mlsanityData to 7 Oct 2026

VAEL: Bridging Variational Autoencoders and Probabilistic Logic Programming

arXiv 2202.04178 ↗First posted 7 Feb 2022cs.PL cs.LGcited by 31

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

We present VAEL, a neuro-symbolic generative model integrating variational autoencoders (VAE) with the reasoning capabilities of probabilistic logic (L) programming. Besides standard latent subsymbolic variables, our model exploits a probabilistic logic program to define a further structured representation, which is used for logical reasoning. The entire process is end-to-end differentiable. Once trained, VAEL can solve new unseen generation tasks by (i) leveraging the previously acquired knowledge encoded in the neural component and (ii) exploiting new logical programs on the structured latent space. Our experiments provide support on the benefits of this neuro-symbolic integration both in terms of task generalization and data efficiency. To the best of our knowledge, this work is the first to propose a general-purpose end-to-end framework integrating probabilistic logic programming into a deep generative model.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 64 of its 74 references that are in the map. First posted on arXiv 7 Feb 2022.

Builds on

64 of 74 references.

References · 64

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  1. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 389
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 7; 2024: 8; 2025: 10; 2026: 6.

31 papers.

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  1. 2023Concept-based Explainable Artificial Intelligence: A Surveycited by 97
  2. 2023Not All Neuro-Symbolic Concepts Are Created Equal: Analysis and Mitigation of Reasoning Shortcutscited by 63
  3. 2025Interpreting CLIP with Hierarchical Sparse Autoencoderscited by 54
  4. 2024Compositional Generative Modeling: A Single Model is Not All You Needcited by 41
  5. 2024BEARS Make Neuro-Symbolic Models Aware of their Reasoning Shortcutscited by 36
  6. 2023Neuro-Symbolic Continual Learning: Knowledge, Reasoning Shortcuts and Concept Rehearsalcited by 33
  7. 2024How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Datacited by 29
  8. 2023Neural Probabilistic Logic Programming in Discrete-Continuous Domainscited by 24
  9. 2023Interpretability is in the Mind of the Beholder: A Causal Framework for Human-interpretable Representation Learningcited by 22
  10. 2024A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcutscited by 19
  11. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
  12. 2024Neural Concept Bindercited by 14
19 more
  1. 2025Neurosymbolic Diffusion Modelscited by 12
  2. 2024Counterfactual Concept Bottleneck Modelscited by 7
  3. 2023GenCO: Generating Diverse Designs with Combinatorial Constraintscited by 3
  4. 2025ABS: Enforcing Constraint Satisfaction On Generated Sequences Via Automata-Guided Beam Searchcited by 3
  5. 2025Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AIcited by 3
  6. 2026Unsupervised Decomposition and Recombination with Discriminator-Driven Diffusion Modelscited by 3
  7. 2023Generating by Understanding: Neural Visual Generation with Logical Symbol Groundingscited by 2
  8. 2025Neurosymbolic Object-Centric Learning with Distant Supervisioncited by 2
  9. 2026Logic Tensor Network-Enhanced Generative Adversarial Networkcited by 2
  10. 2026Differentiable Rule Induction from Raw Sequence Inputscited by 2
  11. 2024A Survey on the Integration of Generative AI for Critical Thinking in Mobile Networkscited by 1
  12. 2024Declarative Design of Neural Predicates in Neuro-Symbolic Systemscited by 1
  13. 2025Deep Generative Models with Hard Linear Equality Constraintscited by 1
  14. 2025Independence Is Not an Issue in Neurosymbolic AIcited by 1
  15. 2025Towards Better Generalization and Interpretability in Unsupervised Concept-Based Modelscited by 1
  16. 2025A Neuro-Symbolic Approach for Probabilistic Reasoning on Graph Datacited by 1
  17. 2026On Improving Neurosymbolic Learning by Exploiting the Representation Spacecited by 0
  18. 2026Parallel Noising in Neural Markov Logic Networkscited by 0
  19. 2026Generate in the Chart, Not on the Boundary: Function-Symbol Grounding for Hard Constraints in LTN-GANscited by 0

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  2. 2024SymbolicAI: A framework for logic-based approaches combining generative models and solvers
  3. 2022NeuPSL: Neural Probabilistic Soft Logic
  4. 2025From Classical Probabilistic Latent Variable Models to Modern Generative AI: A Unified Perspective
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