mlsanityData to 13 Oct 2026

NeuPSL: Neural Probabilistic Soft Logic

arXiv 2205.14268 ↗First posted 27 May 2022cs.LGcited by 34

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

In this paper, we introduce Neural Probabilistic Soft Logic (NeuPSL), a novel neuro-symbolic (NeSy) framework that unites state-of-the-art symbolic reasoning with the low-level perception of deep neural networks. To model the boundary between neural and symbolic representations, we propose a family of energy-based models, NeSy Energy-Based Models, and show that they are general enough to include NeuPSL and many other NeSy approaches. Using this framework, we show how to seamlessly integrate neural and symbolic parameter learning and inference in NeuPSL. Through an extensive empirical evaluation, we demonstrate the benefits of using NeSy methods, achieving upwards of 30% improvement over independent neural network models. On a well-established NeSy task, MNIST-Addition, NeuPSL demonstrates its joint reasoning capabilities by outperforming existing NeSy approaches by up to 10% in low-data settings. Furthermore, NeuPSL achieves a 5% boost in performance over state-of-the-art NeSy methods in a canonical citation network task with up to a 40 times speed up.

Key facts. Cited by 34 papers in the map (data through 13 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 27 of its 83 references that are in the map. First posted on arXiv 27 May 2022.

Builds on

27 of 83 references.

References · 27

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,318
  2. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,539
  3. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,911
  4. 2021Convex optimizationcited by 2,488
  5. 2019Simplifying Graph Convolutional Networkscited by 1,474
  6. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 390
  7. 2019The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervisioncited by 371
  8. 2017A Semantic Loss Function for Deep Learning with Symbolic Knowledgecited by 268
  9. 2015Conditional Random Fields as Recurrent Neural Networkscited by 213
  10. 2017Learning Explanatory Rules from Noisy Datacited by 210
  11. 2020Logic Tensor Networkscited by 197
  12. 2017Neural-Symbolic Learning and Reasoning: A Survey and Interpretationcited by 195
15 more
  1. 2019SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solvercited by 173
  2. 2017End-to-End Differentiable Provingcited by 159
  3. 2019Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoningcited by 150
  4. 2016Harnessing Deep Neural Networks with Logic Rulescited by 135
  5. 2016Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervisioncited by 102
  6. 2020Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspectivecited by 94
  7. 2017Logic Tensor Networks for Semantic Image Interpretationcited by 92
  8. 2021From Statistical Relational to Neurosymbolic Artificial Intelligence: a Surveycited by 72
  9. 2015Hinge-Loss Markov Random Fields and Probabilistic Soft Logiccited by 63
  10. 2020From Statistical Relational to Neuro-Symbolic Artificial Intelligencecited by 63
  11. 2021DeepStochLog: Neural Stochastic Logic Programmingcited by 58
  12. 2016Programming with a Differentiable Forth Interpretercited by 33
  13. 2018Towards Semi-Supervised Learning for Deep Semantic Role Labelingcited by 8
  14. 2020Deep Adaptive Semantic Logic (DASL): Compiling Declarative Knowledge into Deep Neural Networkscited by 3
  15. 2020HyperFair: A Soft Approach to Integrating Fairness Criteriacited by 3

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2022: 1; 2023: 5; 2024: 12; 2025: 8; 2026: 8.

34 papers.

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  1. 2023Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoningcited by 382
  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 37
  5. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
  6. 2024Towards Cognitive AI Systems: a Survey and Prospective on Neuro-Symbolic AIcited by 24
  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. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
  10. 2024Softened Symbol Grounding for Neuro-symbolic Systemscited by 16
  11. 2023Semantic Strengthening of Neuro-Symbolic Learningcited by 12
  12. 2024The Role of Foundation Models in Neuro-Symbolic Learning and Reasoningcited by 11
22 more
  1. 2024ULLER: A Unified Language for Learning and Reasoningcited by 9
  2. 2023Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learningcited by 8
  3. 2025Defining neurosymbolic AIcited by 8
  4. 2024Towards Efficient Neuro-Symbolic AI: From Workload Characterization to Hardware Architecturecited by 7
  5. 2024Using Domain Knowledge to Guide Dialog Structure Induction via Neural Probabilistic Soft Logiccited by 5
  6. 2026DeonticBench: A Benchmark for Reasoning over Rulescited by 5
  7. 2025The DeepLog Neurosymbolic Machinecited by 4
  8. 2024On the use of neurosymbolic AI for defending against cyber attackscited by 3
  9. 2025ABS: Enforcing Constraint Satisfaction On Generated Sequences Via Automata-Guided Beam Searchcited by 3
  10. 2025Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AIcited by 3
  11. 2026NeuroSymActive: Differentiable Neural-Symbolic Reasoning with Active Exploration for Knowledge Graph Question Answeringcited by 3
  12. 2025Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Errorcited by 2
  13. 2023A Novel Neural-symbolic System under Statistical Relational Learningcited by 1
  14. 2024Convex and Bilevel Optimization for Neuro-Symbolic Inference and Learningcited by 1
  15. 2025A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Datacited by 1
  16. 2025Understanding and Improving Adversarial Robustness of Neural Probabilistic Circuitscited by 1
  17. 2026Constraint-Aware Neurosymbolic Uncertainty Quantification with Bayesian Deep Learning for Scientific Discoverycited by 1
  18. 2026Improved Bug Localization with AI Agents Leveraging Hypothesis and Dynamic Cognitioncited by 0
  19. 2026REASON: Accelerating Probabilistic Logical Reasoning for Scalable Neuro-Symbolic Intelligencecited by 0
  20. 2026Parallel Noising in Neural Markov Logic Networkscited by 0
  21. 2026Neuro-symbolic learning over OWL 2 DL via consequence-based compilation to differentiable circuitscited by 0
  22. 2026Think-Verify-Revise: Neuro-Symbolic Visual Reasoning with Vision-Language Models and Dynamic Logic Tensor Networkscited by 0

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  3. 2022Deep Symbolic Learning: Discovering Symbols and Rules from Perceptions
  4. 2026SoftReason: A Fully Differentiable Neuro-Soft-Symbolic Deductive Reasoning Architecture over High-Dimensional Perceptual Data
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  8. 2025Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration