# Learning Relational Representations with Auto-encoding Logic Programs

arXiv: https://arxiv.org/abs/1903.12577 · HTML: https://mlsanity.com/paper/1903.12577/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2019.

## Built on by (most cited first, 13 of 13)

- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Predicate Invention by Learning From Failures](https://mlsanity.com/paper/2104.14426/) (2021)
- [Learning logic programs by combining programs](https://mlsanity.com/paper/2206.01614/) (2022)
- [Top Program Construction and Reduction for polynomial time Meta-Interpretive Learning](https://mlsanity.com/paper/2101.05050/) (2021)
- [A Study of Continuous Vector Representationsfor Theorem Proving](https://mlsanity.com/paper/2101.09142/) (2021)
- [Learning logic programs by discovering where not to search](https://mlsanity.com/paper/2202.09806/) (2022)
- [Learning big logical rules by joining small rules](https://mlsanity.com/paper/2401.16215/) (2024)
- [Learning logic programs by discovering higher-order abstractions](https://mlsanity.com/paper/2308.08334/) (2023)
- [Scalable Knowledge Refactoring using Constrained Optimisation](https://mlsanity.com/paper/2408.11530/) (2024)
- [HorNets: Learning from Discrete and Continuous Signals with Routing Neural Networks](https://mlsanity.com/paper/2501.14346/) (2025)
- [Honey, I shrunk the hypothesis space (through logical preprocessing)](https://mlsanity.com/paper/2506.06739/) (2025)

## Abstract (arXiv)

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods aim at re-representing symbolic relational data in Euclidean spaces. They offer better scalability, but can only numerically approximate relational structures and are less flexible in terms of reasoning tasks supported. This paper introduces a novel framework for relational representation learning that combines the best of both worlds. This framework, inspired by the auto-encoding principle, uses first-order logic as a data representation language, and the mapping between the original and latent representation is done by means of logic programs instead of neural networks. We show how learning can be cast as a constraint optimisation problem for which existing solvers can be used. The use of logic as a representation language makes the proposed framework more accurate (as the representation is exact, rather than approximate), more flexible, and more interpretable than deep learning methods. We experimentally show that these latent representations are indeed beneficial in relational learning tasks.