# Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rules

arXiv: https://arxiv.org/abs/2409.16238 · HTML: https://mlsanity.com/paper/2409.16238/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 48 references that are in the map.
- First posted on arXiv 24 Sep 2024.

## Builds on (most cited first, 20 of 20)

- [Convolutional 2D Knowledge Graph Embeddings](https://mlsanity.com/paper/1707.01476/) (2017)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [Neural Logic Machines](https://mlsanity.com/paper/1904.11694/) (2019)
- [Logical Neural Networks](https://mlsanity.com/paper/2006.13155/) (2020)
- [RNNLogic: Learning Logic Rules for Reasoning on Knowledge Graphs](https://mlsanity.com/paper/2010.04029/) (2020)
- [Scene Graph Generation with External Knowledge and Image Reconstruction](https://mlsanity.com/paper/1904.00560/) (2019)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [Abductive Knowledge Induction From Raw Data](https://mlsanity.com/paper/2010.03514/) (2020)
- [Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks](https://mlsanity.com/paper/2112.03324/) (2021)
- [Neuro-Symbolic Hierarchical Rule Induction](https://mlsanity.com/paper/2112.13418/) (2021)
- [Neural Compositional Rule Learning for Knowledge Graph Reasoning](https://mlsanity.com/paper/2303.03581/) (2023)
- [Softened Symbol Grounding for Neuro-symbolic Systems](https://mlsanity.com/paper/2403.00323/) (2024)
- [Logical Rule Induction and Theory Learning Using Neural Theorem Proving](https://mlsanity.com/paper/1809.02193/) (2018)
- [Best-Effort Inductive Logic Programming via Fine-grained Cost-based Hypothesis Generation](https://mlsanity.com/paper/1707.02729/) (2017)
- [Principled and Efficient Motif Finding for Structure Learning of Lifted Graphical Models](https://mlsanity.com/paper/2302.04599/) (2023)
- [Parallel Neurosymbolic Integration with Concordia](https://mlsanity.com/paper/2306.00480/) (2023)

## Built on by (most cited first, 1 of 1)

- [Probabilistic Circuits for Knowledge Graph Completion with Reduced Rule Sets](https://mlsanity.com/paper/2508.06706/) (2025)

## Abstract (arXiv)

Probabilistic logical models are a core component of neurosymbolic AI and are important in their own right for tasks that require high explainability. Unlike neural networks, logical theories that underlie the model are often handcrafted using domain expertise, making their development costly and prone to errors. While there are algorithms that learn logical theories from data, they are generally prohibitively expensive, limiting their applicability in real-world settings. Here, we introduce precision and recall for logical rules and define their composition as rule utility - a cost-effective measure of the predictive power of logical theories. We also introduce SPECTRUM, a scalable framework for learning logical theories from relational data. Its scalability derives from a linear-time algorithm for mining recurrent subgraphs in the data graph along with a second algorithm that, using a utility measure that can be computed in linear time, efficiently ranks rules derived from these subgraphs. Finally, we prove theoretical guarantees on the utility of the learnt logical theory. As a result, we demonstrate across various tasks that SPECTRUM scales to larger datasets, often learning more accurate logical theories on CPUs in < 1% the runtime of SOTA neural network approaches on GPUs.