mlsanityData to 14 Oct 2026

Neuro-Symbolic Hierarchical Rule Induction

arXiv 2112.13418 ↗First posted 26 Dec 2021cs.LG cs.AIcited by 23

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Abstract (arXiv)

We propose an efficient interpretable neuro-symbolic model to solve Inductive Logic Programming (ILP) problems. In this model, which is built from a set of meta-rules organised in a hierarchical structure, first-order rules are invented by learning embeddings to match facts and body predicates of a meta-rule. To instantiate it, we specifically design an expressive set of generic meta-rules, and demonstrate they generate a consequent fragment of Horn clauses. During training, we inject a controlled pwGumbel noise to avoid local optima and employ interpretability-regularization term to further guide the convergence to interpretable rules. We empirically validate our model on various tasks (ILP, visual genome, reinforcement learning) against several state-of-the-art methods.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 26 of its 48 references that are in the map. First posted on arXiv 26 Dec 2021.

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26 of 48 references.

References · 26

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2016Categorical Reparameterization with Gumbel-Softmaxcited by 2,739
  3. 2016Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotationscited by 2,656
  4. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,148
  5. 2017Neural Motifs: Scene Graph Parsing with Global Contextcited by 414
  6. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 394
  7. 2017A simple neural network module for relational reasoningcited by 346
  8. 2020Neurosymbolic AI: The 3rd Wavecited by 255
  9. 2018Deep Learning: A Critical Appraisalcited by 217
  10. 2017Learning Explanatory Rules from Noisy Datacited by 211
  11. 2017End-to-End Differentiable Provingcited by 161
  12. 2019Neural Logic Machinescited by 145
14 more
  1. 2017Logic Tensor Networks for Semantic Image Interpretationcited by 92
  2. 2015A Deeper Look at Dataset Biascited by 87
  3. 2020Inductive logic programming at 30: a new introductioncited by 85
  4. 2020Learning programs by learning from failurescited by 73
  5. 2019Neural Logic Reinforcement Learningcited by 53
  6. 2015Traversing Knowledge Graphs in Vector Spacecited by 51
  7. 2019Learn to Explain Efficiently via Neural Logic Inductive Learningcited by 38
  8. 2020Neuro-Symbolic Visual Reasoning: Disentangling "Visual" from "Reasoning"cited by 35
  9. 2020The ILASP system for Inductive Learning of Answer Set Programscited by 27
  10. 2018Inductive Learning of Answer Set Programs from Noisy Examplescited by 22
  11. 2019Logical reduction of metarulescited by 19
  12. 2021Differentiable Logic Machinescited by 18
  13. 2019Learning Algorithms via Neural Logic Networkscited by 17
  14. 2018Logical Rule Induction and Theory Learning Using Neural Theorem Provingcited by 13

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Citing papers per year: 2022: 3; 2023: 4; 2024: 7; 2025: 8; 2026: 1.

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  1. 2023Neural Compositional Rule Learning for Knowledge Graph Reasoningcited by 20
  2. 2023Learning Interpretable Rules for Scalable Data Representation and Classificationcited by 14
  3. 2024TELLER: A Trustworthy Framework for Explainable, Generalizable and Controllable Fake News Detectioncited by 10
  4. 2024Latent Logic Tree Extraction for Event Sequence Explanation from LLMscited by 9
  5. 2024LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulationcited by 8
  6. 2025Multimodal LLM-assisted Evolutionary Search for Programmatic Control Policiescited by 8
  7. 2022Learning logic programs by combining programscited by 7
  8. 2023Neuro-symbolic Rule Learning in Real-world Classification Taskscited by 7
  9. 2024Learning Guided Automated Reasoning: A Brief Surveycited by 7
  10. 2023Generalisation Through Negation and Predicate Inventioncited by 5
  11. 2022Hierarchical Symbolic Reasoning in Hyperbolic Space for Deep Discriminative Modelscited by 3
  12. 2024stl2vec: Semantic and Interpretable Vector Representation of Temporal Logiccited by 3
11 more
  1. 2024Learning logic programs by finding minimal unsatisfiable subprogramscited by 1
  2. 2024Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rulescited by 1
  3. 2025Enhancing Zero-Shot Image Recognition in Vision-Language Models through Human-like Concept Guidancecited by 1
  4. 2025Towards Automated Semantic Interpretability in Reinforcement Learning via Vision-Language Modelscited by 1
  5. 2025Curriculum Abductive Learningcited by 1
  6. 2022A Probabilistic-Logic based Commonsense Representation Framework for Modelling Inferences with Multiple Antecedents and Varying Likelihoodscited by 0
  7. 2025An Empirical Comparison of Cost Functions in Inductive Logic Programmingcited by 0
  8. 2025Disentangling Neural Disjunctive Normal Form Modelscited by 0
  9. 2025RLIE: Rule Generation with Logistic Regression, Iterative Refinement, and Evaluation for Large Language Modelscited by 0
  10. 2025Neuro-Logic Lifelong Learningcited by 0
  11. 2026Beyond Heuristic Prompting: A Concept-Guided Bayesian Framework for Zero-Shot Image Recognitioncited by 0