# Neuro-Symbolic Hierarchical Rule Induction

arXiv: https://arxiv.org/abs/2112.13418 · HTML: https://mlsanity.com/paper/2112.13418/

## 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.

## Builds on (most cited first, 26 of 26)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Neural Motifs: Scene Graph Parsing with Global Context](https://mlsanity.com/paper/1711.06640/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Logic Tensor Networks for Semantic Image Interpretation](https://mlsanity.com/paper/1705.08968/) (2017)
- [A Deeper Look at Dataset Bias](https://mlsanity.com/paper/1505.01257/) (2015)
- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [Learning programs by learning from failures](https://mlsanity.com/paper/2005.02259/) (2020)
- [Neural Logic Reinforcement Learning](https://mlsanity.com/paper/1904.10729/) (2019)
- [Traversing Knowledge Graphs in Vector Space](https://mlsanity.com/paper/1506.01094/) (2015)
- [Learn to Explain Efficiently via Neural Logic Inductive Learning](https://mlsanity.com/paper/1910.02481/) (2019)
- [Neuro-Symbolic Visual Reasoning: Disentangling "Visual" from "Reasoning"](https://mlsanity.com/paper/2006.11524/) (2020)
- [The ILASP system for Inductive Learning of Answer Set Programs](https://mlsanity.com/paper/2005.00904/) (2020)
- [Inductive Learning of Answer Set Programs from Noisy Examples](https://mlsanity.com/paper/1808.08441/) (2018)
- [Logical reduction of metarules](https://mlsanity.com/paper/1907.10952/) (2019)
- [Differentiable Logic Machines](https://mlsanity.com/paper/2102.11529/) (2021)
- [Learning Algorithms via Neural Logic Networks](https://mlsanity.com/paper/1904.01554/) (2019)
- [Logical Rule Induction and Theory Learning Using Neural Theorem Proving](https://mlsanity.com/paper/1809.02193/) (2018)

## Built on by (most cited first, 23 of 23)

- [Neural Compositional Rule Learning for Knowledge Graph Reasoning](https://mlsanity.com/paper/2303.03581/) (2023)
- [Learning Interpretable Rules for Scalable Data Representation and Classification](https://mlsanity.com/paper/2310.14336/) (2023)
- [TELLER: A Trustworthy Framework for Explainable, Generalizable and Controllable Fake News Detection](https://mlsanity.com/paper/2402.07776/) (2024)
- [Latent Logic Tree Extraction for Event Sequence Explanation from LLMs](https://mlsanity.com/paper/2406.01124/) (2024)
- [LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulation](https://mlsanity.com/paper/2411.00773/) (2024)
- [Multimodal LLM-assisted Evolutionary Search for Programmatic Control Policies](https://mlsanity.com/paper/2508.05433/) (2025)
- [Learning logic programs by combining programs](https://mlsanity.com/paper/2206.01614/) (2022)
- [Neuro-symbolic Rule Learning in Real-world Classification Tasks](https://mlsanity.com/paper/2303.16674/) (2023)
- [Learning Guided Automated Reasoning: A Brief Survey](https://mlsanity.com/paper/2403.04017/) (2024)
- [Generalisation Through Negation and Predicate Invention](https://mlsanity.com/paper/2301.07629/) (2023)
- [Hierarchical Symbolic Reasoning in Hyperbolic Space for Deep Discriminative Models](https://mlsanity.com/paper/2207.01916/) (2022)
- [stl2vec: Semantic and Interpretable Vector Representation of Temporal Logic](https://mlsanity.com/paper/2405.14389/) (2024)
- [Learning logic programs by finding minimal unsatisfiable subprograms](https://mlsanity.com/paper/2401.16383/) (2024)
- [Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rules](https://mlsanity.com/paper/2409.16238/) (2024)
- [Enhancing Zero-Shot Image Recognition in Vision-Language Models through Human-like Concept Guidance](https://mlsanity.com/paper/2503.15886/) (2025)
- [Towards Automated Semantic Interpretability in Reinforcement Learning via Vision-Language Models](https://mlsanity.com/paper/2503.16724/) (2025)
- [Curriculum Abductive Learning](https://mlsanity.com/paper/2505.12275/) (2025)
- [A Probabilistic-Logic based Commonsense Representation Framework for Modelling Inferences with Multiple Antecedents and Varying Likelihoods](https://mlsanity.com/paper/2211.16822/) (2022)
- [An Empirical Comparison of Cost Functions in Inductive Logic Programming](https://mlsanity.com/paper/2503.07554/) (2025)
- [Disentangling Neural Disjunctive Normal Form Models](https://mlsanity.com/paper/2507.10546/) (2025)
- [RLIE: Rule Generation with Logistic Regression, Iterative Refinement, and Evaluation for Large Language Models](https://mlsanity.com/paper/2510.19698/) (2025)
- [Neuro-Logic Lifelong Learning](https://mlsanity.com/paper/2511.12793/) (2025)
- [Beyond Heuristic Prompting: A Concept-Guided Bayesian Framework for Zero-Shot Image Recognition](https://mlsanity.com/paper/2603.07911/) (2026)

## 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.