# Learn to Explain Efficiently via Neural Logic Inductive Learning

arXiv: https://arxiv.org/abs/1910.02481 · HTML: https://mlsanity.com/paper/1910.02481/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2019.

## Built on by (most cited first, 30 of 38)

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- [EXplainable Neural-Symbolic Learning (X-NeSyL) methodology to fuse deep learning representations with expert knowledge graphs: the MonuMAI cultural heritage use case](https://mlsanity.com/paper/2104.11914/) (2021)
- [Can LLMs Reason with Rules? Logic Scaffolding for Stress-Testing and Improving LLMs](https://mlsanity.com/paper/2402.11442/) (2024)
- [ChatRule: Mining Logical Rules with Large Language Models for Knowledge Graph Reasoning](https://mlsanity.com/paper/2309.01538/) (2023)
- [Neural-Logic Human-Object Interaction Detection](https://mlsanity.com/paper/2311.09817/) (2023)
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- [Neural Compositional Rule Learning for Knowledge Graph Reasoning](https://mlsanity.com/paper/2303.03581/) (2023)
- [Differentiable Logic Machines](https://mlsanity.com/paper/2102.11529/) (2021)
- [Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy](https://mlsanity.com/paper/2406.16087/) (2024)
- [On the Evolution of Knowledge Graphs: A Survey and Perspective](https://mlsanity.com/paper/2310.04835/) (2023)
- [Learning Symbolic Rules for Interpretable Deep Reinforcement Learning](https://mlsanity.com/paper/2103.08228/) (2021)
- [Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning](https://mlsanity.com/paper/2305.12738/) (2023)
- [LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulation](https://mlsanity.com/paper/2411.00773/) (2024)
- [Synthesizing Visual Concepts as Vision-Language Programs](https://mlsanity.com/paper/2511.18964/) (2025)
- [Rule Mining over Knowledge Graphs via Reinforcement Learning](https://mlsanity.com/paper/2202.10381/) (2022)
- [Rule Induction in Knowledge Graphs Using Linear Programming](https://mlsanity.com/paper/2110.08245/) (2021)
- [Temporal Inductive Logic Reasoning over Hypergraphs](https://mlsanity.com/paper/2206.05051/) (2022)
- [Commonsense Knowledge Graph Completion Via Contrastive Pretraining and Node Clustering](https://mlsanity.com/paper/2305.17019/) (2023)
- [Learning Concept-Driven Logical Rules for Interpretable and Generalizable Medical Image Classification](https://mlsanity.com/paper/2505.14049/) (2025)
- [The Road to Generalizable Neuro-Symbolic Learning Should be Paved with Foundation Models](https://mlsanity.com/paper/2505.24874/) (2025)
- [Do Machine Learning Models Learn Statistical Rules Inferred from Data?](https://mlsanity.com/paper/2303.01433/) (2023)
- [Learning Reliable Logical Rules with SATNet](https://mlsanity.com/paper/2310.02133/) (2023)
- [Nature's Insight: A Novel Framework and Comprehensive Analysis of Agentic Reasoning Through the Lens of Neuroscience](https://mlsanity.com/paper/2505.05515/) (2025)
- [LoSemB: Logic-Guided Semantic Bridging for Inductive Tool Retrieval](https://mlsanity.com/paper/2508.07690/) (2025)
- [DISCRET: Synthesizing Faithful Explanations For Treatment Effect Estimation](https://mlsanity.com/paper/2406.00611/) (2024)
- [Large Language Model-Enhanced Symbolic Reasoning for Knowledge Base Completion](https://mlsanity.com/paper/2501.01246/) (2025)

## Abstract (arXiv)

The capability of making interpretable and self-explanatory decisions is essential for developing responsible machine learning systems. In this work, we study the learning to explain problem in the scope of inductive logic programming (ILP). We propose Neural Logic Inductive Learning (NLIL), an efficient differentiable ILP framework that learns first-order logic rules that can explain the patterns in the data. In experiments, compared with the state-of-the-art methods, we find NLIL can search for rules that are x10 times longer while remaining x3 times faster. We also show that NLIL can scale to large image datasets, i.e. Visual Genome, with 1M entities.