphscited by 121
  7. 2022GFlowNets and variational inferencecited by 106
  8. 2022Semantic Probabilistic Layers for Neuro-Symbolic Learningcited by 103
  9. 2020Analyzing Differentiable Fuzzy Logic Operatorscited by 101
  10. 2021Implicit MLE: Backpropagating Through Discrete Exponential Family Distributionscited by 98
  11. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  12. 2021DeepStochLog: Neural Stochastic Logic Programmingcited by 58
  13. 2018Memory Augmented Policy Optimization for Program Synthesis and Semantic Parsingcited by 57
  14. 2022Deep Learning with Logical Constraintscited by 44
  15. 2021Multi-Label Classification Neural Networks with Hard Logical Constraintscited by 36
  16. 2022Backpropagation through Combinatorial Algorithms: Identity with Projection Workscited by 29
  17. 2022Neuro-Symbolic Entropy Regularizationcited by 27
  18. 2019A Boxology of Design Patterns for Hybrid Learning and Reasoning Systemscited by 20
  19. 2021Storchastic: A Framework for General Stochastic Automatic Differentiationcited by 11
  20. 2022Refining neural network predictions using background knowledgecited by 11
  21. 2021Evaluating Relaxations of Logic for Neural Networks: A Comprehensive Studycited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 22; 2025: 16; 2026: 6.

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  1. 2023Amortizing intractable inference in large language modelscited by 97
  2. 2023Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscited by 63
  3. 2024Learning diverse attacks on large language models for robust red-teaming and safety tuningcited by 54
  4. 2024Improved off-policy training of diffusion samplerscited by 48
  5. 2023Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNetscited by 40
  6. 2025Neuro-Symbolic AI in 2024: A Systematic Reviewcited by 38
  7. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 37
  8. 2023Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsalcited by 33
  9. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
  10. 2024How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Datacited by 29
  11. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  12. 2024On the Independence Assumption in Neurosymbolic Learningcited by 18
38 more
  1. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
  2. 2023Pre-Training and Fine-Tuning Generative Flow Networkscited by 17
  3. 2024Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description lengthcited by 17
  4. 2025Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lenscited by 13
  5. 2025Neurosymbolic Diffusion Modelscited by 13
  6. 2024Neuro-symbolic Learning Yielding Logical Constraintscited by 12
  7. 2024Neuro-Symbolic AI: Explainability, Challenges, and Future Trendscited by 10
  8. 2024ULLER: A Unified Language for Learning and Reasoningcited by 9
  9. 2024Latent Logic Tree Extraction for Event Sequence Explanation from LLMscited by 9
  10. 2024On the Hardness of Probabilistic Neurosymbolic Learningcited by 9
  11. 2024LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulationcited by 8
  12. 2023Expected flow networks in stochastic environments and two-player zero-sum gamescited by 7
  13. 2024Data-Efficient Learning with Neural Programscited by 7
  14. 2024EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logiccited by 6
  15. 2025Neural Probabilistic Circuits: Enabling Compositional and Interpretable Predictions through Logical Reasoningcited by 6
  16. 2025Adaptive Destruction Processes for Diffusion Samplerscited by 6
  17. 2024Dolphin: A Programmable Framework for Scalable Neurosymbolic Learningcited by 5
  18. 2025The DeepLog Neurosymbolic Machinecited by 5
  19. 2024Sandra -- A Neuro-Symbolic Reasoner Based On Descriptions And Situationscited by 4
  20. 2024A Fast Convoluted Story: Scaling Probabilistic Inference for Integer Arithmeticcited by 3
  21. 2025ABS: Enforcing Constraint Satisfaction On Generated Sequences Via Automata-Guided Beam Searchcited by 3
  22. 2025Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Errorcited by 3
  23. 2025Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AIcited by 3
  24. 2024Improving Neural-based Classification with Logical Background Knowledgecited by 2
  25. 2024PiShield: A PyTorch Package for Learning with Requirementscited by 2
  26. 2025Gradient-Based Optimization on G"odel Logic as Discrete Local Searchcited by 2
  27. 2025A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Datacited by 2
  28. 2025CTSketch: Compositional Tensor Sketching for Scalable Neurosymbolic Learningcited by 1
  29. 2025Curriculum Abductive Learningcited by 1
  30. 2025Understanding and Improving Adversarial Robustness of Neural Probabilistic Circuitscited by 1
  31. 2026Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Modelscited by 1
  32. 2024A Complexity Map of Probabilistic Reasoning for Neurosymbolic Classification Techniquescited by 0
  33. 2025DeepProofLog: Efficient Proving in Deep Stochastic Logic Programscited by 0
  34. 2026AS2 -- Attention-Based Soft Answer Sets: An End-to-End Differentiable Neuro-Soft-Symbolic Reasoning Architecturecited by 0
  35. 2026EM-NeSy: Expectation Maximization for Neurosymbolic Learningcited by 0
  36. 2026NeSyCat Torch: A Differentiable Tensor Implementation of Categorical Semantics for Neurosymbolic Learningcited by 0
  37. 2026Parallel Noising in Neural Markov Logic Networkscited by 0
  38. 2026Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuitscited by 0

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